1. 數位控制理論簡介

2. Digital Realization of an Analog Type Controller
CLOCK
ADC
COMPUTER
DAC + ZOH
PLANT + 
CONTROLLER

3. Digital Control System
CLOCK
COMPUTER
DAC + ZOH
PLANT
ADC + 
DISCRETIZED PLANT

4. Operation of the analog-to-digital converter (ADC), the digital-to-analog converter (DAC), and the zero order hold (ZOH).
ADC
ZOH
Sampling period

5. Discretization of a Sinussoidal Signal

6. Spectrum of a Sampled Signal
Case 1 :
Continuous-time
spectrum
Spectrum of the
sampled signal
Case 2 :
Continuous-time
spectrum
Overlapping (aliasing)
of the spectrum (distortions!)

7. Anti-Aliasing Filter

8. A Continuous System Showing Input and Output Signal
x(t) t
x(t)
Filter or model of plant
output t

9. The Input-Output of the Continuous System and its Discretized Version
DAC T i
x(t) t
output t

10. Comparison of the Output of the Continuous System and its Discretized Version

11. Choice of the Sampling Period for Digital Control Systems

12. Normalized Time Responses of a Second-Order System to a Step Input
c(t)
1.8
1.7
1.6
= 0.1
1.5
1.4
0.2
1.3
0.3
1.2
0.4
1.1
0.5
0.6
1.0
0.7
0.8
0.9
= 1.0
0.8
1.5
0.7
2.0
0.6
0.5
0.4
0.3
0.2
0.1 1 2 3 4 5 6 7 8 9 10 11 12 13
n t

13. Normalized Frequency Responses of a Second-Order System6
M(u)
 5
 4 3
 2


 1



 1 2 3
u n

14. Control System Using an Analog-to-Digital Converter Followed by a Zero Order Hold
DAC +
ZOH
PLANT
H(s)
ADC

15. Operation of the Zero Order Hold+

16. Pulse Transfer Function for Continuous Systems with Zero Order Hold

17. Pole-Zero Configuraturation of the Sampled System
 j z
- zero
- pole x 1 *
d zeros
 j
We can derive the transfer function of the corresponding sampled model (plant + zero-order-hold)

18. Step responses of the discrete-time system b1/(1+a1z-1) for different values of a1 with b1/(1+a1)=1.
1.00
-.2
0.90
-.6
0.80
-.7
0.70
0.60
a1 = -.8
0.50
Step Response
0.40
a1 = -.9
0.30
0.20
0.10
t /Ts
0.00
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
20.00

19. Stability Domain for the Second-Order Discrete-Time System+1 -1

20. Relation between the parameters of pulse and continuous-time transfer functions for the second-order system

21. Diagram of a PI Analog Controller
Analog PI  
PLANT  

22. Digital Controller
PLANT

23. The control law for an analog PI controller is given by:
For the discretization of the PI controller, p (the derivation operation) is approximated by 1 - q-1. One 6then obtains (t is now the normalized time):
and the equation of the PI controller becomes:

24. Digital PI Controller + +
PLANT  + 

25. Canonical Structure of Digital Controllers+ T -
PLANT R