digital control

1. CHAPTER 2 ANALYSIS OF DOMAIN-Z

14. z TRANSFORMS OF ELEMENTARY FUNCTIONS

74. Computational Method –MATLAB (ctnd) % Finding inverse z transform % ***** Finding the inverse z transform of C(z) is the same as % finding the response of the system Y(z)/X(z) = G(z) to the % Kronecker delta input ***** % ***** Enter the numerator and denominator of C(z) ***** num = [0 0.4673 -0.3393]; den = [1 -1.5327 0.6607]; % ***** Enter the Kronecker delta input x and filter command % y = filter(num,den,x) ***** x=[1 zeros(1,40)]; y = filter(num,den,x) MATLAB Program 2-1

78. % Response to Kronecker delta input ------------------- num = [0 0.4673 -0.3393]; den = [1 -1.5327 0.6607]; x = [1 zeros(1,40)]; k = 0:40; y = filter(num,den,x); plot(k,y,’o’) v=[0 40 -1 1]; axis(v); grid title (‘Response to Kronecker Delta Input’) xlabel(‘k’) ylabel(‘y(k)’) MATLAB Program 2-2

79. Figure 2- 12 Response of the system defined by Equation (2. 31) to the Kronecker delta input.

98. z TRANSFORM METHOD FOR SOLVING DIFFERENCE EQUATIONS (ctnd) Table 2.3 z transform of x ( k+m ) and x ( k-m )

107. RECONSTRUCTING ORIGINAL SIGNALS FROM SAMPLED SIGNALS (ctnd) Figure 2- 13 A frequency spectrum.

113. Figure 2- 14 Plots of the frequency spectra |X*(jω))| versus ω for two values of sampling frequency ω s : (a) ω s > 2ω 1 ; (b) ω s < 2ω 1

119. Figure 2- 16 Frequency spectra of the signals before and after ideal filtering. Ideal Low-Pass Filter (ctnd). Figure 2-16 shows the frequency spectra of the signals before and after ideal filtering.

124. Figure 2- 17 Impulse response g I ( t ) of ideal filter.

128. Figure 2.18 (a) Frequency-response curves for the zero-order hold; (b) equivalent Bode diagram when T = 1 sec.

133. Figure 2- 20 Diagram showing the regions where folding error occurs

136. Figure 2- 21 Frequency spectra of an impulse-sampled signal x*(t). Aliasing (ctnd).

147. MAPPING BETWEEN THE s PLANE AND THE z PLANE (ctnd) Left plane Right plane Unit circle Figure : Mapping s plane  z plane

163. STABILITY ANALYSIS OF CLOSED-LOOP SYSTEMS IN THE z PLANE

169. Figure 2- 34 Closed-loop control system of Example 4-2.

174. Table 2. 4 General Form Of The Jury Stability Table

181. Table 2. 5 Jury Stability Table For The Fourth-Order System

185. Table 2. 6 JURY STABILITY TABLE FOR THE SYSTEM OF EXAMPLE 4-4

187. THANK YOU END OF CHAPTER 2