數位控制理論簡介

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

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

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

Discretization of a Sinussoidal Signal

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!)

Anti-Aliasing Filter

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

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

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

Choice of the Sampling Period for Digital Control Systems

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

Normalized Frequency Responses of a Second-Order System 6 M(u)  5  4 3  2    1     1 2 3 u n

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

Operation of the Zero Order Hold +

Pulse Transfer Function for Continuous Systems with Zero Order Hold

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

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

Stability Domain for the Second-Order Discrete-Time System +1 -2 -1 1 2 -1

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

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

Digital Controller PLANT

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:

Digital PI Controller + + PLANT  + 

Canonical Structure of Digital Controllers + T - PLANT R