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RegSim

MANUAL

Thomas Gustafsson

October 2003

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Contents

1 Introduction 3

2 Model Language 4

2.1 Introductory Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Definition of Name and Type of Systems . . . . . . . . . . . . . . . . . . . . . 62.3 Definition of Special Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 Global Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.4 Initial values for states and outputs . . . . . . . . . . . . . . . . . . . . . . . . 9

2.5 Describing the process mathematically . . . . . . . . . . . . . . . . . . . . . . 10

2.6 Combining Different Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.6.1 Connecting System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.6.2 Without connecting system . . . . . . . . . . . . . . . . . . . . . . . . 11

2.7 Examples of some system descriptions . . . . . . . . . . . . . . . . . . . . . . 11

2.7.1 Second order differential equation . . . . . . . . . . . . . . . . . . . . 11

2.7.2 Third order differential equation . . . . . . . . . . . . . . . . . . . . . 132.7.3 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.7.4 Matrix Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 The RegSim Commands 16

3.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 How to give arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.1 Method 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.2 Method 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.3 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3 History of command given . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4 The Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Command Files 57

4.1 Invoking by a MACRO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5 The Syntax for Expressions 59

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Chapter 1

Introduction

In your hand you are holding a document which gives the directions for RegSim, a programme

that is very useful in developing and testing of control engineering projects. Furthermore, thanks

for the general nature of this programme its application area is quite wide.

With RegSim one can:

Simulate arbitrary combination of continuous time and discrete time systems. Thesesystems can be linear or non-linear.

Can drive discrete systems in real time using the facilities provided to communicate with

real world using A/D and D/A card.

Presents simulation or real time results graphically. This also gives the possibility foranimation.

A new way to work

Think of this possibility.!! You can develop and test a new controller design for a process, and

this work usually includes few steps.

1. Identify the process, and develop a mathematical model for the process

2. Design a controller

3. Test the controller function through the simulation of the process and the controller.

4. Test run of the controller

All who have tried this task one time or another have definitely experience how the first test run

went wild without one knowing what really went wrong. It is in this aspect the RegSim gives a

big advantage. You can really use RegSim both in phase 3 and 4, with the same controller. That

is, just by simple command you can drive the controller with the simulated system or with the

real process. In this way one can compare the reality and the system model.

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Chapter 2

Model Language

Any process that you intend to simulate must be described in a way the RegSim understands.

The RegSim supports the simulation of both Continuous Time Systems and Discrete Time Sys-

tems. A RegSim programme to simulate a large process can be in one file or it can be divided

in to subsystems, and each can be implemented in different files. Each of these RegSim files

which describes either a whole system or a subsystem must contain the following parts.

Definition of name and type of the system

Declaration of the special variables

Give initial values for the state variables and the output variables

Mathematical description of the process

END

2.1 Introductory Example

This example shows how we can describe a first order differential equation and simulate it for

different input signals using RegSim.

Differential equation is given by

x = a (u(t) x(t))

The translation of it into the RegSim system isCONTINUOUS SYSTEM first " defines the name "first"

STATE x " declares the special variables

DER dx " derivative variable of the state x

TIME t " declares the time variable

d x = a*( u - x )

u = IF t > 5 THEN 0 ELSE 1 " u is a unit step starting at t = 5.

a : 0.4

END

If this RegSim programme is stored in the file first.t, then to simulate it we must first compile

it using the command COMP.

First to invoke RegSim give the command ega (or cga) to invoke the appropriate graphics driver,

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2.1 Introductory Example 5

and then give the command REGSIM. Once the REGSIM is invoked and the cursor >> appear-ers in the command window give

comp first.t

to compile the system. If you like to see how the variable x changes, then give

plot x

To initialize the state of the differential equation give

init

simu

This will give the curves shown in figure 2.1

Figure 2.1: First order system

If you want to repeat the simulation with a = 0.7, then you give the following commands

par a 0.7

init

simu

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6 Model Language

2.2 Definition of Name and Type of Systems

A system can either be a continuous or a discrete time system. The first line of the RegSim

program indicates this.

CONTINUOUS SYSTEM

or

DISCRETE SYSTEM

There is also a third type known as the CONNECTING SYSTEM and is described in section 2.6.

2.3 Definition of Special Variables

A variable is classified in two different ways, what type of value it has ( Boolean, Real or

Matrix) and what the function of the variable, i.e if it is an input, output, state or a parameter,

RegSim can automatically recognize variables of types Real and Matrix and if the functions are

parameter, output or a basic variable.

For other kinds of variables it is necessary to deklare either the type or the function before it

can be used. A deklaration is of the form

...

where is one of:

INPUT These variables get there values from other systems. See example of use in

section 2.6.1.

OUTPUT These variables are marked as the ones that can be used by other systems. If an

undeclared variable is used from another system, then it is automatically marked

as an OUTPUT variable. Hence this command is functionally redundant, but

increases the readability of the programme.

The variables of OUTPUT type can be assigned a initial value.

TIME If you wish to have access to the time, a variable name has to be declared for

time.

STATE Declaration of the State variables. This can be assigned a initial value. Default,

the initial value is taken zero.

DER Used only in continuous systems to declare the derivative of the state variables

declared under STATE. The derivatives should be declared in the same order as

the states are declared in STATE. With the following declaration

CONTINUOUS SYSTEM MOTORSTATE x y

DER dx omega

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2.3 Definition of Special Variables 7

then x and y are states, dx and omega their derivatives, i.e dx = x andomega = y.

NEW Used only in discrete time systems to declare the new value of the state variables

declared under STATE. NEW is similar to DER in continuous systems. The the

NEW variables should be declared in the same order as the states are declared

in STATE. With the declaration

DISCRETE SYSTEM CONTROL

STATE z c

DER nz qw

TSAMP ts

TIME t

ts = t + h

then z and c are states, nz and qw are the new states, i.e z(t + h == nz(t) andc(t + h) = qw(t). From this one understands that the states z and c cannot begiven values explicitely, this is done automatically by RegSim that assures that

the states will have the correct values in the beginning of each sample.

TSAMP Must be included in discrete time systems to specify when the next sampling

should be made. When the RegSim is driven in real time (REGU), the sampling

time is decided by the variable SAMPTIME which is in every discrete time

system. To get the same sampling intervall both during simulation and real-

time control do something like this

TSAMP tsTIME t

ts = t + samptime/1000

MATRIX MATRICES and VECTORS can be declared. This can be done in any of the

above declarations (STATE, DER, NEW, INPUT, OUTPUT), or with MATRIX.

INTEGER Declaration of whole numbers.

BOOLEAN Declaration of logic variables.

2.3.1 Global Variables

In RegSim there is a number of Global Variables.

Simtid Defines how long the simulation has to be done (Simulation Time). The simula-

tion time has nothing to do with real time. The simulation time can be faster or

slower than the true time. There is a possibility of synchronizing simulation time

with real time. See command PLOT for more information.

Minstep The minimum step size in the integration routine. If this step length is used many

times during the simulation, then a message is given after the simulation.

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8 Model Language

Break When the time given by break is reached the simulation is stopped, and requests

for a new break time that gives the next time instant the simulation has to be

stopped.

Epsilon With this variable we can define how accurate the simulation must be. The normalvalue is = 104, and this means that the absolute value of the mean value of thestate variables relative error shall be less than 104.

Tid Contains the simulated time.

Inttime Resolution of the real time clock in milliseconds. Maximized by the programme

so that a little time as possible is taken for the administration of the real time

kernel.

If for example two discrete time systems have sample time 20 and 50 millisec-

onds respectively, then the Initime is set to the greatest common denominator, i.e.10 ms. If the sampling times are 21 and 50 ms, then Initime is set to 1 ms, to

guarantee that both the processes are executed at the correct time instant. The

real time kernel works 10 times faster than before and this is often noticed in the

plotting.

Samptime This variable is declared in all the discrete time systems and used to decide the

sample time when used in real time (REGU). Samptime is a whole number which

is given in milliseconds. In simulation used with TSAMP.

Samptime need not to be declared and may simply assigned a value either in

INITIAL block or using PAR-command.

@ The variable used in the command Graph.

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2.4 Initial values for states and outputs 9

2.4 Initial values for states and outputs

RegSim has a command Init which must be given before a new simulation. The command

assigns a known inital value to all state and output variables that usually is equal to zero. Ifvalues other than zero is needed, they can be given in two ways. One can use the command

PAR, or declare the initial values in a block in the RegSim programme.

This block starts with INITIAL and ends with SORT, and in between all the initial values are

assigned according to the following syntax,

STATE x1 z{3} yOUTPUT cont

INITIAL

styr = 0.45

x1 = sin(p)

z = {1,0,0}SORT

The example will only work if p is either a parameter or a timeindependant variable.

It is not possible to change a initial value given in this way.

If you are changing the initial values often, and hence wish to store a set of initial values so that

they can be used later, the command SAVE can be used to save them. The command LOAD

can be used to retrieve them.

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10 Model Language

2.5 Describing the process mathematically

After all necessary declarations follows the mathematical description of the process one likes

to simulate. The mathematical description consists of the following two types,

variablename = arithmetic expression

or

variablename : numerical value

The first of them describes how the value of a variable could be computed while the other defines

a parameter. The difference is that a parameter normally has a fixed value during the simulation,

but with the help of a command the value can be changed during or between simulations. A

variable, one cannot change the value (except the initial values of state variables and output

variables), and is decided by the expression.

The order the mathematical expressions are written in the RegSim programme is not important

because RegSim sorts all the mathematical expressions in the order they are executed, and each

variable and parameter has a value when they are been used. However, algebraic loops of

following type are not permitted,

c = sin(t)

a = b + c

b = a + c

Furthermore a variable or a parameter should not be on the left hand side more than once. Ifthis is done, the sorting of the expressions can not be done by RegSim.

During sorting the different expressions are also classified in the following manner, Time in-

variant, Derivative computation, Continuous and Time Discrete. Such classification helps very

effective computation. The normal user usually does not notice this, but can be seen when

command DEBUG is used.

2.6 Combining Different Systems

Let the total process we wish to simulate is as shown in figure 2.2.

- - - -

6

Regulator Process

Givare

ref yu

yg

Figure 2.2: A feedback control system three different sub systems

The three systems, namely the process, the sensor and the controller can be combined together

to define a complete feedback control system. This can be done in two ways.

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2.7 Examples of some system descriptions 11

2.6.1 Connecting System

The first approach uses an additional system, the so called CONNECTING SYSTEM, where

all the couplings are specified. In our example it looks as follows,

CONTINUOUS SYSTEM reg

INPUT e

OUTPUT u

u = .......

END

CONTINUOUS SYSTEM process

INPUT u

OUTPUT y

y = .......

END

CONTINUOUS SYSTEM givare

INPUT y

OUTPUT yg

yg = .......END

CONNECTING SYSTEM conn

y[givare] = y[process]

u[process] = u[reg]

e[reg] = ref - yg[givare]

ref : 1.5

END

2.6.2 Without connecting system

Taking that all the variables are global, it is possible to couple different systems without us-

ing the connecting system. If a variable from another system is referred to, then it is done

by using the variable name with the system name inside the square brackets, i.e. varaible-

name[systemname]. The above example would then look as follows,

CONTINUOUS SYSTEM reg

OUTPUT u

e = ref - yg[givare]

u = .......

ref : 1.5

END

CONTINUOUS SYSTEM process

OUTPUT y

u = u[reg]

y = .......

END

CONTINUOUS SYSTEM givare

OUTPUT yg

y = y[process]

yg = .......

END

2.7 Examples of some system descriptions

2.7.1 Second order differential equation

The non-linear second order differential equation considered here is the van der Pols equation,

x + (x2 1)x + x = 0

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12 Model Language

We want to find (plot) the phase curves, i.e. x vs x for different initial values. To do this thesecond order system is first described as two first order differential equations by defining the

following two state variables,

x1 = x

x2 = x

The the van der Pole equation can be written in two first order differential equations as follows,

x1 = x2

x2 = (x2

1 1)x2 x1

The corresponding RegSim code is given by

CONTINUOUS SYSTEM Pol

STATE x1 x2

DER d1 d2

d1 = x2

d2 = -( sqr(x1) - 1 )*x2 - x1

END

To draw the phase plane plot shown in figure 2.3, the following commands were given,

scale -x -5 5 -y -6 6

plot -x x1 x2

Figure 2.3: The phase plane for the van der Pols equation

(The -x option in the plot command is given to plot between x1 and x2. If -x option is not given,

i.e. plot x1 x2 then the default x-axis is the time axis.)

Now select suitable initial value for the states x1 and x2. The phase plane shown in figure 3 can

be obtained if the simulation time is set to simtid = 20, and the following initial values for

(x1,x2) are used.

(-3,5), (-2,5), (3,5), (-5, 0), (-0.01,0), (0.01,0), (5,0), (-3,-5), (2,-5), (3,-5)

The RegSim commands are as follows,

par x1 -3;par x2 5;init;simu

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par x1 -2;init;simu

par x1 3;init;simu

par x1 -5;par x2 0;init;simu

par x1 -0.01;init;simu

par x1 0.01;init;simu

par x1 5;init;simu

par x1 -3;par x2 -5;init;simu

par x1 2;init;simu

par x1 3;init;simu

2.7.2 Third order differential equation

The third order linear differential equation is given by

d3y

dt3+ a1

d2y

dt2+ a2

dy

dt+ a3y = Ku

This third order differential equation can by described by three first order differential equation

as follows by defining the state variables x1 = y, x2 = dx1/dt and x3 = dx2/dt.

dx1dt

= x2

dx2dt

= x3

dx3dt

= Ku a1x3 a2 x2 a3x1

The output is given by

y = x1

The corresponding RegSim programme is given by

CONTINUOUS SYSTEM third

STATE x1 x2 x3

DER dx1 dx2 dx3

OUTPUT y

TIME tdx1=x2

dx2=x3

dx3=K*u-a1*x3-a2*x2-a3*x1

y=x1

a1:1

a2:.5

a3:.1

K:1

u:1

END

Any higher order ordinary differential equation can be implemented in RegSim, by describing

it by all first order differential equations in the same as given in this example.

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14 Model Language

2.7.3 Data acquisition

This example shows how a measurement from the real world e.g. water level, voltage, temper-

ature etc., can be obtained provided that the appropriate interface facilities are provided. Alsonote how SAMPTIME and TSAMP is used.

DISCRETE SYSTEM accqu

TSAMP ts

TIME t

INITIAL

samptime = 100 " sampling interval = 100 ms

SORT

ts = t + h " This is used with

h = samptime/1000 " simulation

out = daut(0, rand (umin, umax)) "sends an output signal

umin: 0 "minimum output signal [volt]

umax: 10 "maximum output signal [volt]

in = adin(0) "inputting a signal from channel 0

END

For data acquisition using the above programme which is stored in file dacc.t, the following

MACRO (daccqui.mcr) can be used.

MACRO daccqui period filename

"filename - name of a file that is used in the macro

"period - is a parameter, the value of which is passed to the macro

"DACCQUI - the the name of the macro fileecho off

COMP dacc.t

SCALE -x 0 100 -y 0 10

PLOT in out

PAR samptime $(period)

STORE -f $(filename) in out

CLEAR

WRITE Press F8 when data acquisition is over

REGU

To analyse the collected data, one can use for example MATLAB. To be able to do this, the datarepresented in RegSim format must be transferred to the data acceptable by MATLAB. Such

conversion is possible using the programme REG2MAT.

2.7.4 Matrix Computation

To demonstrate how matrix computations are used in RegSim, a discrete time Kalman filter

described by the following equations are implemented using RegSim.

xk+1 = xk + uk + Kk (y Cxk)

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Kk = PkCT

R2 + CPkCT1

Pk+1 = PkT + R1 KkCPk

T

=

1 0 0.40.1 0.8 0.00.2 0 0.8

R1 = 2T

R2 =

The Corresponding RegSim code is given by

DISCRETE SYSTEM Kalman

STATE X tak{

3}

P{

3,3}NEW N X tak{3} N P{3,3}

TSAMP ts

TIME t

Theta : {{1,0,0.4},{0.1,0.8,0},{0.2,0,0.8}}Gamma : {0.2,0.1,1}C : {1,0,1}R1 = Gamma*Gamma*sqr(sigma)

K = Theta*P*C/(R2 + C*P*C)

N X tak = Theta*X tak + Gamma*u + K*( y - C*X tak)

N P = Theta*P*Theta + R1 - K*C*P*Theta

y = adin(0)

ts = t + h

h : 0.2

sigma : 0.2

R2 : 0.5

END

note!

When exporting or importing matrices it is important that the system which exports the matrices

be given first in the compiling list of programmes in COMP. If not the importing programme

would declare the matrix as a scalar, and this will result in an error in the compilation.

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Chapter 3

The RegSim Commands

The RegSim is driven by Commands. The commands are either built in in RegSim, for example

AXES, or it can be an alias or a name of an command file. One or more commands can be given

in one line, and the commands are separated by semicolons.

For every built in command there is a Function key that can be used very quickly.

3.1 Notation

Following notation is used in describing a command.

op1 |. . . | opn Defines different options which MUST be given with the command.

[. . . ] Denotes that what is inside the square brackets can be left out.

{...}* A star denotes that what is inside the brackets can be repeated.

value A numerical argument.

name Name of a variable.

filename Name of a file which can be given with the path.

expr Regular expression, e.g. 1+sin(x). Note that a space is considered as a

separator and hence 1 +sin(x) is interpreted as two separate expressions

when two are permitted. However, if only one expression is expected then the

space has no importance. To be on the safe side one can include an expression

within parenthesis.

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3.2 How to give arguments 17

3.2 How to give arguments

A number of commands in RegSim can accept one or more arguments, for example one can

write

plot x y

Where x and y are arguments to the command PLOT. The command interpreter in RegSim

uses the space between arguments as a separator. For example if you give

plot x+y

there is one argument given by x+y, and the sum of x and y is plotted. On the other hand if

you give

plot x +y

then there are two arguments x and +y, and two curves, both x and y are plotted. To avoid

this confusion and unexpected results the following two methods can be adopted as precautions.

3.2.1 Method 1

Include the argument within the citation marks. For example

plot "x + y"

The command interpreter take away the citation marks and interpret the above command asequivalent to

plot x+y

3.2.2 Method 2

Include the argument within the parenthesis. For example

plot (x + y)

When there is only one argument expected then the parenthesis has no functionality. It is alsonot necessary to include the whole expression inside the brackets. It is sufficient to include only

the part where the space can be critical. For example

plot ( 5*(4 + sin(x))/(1 + sqr(y)) )

can give the same result as

plot 5*( 4 + sin(x) )/( 1 + sqr(y) )

3.2.3 Options

A option has an argument with two symbols, the first one being the minus-sign. For example

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18 The RegSim Commands

simu -c (x > 0)

Here -c is an option and ( x > 0 ) is an argument.

This can leads to problems if one uses a single digit negative number as an argument. Toovercome this problem one can use the method 2 described in the previous subsection. For

example

graph -i 0 (-2) 0 2

draws three strokes at y = 2, y = 0 and y = 2, but

graph -i 0 -2 0 2

draws two strokes at y = 0 and y = 2, in window 2.

Note that the method 1 does not work in this case because the citation sign will be taken away

from the argument.

3.3 History of command given

The a number of the latest RegSim commands given in the command window are automatically

stored in history list in RegSim. One can bring back these commands using the keyboard keys

and .

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3.4 The Commands 19

3.4 The Commands

Aritmmetic operations + - * /\

Purpose Aritmmetics for scalars and matrices.

Usage A + BA - B

A * B A .* B

A / B A ./ B

A \ B A .\ BA

Description Works both with scalars and matrices. RegSim has two different types of arith-

metic operations. Matrix arithmetic operations are defined by the rules of linearalgebra. Array arithmetic operations are carried out element-by-element. The

period or decimal point character, ., distinguishes the array operations from the

matrix operations. However, since the matrix and array operation are the same for

addition and subtraction, the character pairs .+ and .- are not used.

+ Addition. A+B adds A and B. A and B must have the same dimensions, unless

one is scalar. A scalar can be added to a matrix of any dimension.

- Subtraction. A-B subtracts B from A. A and B must have the same dimen-

sions, unless one is scalar. A scalar can be subtracted from a matrix of any

dimension.

* Matrix multiplication. A*B is linear algebraic product of the matrices A and

B. The number of columns ofA must equal the numner of rows ofB, unless

one of them is a scalar. A scalar can multiply a matrix of any dimension.

.* Vektor multiplication. A.*B is the element-by-element product of the arrays

A and B. A and B must have the same dimensions, unless one of them is a

scalar.

\ Backslash or matrix left division. If A is a square matrix, A\B is roughlythe same as inv(A)*B, execpt it is computed in a different way. IfA is an

n-by-n matrix and B is a column vector with n components, or a matrix with

severeal such columns, then X=A\B is the solution to the equation AX=Bcomputed by Gaussian elimination.

IfA is an m-by-n matrix with m = n and B is a column vector with m com-ponents, or a matrix with several such columns, then X=A\B is the solutionin least square sence to the under- or overdetermined system of equations

AX=B.

.\ Array left division. A\B is the matrix with elements B(i,j)/A(i,j). Aand B must have the same dimensions, unless one of them is a scalar.

/ Matrix right division. B / A is roughly the same as B*inv(A). More

precisely B/A = ( A\B ).

./ Array right division. A./B is the matrix with elements A(i,j)/B(i,j).

A and B must have the same dimensions, unless one of them is a scalar.

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A scalar operation ax calculates ax

Matrix transpose. A is the linear algebraic transpose ofA.

absPurpose Absolute value

Usage Y = abs(X)

Description The function abs(X) calculates the absolute value of all elements in the matrix

X.

acos, asin, atanPurpose Inverse trigonometric funcitions

Usage Y = acos(X)

Y = asin(X)

Y = atan(X)

Description Operates element-wise on matrices

adinPurpose Input from an A/D-converter

Usage y = adin(channelnr)

Description This function is useful only if the computer has A/D-converters and RegSim has

the right configuration.

alg

Purpose To choose the integration algorithm.Usage Alg [ ON | OFF ]

Description Currently there are two algorithms that one choose between. One a third or-

der Runge-Kutta (Felhberg) and the other a fifth order (DOPRI). The Felhbergs

method is faster, but some times can leads to instabilities in the step length com-

putation, specially if the system is stiff. The second method handles stiff systems

without much tendencies towards instabilities. However it has difficulties in han-

dling relay and other similar non-linearities.

When RegSim is started it uses the Fehlbergs method, but when given alg on

uses DOPRI-method.

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3.4 The Commands 21

aliasPurpose To assign an name to a group of RegSim commands

Usage Alias name commandstring

Description With this command one can define a new command, for example one construct

the command go

>> alias go (axes;init;simu 100)such that each time the command >> gois given the commands axes, init and simu are executed in that order. In principle

any number of alias can be defined. Using the command MAKE all the alias can

be saved in a command file.

arrowPurpose To initiate the functions right, up and pgup

Usage shift F2

Arrow [-c] [-r] [-l] [-u] [-d] [-U] [-D]

Description This command can be used to initialize the functions right, up and pgup to the

desired initial value.

Options -r set right= 1.0

-l set right= 1.0-u set up= 1.0

-d set up= 1.0

-U set pgup= 1.0

-D set pgup= 1.0

-c set all functions= 0.0

atan2Purpose arctangent

Usage a = atan2(y,x)

Description The function atan(y,x) calculates the arctangent for y/x. The result is in

the interval [, ] wich is different from atan(y/x) that has the interval[/2, /2].

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axesPurpose To draw axes and clear graphic windows

Usage F1Axes [ -1 | -2 | -3 ... ]

Description Draws aexs and clears all or the windows that are in the argument list. If the

scaling of a window is changed, then this window will be cleared irrespective of

what is given in the argument. The scaling is decided by the values that are in the

status routine (see command Scale).

beep

Purpose Gives a beep soundUsage Beep

begPurpose limit function

Usage y = beg(x,xlow,xhigh)

Description The scalar function beg returns max(xlow, min(x, xhigh))

byePurpose Exits Regsim

Usage Bye

calcPurpose Computes simple expressions.

Usage Ctrl F7Calc [expr]

Description Computes and writes the value of an expression.

Example C a l c 1 > 0

Value = TRUE

Calc 2*2 5 - 4

Value = 46

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3.4 The Commands 23

cdPurpose To change the working directory

Usage Shift F3cd [dir]

Description Changes to an desired working directory. If cd given without an argument then

the present directory is shown.

Example cd a:

cd ..

cd

clearPurpose To clear a part of the command routine from text

Usage Clear [ rad ]

Description If Clear is given without arguments, then the whole command routine is cleared

and the cursor is placed at the beginning of the first line.

compPurpose To compile those files which describe the process

Usage F9Comp [{filename}*]

Description Compiles the file or files that describe the system that we intend to simulate. Note

that all the files must be named, even the Modula-2 systems that were loaded with

Loadfunc.

If the complier detects an error in the system description, a message will be sent.

If there are a lot of errors, then it will be difficult to find all the errors, and hence

it is suitable to use the command Debug.Using TAB one can call back the previous file list.

companPurpose Creates a companion matrix

Usage A = compan(p)

Description If p is a row vector then compan(p) is a mtarix with the first row equal to

the input vector and with ones in the sub diagonal. If p is a column vector then

compan(p) is a matrix with the first column equal to the input vector and with

ones in the super diagonal.

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convPurpose Convolution and polynomial multiplication.

Usage c = conv(A,B)

Description With m as the length of the vector A and n as the length of vector B the resulting

vector is length n+m-1 and the elements are

C(k) =j

A(j)B(k + 1 j)

Where the sum is over all j that gives a valid index for A and B.

If A and B are vectors of polynomial coefficients, convolving them is equivalent

to multiplying the two polynomials.

cosPurpose Cosine

Usage Y = cos(X)

Description The function cos(X) returns the cosine of all elements of the matrix X.

dautPurpose Analog output from a D/A-converter

Usage y = daut(channel,x)

Description If the computer has a D/A-converter this function can be used to change the output

of the D/A-converter. The function returns the new voltage.

Se also adin

debugPurpose Send the compilation to the debug mode.

Usage Ctrl F9Debug [ ON | OFF ]

Description Gives some extra information during compilation. If DEBUG is used with com-

piling it gives a list of all the errors or if there are no errors the programme will be

listed in the sorted form.

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3.4 The Commands 25

defaultPurpose To give the parameters in command files a value.

Usage name textstring

Description With this command it is possible to make sure that all the formal variables in a

command file have a value.

Example If the command file

MACRO sim3 time value

default time 20

default value 15

par simtid $(time)

par ti[reg] $(value)

init

simu

is called without any argument, then the simulation time is 20 and the parameter

ti[reg] gets the value 15. If the next call is

>> sim3 100then the simulation time becomes 100 and ti[reg] = 15.

definePurpose Defines new global parameters

Usage Define name

Description Used to define new global parameters.

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delayPurpose Simulation av time delays

Usage y = delay(td,x,t)

Description If you want to simulate a time delay

y(t) = x(t td)

In regsim this can written as

TIME t

y = delay( td, x, t )

td : 0.5

It is also possible to simulate systems of the type

y(t) = y(t td) + u(t)

In Regsim:

CONTINUOUS SYSTEM ex1

INPUT u

TIME t

y = delay(td,y,t) + u

td : 0.34

detPurpose Matrix determinant

Usage d = det(X)

Description det(X) is the determinant of the square matrix X.

diagPurpose Diagonals of a matrix

Usage Y = diag(X)

Description diag(X) is the main diagonal of X.

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3.4 The Commands 27

diffPurpose Differanse

Usage Y = diff(X)

Description Diff for a vector

X =

x(1) x(2) . . . x(n)

is x(2) x(1) x(3) x(2) . . . x(n) x(n 1)

diff(X), for a matrix X, is the matrix of column differences.

dirPurpose Lists the files in the working directory

Usage Shift F6Dir [pattern]

Description Gives a list of all the files in the current working directory which matches with the

pattern. Using

dir *.*

give all the files in the directory.

dosPurpose Jumps temporarily to MS-DOS

Usage Alt F5Dos

Description Leaves the control to MS-DOS. To return to RegSim the command EXIT must be

given.

echoPurpose On and off the echo

Usage Shift F8Echo [ ON | OFF ]

Description If the echo is off, then it suppress the text of the command appearing in the com-

mand window when a command file or loops are executed.

If echo is given without an argument then it changes the status and the new status

is written out.

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editPurpose Starts an editor of your choice.

Usage Ctrl F5Edit [ filename ]

Description The command starts the normal editor Temac if it exists in any of the directories

declared in the MS-DOS variable PATH. If the file name is given as an argument

then the editor reads in that file. At the end of the editing the RegSim takes the

control and one can continue as if before calling the editor.

It is possible to choose another editor other than Temac. This is done by setting the

MS-DOS variable EDITOR equals to the file name where the editor exists. The

simple way to do this is to include the following line in the AUTOEXEC.BAT file.

SET EDITOR = pt.exeor

SET EDITOR = c:\ prog \ emacs.exe

endPurpose The last line in a command loop.

Usage End

Description See Loop and Foreach.

expPurpose Exponential function ex

Usage Y = exp(X)

Description exp(X) is the exponential of the elements of X.

execPurpose To execute a DOS-command

Usage doscommandExec doscommand

Description Used to run another programme from RegSim or to execute a dos command.

exitPurpose End the execution of the RegSim package

Usage Shift F10Exit

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3.4 The Commands 29

exitloopPurpose Stop execution of a loop command.

Usage Exitloop

Description See the command loop.

fastPurpose To select among fast or slow plotting.

Usage Fast [ ON | OFF ]

Description When simulating a system which contains both discrete time and continuous sys-

tems, it may be desirable to plot the continuous systems variables even directly

after sampling. The simulation is not affected by this, but only presents the vari-

ables on the screen in a more accurate way. The variables for which it is applicable

is the variables of the continuous time system that are directly depending on the

variables in the discrete time system.

If fast is ON, then the plotting is faster because RegSim does not bother to plot

direct after sampling.

foreachPurpose To create a command loop

Usage Foreach name (argumentlist)

Description Functions quite similar to Loop. The difference is that the number of repetitions

are are decided by the number of elements in the argument list. In each repetition,

the loop variable name gets a new value from the argument list.

The argument list consists of arbitrary number of text strings which are separated

by space. If the space is desired in a text string, then it is included between the

citation sign .

All occurrences of %(name) are supplied with the actual value of loop-variable.

Example Foreach x ( 0 1 x[proc] x2[proc] 5 )

par ztime %(x)

init

simu

end

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graphPurpose Direct plotting of expressions

Usage Shift F9Graph [ -i nr ] [ -n ] [ -X expr expr ] [ plotoptions ]

Description With graph the functions can be plotted directly. As the independent variable @

can be used. Automatic scaling will be done if mode=A (see command MODE).

Options -i Divides the plotting to nr intervals. More the number of intervals smoother

the curves would be.

When using polygon plotting or box plotting, it is suitable to give the option

-i 0, then the polygon is drawn only once.

-n When this option is given the old interval limits are used. Without option,

the program would ask between which values @ should vary.

-X With this option one can decide between which values the variable @

should vary under plotting.

For more, see PLOT.

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3.4 The Commands 31

hcopyPurpose Gives a copy of what is on the plot window of the monitor in a Postscript Laser

printer.

Usage F10Hcopy [ ON | OFF ] [ PS | EPS ] [ -f filename ]

Description With hardcopy active (this is indicated Hcopy(ON) in the bottom left corner) saves

all what is drawn on the screen to a file. A name can be given to the file using

option -f. If one wants to take a copy of the screen the the following command

is given

>> Hcopy PS [-f filename]This produces a file with name filename.PS, which can be sent to a laser writer

which understands Postscript.

With

Hcopy PS [ -f filnamn ]

a Postscript file which can be imported to Lotus Manuscript or Latex can be pro-

duced.

To produce a file one can give the following command sequence

hcopy on

axes

init

simu

hcopy off ps

Or we can create an alias as follows

alias hc (hcopy on;axes;init;simu;hcopy off ps)

This alias can for example be inserted in the file REGSIM.MCR which is read

when RegSim is started. In this way the command is always defined.

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helpPurpose Give some help

Usage F10Help [ kommando ]

Description Use and see the results.

if-else-endifPurpose If-else construction in the command files.

Usage IF boolean expr ELSIF boolean expr ELSE ENDIF

Description Gives the possibility of conditional execution of command files.

Example IF (x + xtd) > 0.5

scale -x 0 x+xtd

ELSE

scale -x 0 0.5

ENDIF

if-then-else

Purpose Conditional calulation

Usage y = IF boolean expression THEN expr1 ELSE expr2

Description It the boolean expression is true the the value of the expression is expr1, if it is

false then the value is expr2.

expr1 and expr2 must be of the same type and size

Example y = I F x > 0 T H E N 4*t ELSE 45

o p e n = z < 0

dx = IF open THEN{

1,2,0}

ELSE 0.1*

x - u

It is possible to break for a new row after THEN and ELSE

infoPurpose Open or close the information window

Usage Info { off | on }

Description The information window is normally visible to the left of the command window.

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3.4 The Commands 33

initPurpose Initializes the state variables etc.

Usage F2Init

Description Initializes the states, output signals etc. This command ought to be used when one

wish to start up a simulation or control with known initial values.

installPurpose Initialize the screen dump in an AT-computer with EGA-graphics

Usage Alt F3Install

Description Before one can do a screen dump from an AT-computer with EGA-graphics, one

must tell which port must be used and at the same time whether a simple or better

quality copies are needed (the better takes twice the time).

intPurpose Conversion to integer

Usage y = int(x)

Description int(x) returns the integer part of x, the result has the type integer.

The function rounds towards zero.

invPurpose Matrix inverse

Usage Y = inv(X)

Description inv(X) is the inverse of the square matrix X.

In practise it is more efficient to use matrix divsion to solve systems of linear

equations. The equation A*x = b has the solution x = inv(A)*b , but it

is more efficient to use the solution x = A\b that uses gauss elimination.

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listPurpose List the values of the parameters etc.

Usage F4List [ {systemname}* ]

Description This command gives a list of all the state variables, other variables and parameters

along with the values they have at the present time of the simulation. To find the

value of a single variable, the command PAR is recommended.

One can specify variables of which system or systems one likes to have a look.

One of these systems is the Global which contains all global variables, for example

Simtid and Epsilon.

lnPurpose Natural logarithm

Usage Y = ln(X)

Description ln(X) is the natural logarithm of the elements of X

load

Purpose Brings parameter values from a file.

Usage Alt F1Load [ filename ]

Description Brings parameter values and the initial values from a file which has been created

earlier with an text editor or with command Save.

locatePurpose Places the cursor.

Usage Locate [ expr [ expr ] ]

Description Places the cursor at the line and column given by the expressions. The first ex-

pression gives the row(line) and the second expression the column. If any of the

expressions is left out then their values are set to 0.

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3.4 The Commands 35

logPurpose Common (base 10) logarithm

Usage Y = log(X)

Description log(X) is the base 10 logarithm of the elements of X

loopPurpose Create a command loop.

Usage Loop

Description A command loop is a group of commands that begins with command Loop and

end with command End. The commands in this loop are executed until the com-

mand Exitloop is executed or the operator press the Esc after getting tired.

An example of a command loop is

define x

par x 10

loop

par ramptid[ramp] 2+x/10

init

simu

par x x+1

i f x = 1 1

exitloop

endif

end

makePurpose Generates a command file.

Usage Make [ filename ]

Description With this command one can save almost all the regsim-environment, scaling, win-

dow sizes, plot commands etc. so that one can create back the same environment

later. Another application is the creation of a skeleton for a command file. For ex-

ample after some experiments with window sizes, scales, parameter changes etc.,

when one is satisfied with all the settings and would like to create a command file

with these settings, the the command Make can be used to generate the desired

file automatically.

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makefuncPurpose Creates a table function.

Usage Makefunc {filename}*

Description With this command one can create a new function or define a old table function.

The table contains function values for given points. If the function value for a

point in between is needed it is obtained by linear interpolation.

The functions are defined in a file in the following format

[ PERIODIC ] FUNCTION namn

x1, f(x1)

x2, f(x2)

.

.

.

xn, f(xn)

END

The ordering of the data points is not important. The number of points must be

less than 399. If the prefix Periodic is used, then the function becomes periodic

with period = max(x) - min(x).

max, minPurpose Largest or smallest element

Usage y = max(a,b)

y = min(a,b)

Description max(a,b) is the largest element in X.

min(a,b) is the smallest element in X.

See also mmin and mmax.

maxwinPurpose Changes the number of visible windows.

Usage m a x w i n [ 1 | 2 | 3 | 4 ]

Description Decides how many window must be shown on the screen. In this version maxi-

mum of 4 windows can be shown at the same time.

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3.4 The Commands 37

meanPurpose Average or mean value

Usage m = mean(X)

Description For vectors, mean(X) is the mean value of the elements in X. For matrices,

mean(X) is a row vector containing the mean value of each column.

medianPurpose Median value

Usage m = median(X)

Description For vectors, median(X) is the median value of the elements in X. For matrices,median(X) is a row vector containing the median value of each column.

memPurpose Give information of the memory.

Usage Mem

Description Tells how much unused memory is left, in terms of number of paragraphs. A

paragraph = 16 byte.

menuPurpose Menu based changing of parameter values.

Usage Shift F7Menu

Description This command is used together with par -m to create menus.

There are two levels. The upper level contains titles which are given using the

command par -m. The second level contains the variables associated with each

title of the upper level. The variable are also given by the command par -m.

Try this

par -m System simtid epsilon flat break

menu

Once menu is invoked (by typing Menu), to select a title using the arrow keys and

pressing ENTER. To leave a menu press Esc. Once the title is invoked the variable

can be selected using the arrow keys again.

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mmaxPurpose Largest element

Usage Y = mmax(X)

Description For vectors, mmax(X) is the largest element in X. For matrices, mmax(X) is a

row vector containing the maximum element from each column.

mminPurpose Smallest element

Usage Y = mmin(X)

Description For vectors, mmin(X) is the smallest element in X. For matrices, mmin(X) is arow vector containing the minimum element from each column.

modePurpose Changes the mode for scaling of the axes.

Usage shift F5M o d e [ - 1 | - 2 | - 3 | - 4 ] [ - o | - a | - s | - y ]

Description Decides the mode for scaling of the axes with commands Show and Graph. Thecurrent mode is shown in the left bottom of the screen. It can be (.) the old value

is used, (A) automatic scaling, (Y) automatic scaling only for Y-axis or (S) auto-

matic scaling so that the scale factors for both axes are the same.

If the screen is divided into few windows, then we can obtain the status for respec-

tive window. For example (.S.A) means that the window 2 does automatic scaling

etc.

Options -o MODE = (.)

-a Automatic mode, MODE = (A)

-s Automatic mode, MODE = (S)-y Automatic mode, MODE = (Y)

-1 Specifies for which window the changing is valid. If options are left out then

all the windows are included.

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3.4 The Commands 39

mshiftPurpose Rowshift of a matrix

Usage Y = mshift( X, U )

Description All rows of the matrix X is shifted one position, and the first row is then replaced

with U.

See also shift.

Example mshift({{1,2,3},{2,4,1},{3,2,7}},{7,8,9})7. 8. 9.

1. 2. 3.

2. 4. 1.

normPurpose Matrix or vector norm

Usage n = norm(X)

Description For a matrix, norm(X) is the largest singular value of X, max(svd(X)).

For a vector, norm(X) = sqrt(sum(X)).

optPurpose Faster simulation

Usage Opt [ ON | OFF ]

Description If Opt is invoked then the RegSim tries do an extra optimization to speed up the

simulation.

palette

Purpose To change the colours.

Usage Palette

Description Gives a possibility to choose the colours of most of the graphic windows and the

curves. The desired colour parameters can be saved in a file REGSIM.INI which

must be in the same directory as REGSIM.EXE.

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parPurpose To change the parameter values or the initial values.

Usage F7Par [ [ -s ] name [expr] ]

Par -d

Par -m Title {name}*Par -q name

Description Changes or shows the value of a state, variable, parameter etc.

If name is a state or an output, then the initial value can be changed.

If the value is omitted then shows the value of the given variable.

If variables with same name exit in many systems then a menu with all these

variables are shown and one can select the desired one.

This variable can be used with both simulation and control.

Options -m Used to create a menu with name Title and as elements the variables which

follows. See the commando Menu.

-d Take away all the menus. This happens automatically with the compilation

of a new system.

-s Only for state variables. Changes this value instead of the initial value. Use-

ful to simulate impulse disturbances.

pausePurpose Temporary pauseUsage Pause [ text ]

Description Writes out the text TEXT and waits for a press of a key.

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3.4 The Commands 41

plot

Purpose Specifies which variables must be plotted under simulation and control.

Usage F6

Plot [-R expr] [-1|-2|-3|-4] [-N | -L | -B] [-r] [-c nr]

[-i nr] [-h text] [-x expr] [{expr}*]

Description Specifies what should be plotted during simulation or control. The parameters are

separated by space.

It is possible to plot many objects in different windows. A object can be of type

Normal, Line, square or box. A new object is created using one of the options

N,L,b,B. A object inherits its colours from the preceding object.During controlling (real time running) the different windows are updated in even

intervals and this interval can be changed with command Plotpar.

Options -c Use colour number nr (0 nr 8) for the curves that will follow. Withthis it is possible to get different colours on different segments in polygon

plotting.

-C Conditional plotting. The option followed by a boolean expression. The

condition is associated with an object. Whether the object would be plotted

or not is decided by the condition. This can be used to take away temporary

contours.-i Use colour number nr to the first curve and nr+1 to the second, etc. If

either the options c or i is given then -i 0 is used.

-F reads in a named file and interpret its content as a parameter. Advantageous

to use when the expression undealably long.

-h Specifies what must be the captions of the curves. If space is desired in the

caption then it must be enclosed with the citation signs .

-r Used in connection with polygon plotting and box plotting, to erase the fig-

ure when a new one is drawn. This is a simple way to do animation.

If used in Normal plotting (-N), then this option works in a different mannerand rolls the window from right to left and the curves continue to be plotted

in the right hand side of the window.

-N New object, Normal plotting. Used for example to end polygon plotting.

-L New object, polygon plotting. The x and y coordinates of two point have to

be given and a straight line connecting these two points are drawn. At least

four arguments have to be given.

-b New object, square plotting. Exactly four arguments have to be given, they

are the coordinates of the two diagonal ends of the square.

-B New object, Box plotting. Exactly four arguments have to be given, they arethe coordinates of the two diagonal ends of the square. The square is filled

with a colour.

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-x To change the independent variable in Normal plotting.

-R Used in real time plotting. An expression is used to decide when the plotting

can be done.

-1 Selects window 1 etc. Begins also a new object of type Normal.

Example plot x y

Plots variables x and y with respect to time.

Graph -x sin(@) cos(@) -L -c 4 0 0 sin(@) cos(@)

draws a wheel with spokes.

Graph -F figur.1

Reads the figur.1 which can contain

#

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3.4 The Commands 43

pgupPurpose Interaction with the user

Usage y = right()

Description This function can return the values -1, 0 and 1 depending on wich of the keys

PGDN, HOME and PGUP has been pressed. With this function it is possible to

give inputs from the keyboard to process

Give the command arrow too use the function during real time control regu.

plotperPurpose Decides the period time for updating different windows used during real time

running.

Usage ctrl F6plotper [ -1 | -2 | -3 | -4 ] [{expr}*]

Description With this command one can change the period time for plotting during the real

time running (see REGU). The period time is given in milli seconds.

One should nod choose too short period times because it lowers down the system

speed. Furthermore one ought to select a period times that are multiples of differ-

ent sampling times used in the system (see initime and regu).

During animation it is suitable to use period time as 50 or 100 ms.

Example plotper 50 100

sets period time for window 1 to 50 ms and for window 2 to 100 ms.

plotper -4 40

sets the period time of window 4 to 40 ms.

pputPurpose Change value on digital output

Usage y = pput(x)

Description Changes the value on the digital output.

printscrPurpose Dumps screens contents to a printer.

Usage Alt F2Printscr

Description It is useful when one needs to do a print screen in a command file

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qsortPurpose Sortering av element i vaxande ordning

Usage Y = qsort(X)

Description For en vektor sa sorterar qsort(X) elementen i vaxande ordning. For en matris

sa sorterar qsort(X) varje radvektor i vaxande ordning.

quitPurpose Exits regsim

Usage quit

Description See also BYE and EXIT.

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3.4 The Commands 45

reguPurpose Start or stops a real time system.

Usage F8Regu

Description Starts a real time running of the discrete time systems. The continuous systems

that are defined become inactive.

Informs that the function simulating() returns the value FALSE

After the real time running has started, one can come back to the command in-

terpreter, and this means that commands can be executed while real time running

continues. For example one can change the size of the window, change scales,

parameters, sampling time etc.

The real time running is handled by a real time kernel which is driven with certain

periodicity (see initime). The period time is decided from the sampling time ofthe discrete systems, plotting period time (see Plotper), data logging period time

(see store) and a internal process with period time of 1 s.

The discrete system has the highest priority because they are executed first and if

there is time left then the logging and plotting is done.

If the discrete systems can not be executed during the given sampling time then

the real time running is stoped. But not if the plotting can not find time in every

period.

For real time running, the sampling time of a discrete system is decided by the

variable SAMPTIME which automatically defined in all discrete systems. SAMP-

TIME is a integer variable with units milliseconds.For not to confront troublesome differences during simulation (where next sam-

pling is decided by a TSAMP-declared variable), the following construction can

be used if one expect to use the system for both simulation and real time running.

DISCRETE SYSTEM test

STATE ......

NEW .......

TIME t

TSAMP ts

INITIAL

samptime = 100

SORT

ts = t + samptime/1000

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rightPurpose Interaction with the user

Usage y = right()

Description This function can return the values -1, 0 and 1 depending on wich of the keys ,HOME and has been pressed. With this function it is possible to give inputsfrom the keyboard to process


arrow.

satPurpose Limit function

Usage y = sat(x)

Description The function sat returns a matrix that is a copy of X with all elements limited such

that |yij| 1

Example sat({5,0,-3})1. 0. -1.

sat(2.34)

1.

savePurpose Saves parameter values in a file.

Usage Ctrl F1Save [ filename ]

Description Save all parameters and initial values in a file which can in a later occasion be

read by Load. This file is a pure text file and can be changed as desired. One can

also write ones own file so that in a simple manner can change few parameters at

the same time.The file must have the following format

SYSTEM systemnamn

variablename : numerical value

.

.

END

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3.4 The Commands 47

scalePurpose Changes the scale factors of the axes.

Usage F5Scale [ -1 | -2 | -3 | -4 ] [ -x expr expr ] [ -y expr expr

]

Description Changes the scaling. If function in invoked by using F5, the cursor is placed in a

box which appears on the screen.

The cursor can be moved using and .One can also change the scale factors by writing the new value and pressing the

ENTER.

With PGUP and PGDN one can move up and down between the different boxes

corresponding to different windows.

By pressing the Escape (ESC) the box will vanish in the same way as it appeared

and the cursor is back in the command window.

Options -x Changes the scales of the x-axis

-y Changes the scales of the y-axis

-1 Specifies for which window the scaling is valid. If this option is omitted then

the scaling is for the window 1.

setaxesPurpose ON and OFF the axes.

Usage Setaxes [-1|-2|-3|-4] {off | on}*

Description A window can be shown with or without axes. Without axes the effective area

becomes larger.

Example setaxes off on

The window 1 is drawn without axes and window 2 with axes.

setaxes -2 off

Now the window 2 is axisless

setaxes -3 off off

Now window 3 and 4 are axisless.

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setfilePurpose Use stored data as input

Usage PC : setfile [ -v ] [ -n ] [ filename ]

MAC : setfile filename systemname variablename

Description With Regsim it is possible to save data from simulations and real time control in

a file with the command STORE. Data from a STORE file can be used as a input

in simulation with the help of this command.

Options -v (Verbose) Extra information is written.

-n Use original variable names. Normally the varibales are collected in a vector

with the name x.

Example Suppose that the STORE file measure.str contains data from three A/D-

converters. In this example the three signals are LP-filtered with regsim

The system file should look like this

CONTINUOUS SYSTEM filter

DER dy{3}STATE y{3}dx = ( x[measure] - y ) / T

T : 0.2

END

Give this commands to run the filter

setfile measure

comp file filter

plot x y

simu

Observere the extra argument file to the command comp.

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3.4 The Commands 49

setsizePurpose Changes the dimensions of the windows

Usage Setsize [ -1 | -2 | -3 | -4 ] [ -x expr expr ] [ -y exprexpr ]

Description Changes the dimensions. If the function is invoked without arguments the the

cursor is placed in a box which appears on the screen.

The cursor can be moved using and .One can also change the dimension by writing the new value and pressing the

ENTER.

With PGUP and PGDN one can move up and down between the different boxes

corresponding to different windows.

By pressing the Escape (ESC) the box will vanish in the same way as it appeared

and the cursor is back in the command window.

The constraints for x and y are

0 x 80 , 0 y 20

Options -x Changes the window length

-y Changes the window height

-1 specifies for which window the dimension is valid. Of the option is omitted

then the dimensions of the window 1 is changed.

shiftPurpose Shifts the elements in a Skift av element i en vektor eller matris

Usage Y = shift( X, u )

Description All elements in X is shifted on position and the first elements is replaced with tha

scalar u.

See also mshift.

Example shift({1,2,3},4)

4. 1. 2.

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showPurpose Plots the saved variables.

Usage Shift F4Show [ -f filename ] [ see options in Plot ]

Description Plots variables which are stored in a file. Functions same as the Plot and Graph.

The scaling of the axes can be automatic (see command Mode). The storing in a

file is done with the command Store.

If option -f is omitted, it questions after the file that the variables have to be

taken.

The command uses files that have the extension .STR.

signPurpose Sign function

Usage Y = sign(X)

Description sign(X) returns the sign of the argument.

Example sign({45,0,-3.23,0.12})1. 0. -1. 1.

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3.4 The Commands 51

simuPurpose Simulates

Usage F3Simu [ expr ] [ -b value ] [ -s value ] [ -c expr ]

Description Starts a new simulation or continues a simulation which has been interrupted.

A simulation can be interrupted using Esc. The simulation time is decided by the

global parameter SIMTID which can be changed with command PAR or by giving

the new simulation time as an argument to the command.

simu 20

Changes the simulation time to 20.

To be sure that the simulation starts with the correct initial values for the statesand parameters, the command INIT can be given before simulation. This is not

applicable if one continues a interrupted simulation.

The function Simulating gets the value TRUE.

Options -b Interrupts the simulation after value time units.

-c If the expression becomes true the simulation is interrupted immediately.

Note that the expression can not be controlled continuously.

-s Uses the value as the largest permitted step length. By default, 1/100 ofthe SIMTID (simulation time) is taken.

simulatingPurpose Indication that simulation is running.

Usage b = simulating()

x = IF simulating() THEN y ELSE adin(0)

Description This function returns true if a simulation is running with the command simu and

it is false if real time control is started with the command regu.

sinPurpose Sine

Usage Y = sin(X)

Description sin(X) is the sine of the elements of X.

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solvePurpose Solution of systems of linear equations

Usage x = solve(A,b)

Description A system of linear equations A*x = b has the solution x = solve(A,b).

This is equivalent with the solution x = A\b.

sqrPurpose Square

Usage Y = sqr(X)

Description sqr(X) is the square of all elements in. For a scalar this is y = x2.

sqrtPurpose Square root

Usage Y = sqrt(X)

Description sqrt(X) is the square root of the elements of X.

storePurpose Specifies which variables must be stored in a file.

Usage Shift F1Store [ -l ] [ -c expr ] [ -p period ] [ -f filename ] [

{name}* ]

Description Specifies which variables has to be stored in a file during simulation or regulation.

Parameters are separated by space and ends with Return.

If the command is started without argument it asks for a file name. One can call

back the old parameter list with TAB-command.

Options -f If option -f is omitted it asks for the file that has to be used.

-c If this option is used the variables are stored only when the condition expr

is TRUE. This option does not mean that one can save more often than when

this condition.

-l Lists which file is used and which variables have to be saved.

-p If this option is used the variables are saved with a time space of period.

This is equivalent to sampling of the variable with period period. If this

option is omitted or the period is too small, the the variables are stored

only if there is a change in the variables. For continuous system this means

the data is stored in irregular intervals.

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3.4 The Commands 53

sumPurpose Sum of elements

Usage y = sum(X)

Description For vectors, sum(X) is the sum of the elements of X. For matrices, sum(X) is a

row vector with the sum over each column.

svdPurpose Singular value decomposition

Usage s = svd(X)

Description svd(X) returns a vector containing the singular values, sorted in decreasing or-der.

textPurpose To write text in the graphic window.

Usage Text [ -c nr ] [ -1 | -2 | -3 | -4 ] expr expr "text"

Description Writes the text text at the left bottom end of the first letter at the position which

is defined by the two expressions where the first is the x coordinate and the second

is the y coordinate.The position is given with scaled coordinates.

Options -c Gives the text the colour nr

-1 Defines in which window the text must be written.

timePurpose Measuring time

Usage Time

Description A timer is started every odd time the command is given. The timer is stopped and

the elapsed time is written in the command window every even time the command

is given.

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toeplitzPurpose Toeplitz matrix

Usage T = toeplitz(C)

Description toeplitz is a symmetric (or Hermitian) Toeplitz matrix

Example toeplitz(1,2,3,4)1. 2. 3. 4.

2. 1. 2. 3.

3. 2. 1. 2.

4. 3. 2. 1.

tracePurpose Sum of diagonal elements

Usage T = trace(X)

Description trace(X) is the sum of the diagonal elements of X, which is also the sum of the

eigenvalues of X.

transfPurpose Transfer function

Usage y = transf( numerator, denominator, u )

Description Use this function to implement a transfer function from the input u to the output

y, both in continuous and time-discrete systems. One limitation is that the transfer

function must be strictly proper.

Example Too simulate the continuous system

Y(s) =as + 1

s2

+ 3 T s + w2

U(s)

in regsim, write

y = transf( { a, 1}, {1,3*T,w2}, u )

where a, T, w and u are parameters or variables defined elsewhere.

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3.4 The Commands 55

trapPurpose To tell which computations are not allowed.

Usage Trap [-a] [-i] [-d] [-u] [-o] [-z] [-a]

Description Tells which computations are permitted. If an unpermitted computation is en-

countered it stops simulation or control and the computation that is not allowed is

shown in a box on the screen.

Options -i Undefined numbers, e.g. 0/0. If it is allowed then it gets the valueNAN(Not A Number).

-d Unnormalized number. That is number which is too small to be represented

in a normal way.

-u Underflow, a small number which is set to = 0-o Overflow, a large number which is set ti =

-z Division by zero. The result is =

-a all

truncPurpose Truncate

Usage Y = trunc(X)

Description trunc(X) is the integer part of the elements in X.

upPurpose Interaction with the user

Usage y = up()

Description This function can return the values -1, 0 and 1 depending on wich of the keys ,HOME och has been pressed. With this function it is possible to give inputsfrom the keyboard to process


arrow.

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writePurpose To write text in command routines.

Usage Write textstring

Description Used to write out a text string in command routine. Special letters are

\n Change of line in write out.\abc Write out special character CHR(abc) where abc is a three digit decimalnumber.

writeexpPurpose Write out the value of an expression

Usage Writeexp expr

Description This command functions same as the Calc, but the write out is savable so that it

can go with the Write command. The belief is that it can be used in command

files.

Example clear 1

write linelength =

writeexp line[tralla]

write [m]

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Chapter 4

Command Files

Command files are a way of creating ones own commands. To define a command file the first

line in the file must contain the following line

MACRO macroname [parametername *]

this can be followed by arbitrary number of commands, one in each line. If a line begins with

the sign # the the whole line is defined as a comment. This sign be placed any where in the

file even before the MACRO-definition.

To use the parameters in a command file one writes $ (parametername) .

Command file must be in a file with name macroname.MCR.

An example of an command file

MACRO komp reg start stop count

echo off

#

default reg pidreg

default start 1.0

default stop 5.0

default count 10

#

define cdefine kk

define step

p a r c 0

par kk $(start)

par step ($(stop)-$(start))/($(count)-1)

#

clear

write regulator = $(reg)

comp tank.con $(reg).con

loop

#clear 1

write k =

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58 Command Files

writeexp kk

#

par k kk

init

simu

par c c+1

par kk kk+step

if c=$(count)

exitloop

endif

end

4.1 Invoking by a MACRO

To use a command file it be in the working directory or in a directory which is enumerated in

variable MACRO. This can be set using the MSDOS command SET, for example,

set MACRO = c:\macro

A command file is used by writing the name and the necessary arguments. If the arguments are

omitted then they become blank if there are no default command. For example if we use the

command file komp with count = 15 and the rest of the arguments come from default. This

can be done in two ways,

komp pidreg 1.0 5.0 15

or

komp count=15

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Chapter 5

The Syntax for Expressions

The following is the description of the syntex for RegSim in Bakus-Naur form.

variable assignment ::= variable identifier = expression

parameter assignment ::= identifier : constant

| identifier : vector constant []

| identifier : matrix constant

expression ::= relation and relation

| relation or relation

| IF relation THEN relation ELSE expression

| matrix expression

relation ::= simple expression [ relational operator simple expression ]

simple expression ::= [ unary operator ] term adding operator term

matrix expression ::= {vector expression , vector expression}

vector expression ::= {expression , expression}

term ::= factor multiplying operator factor

factor ::= secondary

| secondary

| secondary secondary

secondary ::= [ NOT ] primary

primary ::= constant

| variable identifier

| identifier ( expression , expression )

| ( expression )| matrix constant

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60 The Syntax for Expressions

unary operator ::= + | -

adding operator ::= unary operator

multiplying operator ::= * | /| .* | ./| \

relation operator ::= < | > | =

constant ::= number | real

number ::= digit digit

real ::= number . [number] [ exponent ]

exponent ::= E [ - | + ] number

variable identifier ::= identifier| identifier{number , number}| identifier[ identifier ]

| identifier{number , number}[ identifier ]

identifier ::= letter [ letter | underscore | digit | . ]

matrix constant ::= {vector constant,vector constant}

vector constant ::= {constant ,constant}

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