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Spring 2021
數位控制系統Digital Control Systems
DCS-21
A Design Example
Feng-Li Lian
NTU-EE
Feb – Jun, 2021
DCS21-DesignExample-2
Feng-Li Lian © 2021Problem, Model, Analysis, and Design
IEEE CSS
Publications Content Digest
March 2019
Min Yu , Carlos Arana, Simos A. Evangelou, and Daniele Dini
Quarter-Car Experimental Study for Series Active Variable Geometry Suspension
IEEE T. on Control Systems Technology, 27(2):743-759, Mar. 2019
DCS21-DesignExample-3
Feng-Li Lian © 2021Problem, Model, Analysis, and Design
Discrete-time composite nonlinear feedback control
with an application in design of a hard disk drive servo system
• V. Venkataramanan;Kemao Peng;B.M. Chen;T.H. Lee
• IEEE Transactions on Control Systems Technology
• Year: 2003 | Volume: 11, Issue: 1 | Journal Article | Publisher: IEEE
DCS21-DesignExample-4
Feng-Li Lian © 2021Problem, Model, Analysis, and Design
Observer-based discrete-time sliding mode throttle control
for drive-by-wire operation of a racing motorcycle engine
• A. Beghi;L. Nardo;M. Stevanato
• IEEE Transactions on Control Systems Technology
• Year: 2006 | Volume: 14, Issue: 4 | Journal Article | Publisher: IEEE
DCS21-DesignExample-5
Feng-Li Lian © 2021Problem, Model, Analysis, and Design
A Flexible Robot Arm:
CT Input-Output Model:
CT State-Space Model:
DCS21-DesignExample-6
Feng-Li Lian © 2021Problem, Model, Analysis, and Design
Stability:
Plant Poles & Zeros:
Plant Eigenvalues:
Characteristics:
Root Locus & Bode Plot
Impulse Response & Step Response:
DCS21-DesignExample-7
Feng-Li Lian © 2021Problem, Model, Analysis, and Design
Output (y)Input (u)
Plant (P)
Ref (r)
Signals &
Systems
DCS21-DesignExample-8
Feng-Li Lian © 2021Problem, Model, Analysis, and Design
Design Specifications:
Sampling Time:
DT Models:
Desired Poles & Zeros:
Desired Eigenvalues:
DCS21-DesignExample-9
Feng-Li Lian © 2021Problem, Model, Analysis, and Design
Output (y)Input (u)
Plant (P)
Controller
Ref (r)
1. Model
2. Response
3. Analysis
4. Feedback
5. Control
Signals &
Systems
Control
Systems
DCS21-DesignExample-10
Feng-Li Lian © 2021Problem, Model, Analysis, and Design
Block Diagram of a Typical Control System:
GCr
P
- 1
e yxu
DCS21-DesignExample-11
Feng-Li Lian © 2021Issues: Sampling Times
G(s)
u(t) y(t)
C(s)
e(t)r(t)
G(z)
u[k] y[k]
C(z)
e[k]r[k]
DCS21-DesignExample-12
Feng-Li Lian © 2021Issues: Sampling Times
G(s)
u(t) y(t)
C(s)
e(t)r(t)
G(z)
u[k] y[k]
C(z)
e[k]r[k]
DCS21-DesignExample-13
Feng-Li Lian © 2021Issues: Analog Control and Digital Control
G(s)
u(t) y(t)
C(s)
e(t)r(t)
G(z)
u[k] y[k]
C(z)
e[k]r[k]
G(s) C(s)
G(z) C(z)
G(s)
u(t) y(t)
C(z)
e(t)r(t)
G(s)
u(t) y(t)
C(z)
e(t)r(t)
D/AA/D
G(s) C(z) ???
G(s) C(s)
DCS21-DesignExample-14
Feng-Li Lian © 2021Simulation Study: Root Locus
den = [1 -2 1];
num = [0 0.5 0.5];
sysC = tf( num, den ) den = [1 -2 1];
num = [0 0.5 0.5];
sysD = tf( num, den, 1 )
den = [1 -2 1];
num = [0 1 -0.25];
sysD = tf( num, den, 1 )
den = [1 -2 1];
num = [0 2 -1];
sysD = tf( num, den, 1 )
DCS21-DesignExample-15
Feng-Li Lian © 2021Simulation Study: Root Locus
Root Locus:
DCS21-DesignExample-16
Feng-Li Lian © 2021Simulation Study: Root Locus vs Nyquist Plot
den = [1 -1.5 0.5];
num = [ 0.25*K ];
sysD = tf( num, den, h )
K = 1
K = 2
K = 4
DCS21-DesignExample-17
Feng-Li Lian © 2021Simulation Study: Root Locus vs Bode Plot vs Nyquist Plot
den = [1 1.4 1];
num = [ 1 ];
sysC = tf( num, den )
sysD = c2d( sysC, h )
CT
DT, h = 4
DT, h = 1
DT, h = 0.4
DT, h = 0.2
DT, h = 0.1
DT, h = 0.01
sysD =
1.042 z + 0.07881
-------------------------
z^2 + 0.1167 z + 0.003698
Sample time: 4 seconds
0.3059 z + 0.1902
-----------------------
z^2 - 0.7505 z + 0.2466
Sample time: 1 seconds
0.06609 z + 0.05481
---------------------
z^2 - 1.45 z + 0.5712
Sample time: 0.4 seconds
0.0182 z + 0.01657
----------------------
z^2 - 1.721 z + 0.7558
Sample time: 0.2 seconds
0.004771 z + 0.004553
---------------------
z^2 - 1.86 z + 0.8694
Sample time: 0.1 seconds
4.977e-05 z + 4.954e-05
-----------------------
z^2 - 1.986 z + 0.9861
Sample time: 0.01 seconds
sysC =
1
---------------
s^2 + 1.4 s + 1
DCS21-DesignExample-18
Feng-Li Lian © 2021Simulation Study: Root Locus vs Bode Plot vs Nyquist Plot
rlocus(sysC)
rlocus(sysD)
bode( sysC )
bode( sysD )
nyquist( sysC )
nyquist( sysD )
CT
DT, h = 4
DT, h = 1
DT, h = 0.4
DT, h = 0.2
DT, h = 0.1
DT, h = 0.01
den = [1 1.4 1];
num = [ 1 ];
sysC = tf( num, den )
sysD = c2d( sysC, h )
DCS21-DesignExample-19
Feng-Li Lian © 2021Simulation Study: Step Response
Step Reponses of Different Gains:
DCS21-DesignExample-20
Feng-Li Lian © 2021Simulation Study: Step Response
Hidden Oscillation of Different Sampling Periods:
DCS21-DesignExample-21
Feng-Li Lian © 2021
The Research Procedure in Control Science
Physical
Process
Math
Model
System
Analysis
Control
Design
Differential eqn
Laplace transform
Transfer function
State space form
Root locus
Bode diagram
Nyquist plot
Stability
Robustness
Sensitivity
Controllability
Observability
Estimator
Identification
Regulation
Tracking
PID
Pole placement
Optimal Control
LQR/LQG
Adaptive control
Robust control
Decentralized
(or Multi-person)
Control
Difference eqn
z transform
Transfer function
State space form
Plant
Sensor
Actuator
Computer
Communication
Noise
Disturbance
Differential eqn
Laplace transform
The Design Philosophy of Control Science
