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An Overview of Activities in
CONTROL AND POWER
Qing-Chang [email protected]
Electrical Drives, Power and Control Group
Dept. of Electrical Eng. & Electronics
The University of Liverpool
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 1/77
Outline
Research activities in control
Research activities in power
Other research activities
Practical experiences
New-ACE
Teaching
Funding
Future research plan
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 2/77
Research activities in controlOn the theoretical side, my research has been focus-ing on robust control, time-delay systems, processcontrol, and recently applying the theory of infinite-dimensional systems to time-delay systems. A seriesof problems have been solved:
Projections
J-spectral factorisation
Delay-type Nehari problem
StandardH∞ problem of single-delay systems
Realisation of distributed delays in controllers
Feedback stabilizability of linear systems withstate and input delays in Banach spaces
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 3/77
Major publications
IEEE Trans. Automatic Control: 7
Automatica: 4
OtherIEEE Transactions: 3
IET Control Theory & Applications: 4
One research monograph
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 4/77
ProjectionsFor a given nonsingular matrix partitioned as
[M N
], denote
the projection onto the subspace ImM along the subspace ImN
by P . Then, the projection matrixP is
P =[
M 0] [
M N
]−1
.
Similarly, the projectionQ onto the subspace ImN along the sub-
space ImM is
Q =[
0 N
] [M N
]−1
=[
N 0] [
N M
]−1
.
If MTN = 0, then the projection matrices reduce to
P = M(MTM)−1MT and Q = N(NTN)−1NT .
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 5/77
J-spectral factorisationJ-spectral factorisation is defined as
Λ(s) = W∼(s)JW (s),
where theJ-spectral factorW (s) is bistable andΛ(s)
is a para-Hermitian matrix:Λ(s) = Λ∼(s).= ΛT (−s).
Assume thatΛ, having no poles or zeros on thejω-axisincluding∞, is realised as
Λ =
[Hp BΛ
CΛ D
]= D + CΛ(sI − Hp)
−1BΛ (1)
and denote theA-matrix ofΛ−1asHz, i.e.,
Hz = Hp − BΛD−1CΛ.Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 6/77
Triangular forms of Hp and Hz
Assume that a para-Hermitian matrixΛ as given in (1)is minimal and has no poles or zeros on thejω-axisincluding∞. There always exist nonsingular matrices∆p and∆z (e.g. via Schur decomposition) such that
∆−1p Hp∆p =
[? 0
? A+
]
and
∆−1z Hz∆z =
[A− ?
0 ?
],
whereA+ is antistable andA− is stable (A+ andA−
have the same dimension).Note: No structural information ofHp andHz is needed.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 7/77
Factorisation with two matricesLemma Λ admits aJp,q-spectral factorisation for some unique
Jp,q (wherep is the number of the positive eigenvalues ofD and
q is the number of the negative eigenvalues ofD) iff
∆ =
[∆z
[I
0
]∆p
[0
I
] ]
is nonsingular. If this condition is satisfied, then aJ−spectralfactor is formulated as
W =
[I 0
]∆−1Hp∆
I
0
[I 0
]∆−1BΛ
Jp,qD−∗W CΛ∆
I
0
DW
, (2)
whereDW is a nonsingular solution ofD∗W Jp,qDW = D.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 8/77
Factorisation with one common matrixIn general,
∆z 6= ∆p.
However, these two can be the same.
Theorem Λ admits aJ-spectral factorisation if andonly if there exists a nonsingular matrix∆ such that
∆−1Hp∆ =
[A
p− 0
? Ap+
], ∆−1Hz∆ =
[Az
− ?
0 Az+
]
whereAz− andA
p− are stable, andAz
+ andAp+ are an-
tistable. When this condition is satisfied, aJ-spectralfactorW is given in (2).
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 9/77
The Delay-type Nehari problem
Given a minimal state-space realisationGβ =[
A B
−C 0
],
which is not necessarily stable, andh ≥ 0, characterisethe optimal value
γopt = inf{∥∥Gβ(s) + e−shK(s)
∥∥L∞
: K(s) ∈ H∞}
and for a givenγ > γopt, parametrise the suboptimalset of properK ∈ H∞ such that
∥∥Gβ(s) + e−shK(s)∥∥
L∞< γ.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 10/77
The optimal valueThe optimal valueγopt is
γopt = max{γ : det Σ22 = 0}, Σ22 =[−Lc I
]Σ
Lo
I
,
whereLo andLc are stabilising solutions, respectively, to
[−Lc I
] A γ−2BB∗
0 −A∗
I
Lc
= 0,
[I −Lo
] A 0
−C∗C −A∗
Lo
I
= 0.
Σ =
Σ11 Σ12
Σ21 Σ22
.
= Σ(h) = exp(
A γ−2BB∗
−C∗C −A∗
h)
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 11/77
The structure of K
j
Gβ Z
e−shI
W−1
j
Q
K@@�
--
u
y
z
w
�
-
��
6
6
6
?
?
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 12/77
Example: Gβ(s) = − 1s−a
(a > 0)
Σ22
ah
aγ
The surfaceΣ22 with re-spect toah andaγ
0 1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ah
aγ
aγopt
The contourΣ22 = 0 on theah-aγ plane
SinceI−LcLo = 1−4a2γ2, there is∥∥ΓGβ
∥∥ = 12a . As a
result, the optimal valueγopt satisfies0.5 ≤ aγopt ≤ 1.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 13/77
The standard H∞ problem ofsingle-delay systemsGiven aγ > 0, find a proper controllerK such that theclosed-loop system is internally stable and
∥∥Fl(P, Ke−sh)∥∥∞
< γ.
P
e−shI
K
�
� �
�
y
z
u
w
u1
-
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 14/77
Simplifying the problem
Cr(P )
@@ e−shI
K
-
� � �
w
z u
y
u1
6
Cr(P )
@@
Gα
@@
Cr(Gβ)
@@ e−shI
K
Delay-free problem 1-block delay problem
-
�
-
�
-
� � �
w
z u
y
u1
6w1
z1
y
u1
Gα is the controller generator of the delay-free prob-lem. Gβ is defined such thatCr(Gβ)
.= G−1
α . Gα andCr(Gβ) are all bistable.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 15/77
Solution to the problemSolvability⇐⇒ :
H0 ∈ dom(Ric) andX = Ric(H0) ≥ 0;
J0 ∈ dom(Ric) andY = Ric(J0) ≥ 0;
ρ(XY ) < γ2;
γ > γh, whereγh = max{γ : det Σ22 = 0}.
Z V −1
h
Q
@@
--
u
y-
��
6
?
?
V −1 =
A + B2C1 B2 − Σ12Σ−122 C∗
1 Σ−∗22 B1
C1 I 0
−γ−2B∗1Σ
∗21 − C2Σ
∗22 0 I
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 16/77
Implementation of the controllerAs seen above, the control laws associated with delay systems
normally include a distributed delay like
v(t) =
� h
0
eAζBu(t − ζ)dζ,
or in thes-domain, Z(s) = (I − e−(sI−A)h) · (sI − A)−1.The implementation ofZ is not trivial becauseA
may be unstable. This problem had confused the
delay community for several years and was pro-
posed as an open problem inAutomatica in 2003.
It was reported that the quadrature implementation
might cause instability however accurate the imple-
mentation is.
My investigation shows that:
The quadrature approximation error converges to0
in the sense ofH∞-norm.10
−210
−110
010
110
210
310
−4
10−3
10−2
10−1
100
101
Frequency (rad/sec)
N=1
N=5
N=20 A
ppro
xim
atio
n er
ror
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 17/77
A trivial but significant result
τ t t−h/N
y(τ)
t 0
y(t) p(t)
t
1
0 h/N
∗=
� hN
0y(t − τ)dτ =
� t
t− hN
y(τ)dτ = y(t) ∗ p(t).
� h0 eAζBu(t − ζ)dζ =
N−1∑
i=0
� (i+1) hN
i hN
eAζBu(t − ζ)dζ
≈
N−1∑
i=0
eiA hN B
� (i+1) hN
i hN
u(t − ζ)dζ
=
N−1∑
i=0
eiA hN Bu(t − i
h
N) ∗ p(t)
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 18/77
Rational implementation
1x2xΠ
Nx 1−Nx
B1−Φbu
u
rv
…
ΦΦ+−=Π −1)( AsI
Π Π
…
Π = (sI − A + Φ)−1Φ,
Φ = (
� hN
0 e−Aζdζ)−1.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 19/77
Unified Smith predictor (USP)A numerical problem with the modified Smith predictor (MSP) is
identified. See the simple but a little bit extreme example
P (s) =1
s + 1000+
1
s − 1.
The MSP is
ZMSP(s) =e1000h − e−sh
s + 1000+
e−h − e−sh
s − 1.
According to the IEEE Standard 754,e1000h is regarded to be+∞
(INF) for h ≥ 0.71sec. This is not acceptable in practice.
A unified Smith predictoris proposed to fix this problem. An
equivalent structure of systems incorporating USP is derived and
then applied to solve various problems.Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 20/77
Feedback stabilisation of delay systemsThe feedback stabilizability of the state–input delaysystem
x(t) = A0x(t) + A1x(t − r) + Pu(t) + P1u(t − r)
is equivalent to the condition
Rank[(P + e−rλiP1)
∗ · ϕi]
= di, i = 1, 2, · · · , l.
whereλi ∈ {λ1, λ2, · · · , λl} = {λ ∈ C : det ∆(λ) =
0 andReλ ≥ 0} with ∆(λ) := λI − A0 − A1e−rλ.
The dimension ofKer∆(λi)∗ is di and the basis of
Ker∆(λi)∗ is ϕi
1, ϕi2, · · · , ϕi
difor i = 1, 2, · · · , l .
Appeared in IEEE Trans. Automatic Control as a reg-ular paper. Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 21/77
Research activities in powerFocusing on power electronics & renewable energy
Voltage control of DC-AC converters
Neutral point generation
Grid-friendly inverters: Synchronverters
Regulation of induction generators for wind power
Control of wind turbines
Energy recovery from landing aircraft
Damping control of inter-area oscillations in power systems
DC and AC drives
AC Ward Leonard drive systems
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 22/77
DC-AC converters in the contextof distributed generation
Local generator
Diode
Rectifier
DC-AC
Converter
Micro-grid
grid DC link
Gas turbines Wind-mills etc.
Fuel cells Photo-voltaic etc.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 23/77
Control problems involved
voltage control:
e = Vref − Vc as small as
possible
neutral point control: to
provide a non-drifting
neutral point
power control: to regulate
the active/reactive power
phase-locked loop (PLL):
to synchronise the con-
verter with the grid
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 24/77
Voltage control of DC-AC converters
The single-phase circuit:
The objective is to make sure that the output voltageVout or Vc is a clean sinusoidal signal even when theload is nonlinear and/or the public grid is polluted withharmonics. Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 25/77
Structure of voltage controller
Techniques used:
H∞ control
Repetitive control, where a delay is introducedinto the controller
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 26/77
Formulation of the H∞ control problem
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 27/77
Nyquist plot of the system
−2 −1 0 1 2 3 4 5 6−8
−6
−4
−2
0
2
4
6
8−L(jω)
Re
Im
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 28/77
Simulation results
0 0.05 0.1 0.15 0.2−400
−300
−200
−100
0
100
200
300
400
Time (sec)
Vol
tage
(v)
Vc e
0.36 0.37 0.38 0.39 0.4−400
−300
−200
−100
0
100
200
300
400
Vol
tage
(V
) micro−grid
(external) grid
Time (sec)
(a) Transient response (b) Steady-state response
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 29/77
Experimental results
-20
-10
0
10
20
Vo
lta
ge
[V
]
0.00 0.01 0.02 0.03 0.04 0.05
Time [sec]
#1:1
#1:2
(a) voltage and its reference
-4
-2
0
2
4
Vo
ltag
e e
rro
r [V
]
0.00 0.01 0.02 0.03 0.04 0.05
Time [sec]
#1:1
(b) tracking errorQ.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 30/77
Neutral-point control: Existing schemes
Split DC link
Conventionalneutral leg
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 31/77
Neutral-point control: Proposed scheme
Control objective: to forceic ≈ 0 so that the pointNwill be the mid-point of DC supply.
No need to re-design the converter;
The controller is decoupled.Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 32/77
H∞ control design
This is a double-integrator system.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 33/77
Experimental results
Vave
0.2V/div
iN
50A/div
iL
50A/div
ic
20A/div
0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27
Time (sec)
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 34/77
Grid-friendly invertersMany strategies have been set to explore renewable en-ergy sources, such as wind and solar power, to lead toa low carbon economy. However, the increasing shareof the electricity generated from these sources (whichis often fed into the grid via inverters) could be a po-tential threat to the overall stability of the future powersystem when it reaches a certain level. Utility com-panies would expect to minimise the impact of a largenumber of grid-connected inverters on the power sys-tem. Moreover, how to share load among these invert-ers autonomously is also a problem.Our Solution:Synchronverters: Inverters that mimic synchronous generators
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 35/77
Synchronous generators
M
M M
Rs , L Rs , L
Rs , L
Rotor field axis
( 0=θ )
Field voltage
Rotation
N
v = −Rsi − Ls
di
dt+ e,
e = Mf if θsinθ−Mf
dif
dtcosθ,
Te = pMf if
⟨i, sinθ
⟩,
Q = −θMf if 〈i, cosθ〉 ,
Jθ = Tm − Te − Dpθ.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 36/77
The synchronverter
+
-
Ls , Rs va
vb
vc
ia
ib
ic
ea
eb
ec
VDC
C
vga
vgb
vgc
Circuit Breaker
Lg , Rg
(a) The power part
Te Eqn. (7) Eqn. (8) Eqn. (9)
s
1
Dp
Tm
-
θ θ&
i
e
Mf if
Q
Js
1
-
(b) The electronic partQ.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 37/77
Experimental setup
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 38/77
Experimental results: I
Time (Second)
Fre
quen
cy(H
z)
(a) synchronverterfrequency
Time (Second)
P(W
)an
dQ
(Var
)
P@@I
Q��
(b) real powerP andreactive powerQ
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 39/77
Experimental results: II
Time (Second)
Fre
quen
cy(H
z)
(a) synchronverterfrequency
Time (Second)
P(W
)an
dQ
(Var
)
PXXy
Q�
(b) real powerP andreactive powerQ
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 40/77
Regulation of induction generatorsfor wind power
Q
P
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 41/77
Control of wind turbines
Patented by Nheolis, France, installed on the department’srooftop
Experiments show that the new wind turbine is very efficient.Themaximum mechanical power of a prototype with a 2m (diame-ter) rotor reached 12kW at a wind speed of 20m/s. The nominalpower is 4.1kW at 14 m/s. A 1-meter 3-bladed prototype recorded2.8kW mechanical power at 14 m/s. This is much more efficientthan any commercial wind turbines available.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 42/77
Buck Converter
Boost Converter
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 43/77
Energy recovery from landing aircraft
Coils
Risen slope to fall when energy recovery is activated
Aircraft
Runway Magnets with alternative poles (N, S, N, …)
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 44/77
Voltage and current (zoomed)
0 0.1 0.2 0.3 0.4 0.5-6000
-4000
-2000
0
2000
4000
6000
Pha
se A
vol
tage
0 0.1 0.2 0.3 0.4 0.5-1
-0.5
0
0.5
1x 10
5
Time
Pha
se A
cur
rent
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 45/77
0 5 10 15 20 25 30-6000
-4000
-2000
0
2000
4000
6000P
hase
A v
olta
ge
0 5 10 15 20 25 30-2000
-1000
0
1000
2000
Time
Pha
se A
cur
rent
(a) Phase current andthe generated voltage
(phase)
0200400600800
d
0
50
100
v
-10
-5
0
a
0
1
2x 10
7
p
0 5 10 15 20 25 300
5
10x 10
7
Time
E
(b) Distance, speed,deceleration, power and
energy
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 46/77
Damping control of inter-area oscilla-tions in large-scale power systems
TCSC: Thyristor Controlled Switched Capacitors
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 47/77
AC-DC converters: DC drives
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 48/77
AC-DC-AC converters: AC drives
Philips Semiconductors
VVVF speed control by:
using the PWM circuit HEF4752V shown above
using Intel 8051 microcomputer to generate spacevector PWM signal
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 49/77
Ward Leonard drive systems
Constant speed
Variable speed
Controllable field Fixed field
Prime mover
Load
Conventional (DC) Ward Leonard drive systems
Variable speed
Variable speed
Fixed field
SM/IM Load
SG Prime mover VDC
Inverter
AC Ward Leonard drive systemsQ.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 50/77
Exp. results: high-speed, no load
(a) speed (b) torque
(c) current (d) voltageQ.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 51/77
Exp. results: low-speed, no load
(a) speed (b) torque
(c) current (d) voltageQ.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 52/77
Other research activitiesRapid control prototyping
dSPACEMICROGenTexas Instruments kits
Embedded systems and control
Process control
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 53/77
Rapid control prototyping (RCP)There are two sets of
dSPACE+Matlab/Simulink/SimPower in the lab.
Single-board PCI hardware for use in PCs
powerful development system for RCP
Real-Time Interface provides Simulink® blocksfor graphical configuration of A/D, D/A, digitalI/O lines, incremental encoder interface and PWMgeneration
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 54/77
MicroGen
A universal electronic control unit with MPC555built-in
Software-configurable I/O and signalconditioning
Using industry standard SimuLink®
Enabling technology for RCP and HiL applica-tions
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 55/77
Texas Instruments kitsTI has donated about 20 sets of different digital signalcontrollers (including TMS320F28335) equipped withthe full version of latest Code Composer Studio 4.0.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 56/77
Embedded systems & controlDifferent development kits for embedded control:
Wind River Workbench + Wind River Probe
Freescale MPC5567
Mathworks xPC target
EasyPIC4
dsPICPro2
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 57/77
Wind RiverSupport a wide range of processors
USB 2.0-compliant host connection
High-speed JTAG run control and
program download
Hot-plug-capable interconnect system
RTOS: VxWorks, Linux, and ThreadX
Built-in hardware diagnostics
Flash memory programming
Source-level debugging
Support for Memory Management Units
Open API integration
Wind River Probe
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 58/77
FreescaleMPC5567
132 MHz PowerPC-based e200z6 core
a dual-channel FlexRay controller (10 Mbit/sec)
Fast Ethernet controller, 5 FlexCAN modules
40-channel dual analog-to-digital converter (ADC)
24-channel PWM
32-channel direct memory access (DMA) controllerQ.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 59/77
Mathworks xPC target
Provide a high-performance host-target environment
Design a control system using Simulink® and Stateflow®
Generate code with Real-Time Workshop® and Stateflow
Coder™ and download the code to a target PC running the
xPC Target real-time kernel
Execute the code in real time on low-cost PC-compatible
hardware
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 60/77
EasyPIC43 in 1: Development, USB 2.0 programmer, ICD
Supports 8, 14, 18, 20, 28 and 40 pin PIC
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 61/77
dsPICPro2Supports dsPIC in 64 and 80 pins package.
USB 2.0 programmer on board + A/D + D/A
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 62/77
Chemical process control (1992)
16 reactors, controlled by 3 industrial computers
Effective object code > 100 KB (Intel 8086 assembler)
Analogue control variables include pressure, temperature,
level, flow and weight etc.Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 63/77
Integral processes with dead timeIntegral process with dead-time (IPDT): G(s) = Gp(s)e−τs = k
se−τs
Consider the disturbance observer-based control scheme (Zhong and Normey-Rico, 2001)
f f f
f f
- C(s)
Gm(s) e−τms
Gp(s)e−τs
G−1m (s)
Q(s)
�
�
- ��- �
6 6
?
?
d
r u y
n
−−
−
Disturbance Observer
c
d
- - - --
h h
h
CGm(1+CGm)F (s)
F (s)
Gm(1−Qe−τms)Gp(s)e−τs
Q(s)F (s)
� �
6
?
?
d
r u y
n
−
- - - - --
(a) Disturbance observer-based control scheme (b) equivalent structure for implementation
where
Gm(s) =k
s, C(s) =
1
kT, Q(s) =
(2λ + τm)s + 1
(λs + 1)2, F (s) =
1
λs + 1
andλ is a free design parameter.
Setpoint response: Gyr(s) = 1T s+1
e−τms
Disturbance response: Gyd(s) = ks
(1 − Q(s)e−τms
)e−τms
Measurement noise response: Gyn(s) = Q(s)e−τms
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 64/77
Robust stability region
−1−0.5
00.5
11.5
2−0.7
−0.5−0.3
−0.10.1
0.30.5
0.7
0
1
2
3
4
5
6
β
∆K/K∆τ/τ
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
τ∆/τm
∆k/k
0.20.2
0.5
0.5
0.5
0.5
1
11
1
11
1.51.5
1.5
1.5
1.5
1.5
1.5
2
2
2
2
2
2.5
2.5
3 3
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 65/77
Deadbeat responseTheorem The considered system rejects a step distur-bance att = T2 (T2 > T1 > 0) if Q(s) is chosenas
Q(s) =q0 + q1e
−T1s + q2e−T2s
λs + 1
with
q0 = eT2/λ(λ+τm+T1)−eT1/λ(λ+τm+T2)
T2−T1+T1eT2/λ−T2e
T1/λ
q1 = λ+τm+T2−eT2/λ(λ+τm)
T2−T1+T1eT2/λ−T2e
T1/λ
q2 = − λ+τm+T1−eT1/λ(λ+τm)
T2−T1+T1eT2/λ−T2e
T1/λ
whereλ > 0 is a free parameter.Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 66/77
Robustness indicatorPoint AJ =
∑2
i=0|qi|
λcan be interpreted asa robustness indicator:
The lower the point A, the better the robustness.
In order to obtain the largest robust region for givenT2 andλ, minimise the robust indicator:minT1
J = minT1
∑2i=0 |qi|
λ
whereJ can be re-written as
J =1
λ
(1 +
2(λ + τm)(eT2/λ − 1) − 2T2
T2 − T1 + T1eT2/λ − T2eT1/λ
)
Since2(λ + τm)(eT2/λ − 1) − 2T2 > 0 and
T2 − T1 + T1eT2/λ − T2eT1/λ > 0 for T2 >
T1 > 0 andλ > 0, J is always larger than1λ
.
DifferentiateJ with respect toT1 and let it be0,
then
−1 + eT2/λ − T2
λeT1/λ = 0
Solve it, we have
T1
T2= λ
T2ln eT2/λ−1
T2/λ
0 1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
T2/λ
T 1/T2
When T2/λ → 0, T1 → 0.5T2; when
T2/λ → ∞, T1 → T2. Thus,T1 is always
less thanT2, as expected.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 67/77
Robustness indicator (cont.)Denote
α =λ
τmandβ =
T2
τm
then the minimal cost is
Jo =1
ατm
1 +
2(1 + 1α
)(eβ/α − 1) − 2β/α
β/α + (eβ/α − 1)(
ln eβ/α−1β/α
− 1)
12
34
5 Λ�Τm �
12
34
5T2�Τm
0
50
100
150
ΤmJo
12
34Λ�Τ �
0
50
100
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 68/77
Simulation exampleConsider a process with
Gm(s) =1
s, τm = 5 sec,
assume that the worst multiplicative uncer-
tainty is∆(s) = 10.1s+1
e−0.5s − 1.
Control parameters:
T2 = 2τm = 10sec
λ = 0.5τm = 2.5sec
T1 = 6.5sec
q0 = 2.36, q1 = −1.75, q2 = 0.39
(a) Nominal case (b) The worst case
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 69/77
Practical experiencesSoftware design
Intel 8086 assembly language:> 100kB binary codeC language: > 10,000 linesDatabase/Javascript
Hardware design
Micro-computers:Intel 8051, Zilog Z80, Motorola ...DC, AC drives etcLift control systemsSystem design experience
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 70/77
New-ACE: www.newace.org.ukLeading a nation-wide collaborative network: New-ACE, which
is funded by a £88k EPSRC grant.
Partners:Imperial, Sheffield, LoughboroughandQueen’s
Belfast.
Advisory members: D.J.N. Limebeer (Imperial),
D.H. Owens (Sheffield), R.M. Goodall (Loughborough),
G. Irwin (Queen’s Belfast), Q.H. Wu (Liverpool).
Main activities and outcomes:
to organise six workshops in subject areas including
renewable energy and control in power electronics
to submit 6~12 joint proposals in the coming three
years.Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 71/77
Objectives of the New-ACEto provide a platform for the members toexchange ideas, experience and practise
to develop and strengthen long-term collaborationactivities, including joint applications andcollaborations with industry
to support potential future leaders in controlengineering and related areas
to develop and sustain a strong future for controlengineering in the UK
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 72/77
TeachingPhilosophy:
Teaching and research help each other.
Quality teaching provides a constant flow of ex-cellent students for research.The best student of 2007, whose FYP
was directed by me, has been attracted to study for a PhD degree under my supervision.
He won both the principal Faculty undergraduate award and the IET Prize.
Modules taught this year:
Power electronics and electromechanics
Energy conversion and power systems
Digital control
Discrete-time signals and systemsQ.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 73/77
FundingCurrent projects:
Royal Academy of Engineering, £41k
EPSRC: EP/H004351/1, £112k
EPSRC: EP/H004424/1, £68k
EPSRC: EP/E055877/1, £88k
EPSRC: one DTA studentship
EPSRC and Add2: DHPA Award, £90k
ESPRC and Nheolis: DHPA Award, £90k
Completed projects:
EPSRC: EP/C005953/1, £126kQ.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 74/77
Research teamOne part-time secretary
Currently 5 PhD students, one postdoctoral research fellow
and two Honorary Researchers
Another postdoc researcher and one PhD student to join
soon (funding already secured)
A former postdoctoral research fellow is still in active
collaboration.
Also closely working/worked with researchers from Brazil,
China, France, Italy, Israel, Netherlands, Singapore and
USA, in addition to those from the home department, the
Dept of Engineering and other UK universities and industry.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 75/77
Future research topics
Control Theory & Engineering
Renewable Energy: • Wind power • Solar power • Other energy sources
Power Electronics: • Grid-connected inverters • Inverter-dominated power systems • DC drives and AC drives • Applications in power systems etc
Enabling Control Theory: • Robust H∝ control • Time-delay systems • Grid monitoring, control and stability
Industrial collaboration to consolidate research
Theoretical research to deepen the depth of researchQ.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 76/77
VisionClosely working with colleagues, to develop the team
into an international key player in research and teach-
ing in control, power electronics and renewable en-
ergy, with long-term collaborations with industrial
partners and world-leading research groups.
Breadth of research: focusing on control theory,power electronics and renewable energy;developing activities in automotive electronicsand process control.
Depth of research: Looking for fundamental prob-lems; providing significant/simple solutions.
Q.-C. ZHONG: AN OVERVIEW OF ACTIVITIES IN CONTROL THEORY & ENGINEERING – p. 77/77