Modern Control Engineering
aa 170 Chapter 5 / Transient and Steady-State Response Analyses c(t) 0.5 1 0 Allowable tolerance Mp td t 0.05 or 0.02 tr tp ts F ...
aa Section 5–3 / Second-Order Systems 171 jv jvd vn s b zvn s vn 1 – z^2 Figure 5–9 0 Definition of the angleb. Note that not ...
aa 172 Chapter 5 / Transient and Steady-State Response Analyses Peak timetp: Referring to Equation (5–12), we may obtain the pea ...
aa Section 5–3 / Second-Order Systems 173 1 c(t) 1 +^1 1 – z^2 1 +e zvnt 1 – z^2 T=^1 zvn 1 –e zvnt 1 – z^2 0 1 –^1 1 – z^2 ...
aa 174 Chapter 5 / Transient and Steady-State Response Analyses z % 100 90 80 70 60 50 40 30 20 10 0 0.5 1.0 1.5 Mp Mp: Maximum ...
aa Section 5–3 / Second-Order Systems 175 It is important to note that the equations for obtaining the rise time, peak time, max ...
aa 176 Chapter 5 / Transient and Steady-State Response Analyses R(s) C(s) (a) 1 s K Js+B Kh R(s) C(s) (b) K s(Js+B+KKh) + + ...
aa Section 5–3 / Second-Order Systems 177 This value must be 0.2. Thus, or which yields The peak time tpis specified as 1 sec; t ...
aa 178 Chapter 5 / Transient and Steady-State Response Analyses 1.0 0.8 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1.0 0 24681012 vnt c( ...
aa Section 5–4 / Higher-Order Systems 179 c(t) 0 Unit-impulse response 1 +Mp tp t Figure 5–15 Unit-impulse response curve of the ...
aa 180 Chapter 5 / Transient and Steady-State Response Analyses + R(s) C(s) G(s) Figure 5–16 H(s) Control system. Transient ...
aa Section 5–4 / Higher-Order Systems 181 C(s). If there is a closed-loop zero close to a closed-loop pole, then the residue at ...
aa 182 Chapter 5 / Transient and Steady-State Response Analyses Dominant Closed-Loop Poles. The relative dominance of closed-loo ...
aa Section 5–5 / Transient-Response Analysis with MATLAB 183 0 s s jv In this region z 0.4 s t^4 s^ Figure 5–17 Region in the co ...
aa 184 Chapter 5 / Transient and Steady-State Response Analyses In this expression a zero is padded. Note that if zeros are padd ...
aa Section 5–5 / Transient-Response Analysis with MATLAB 185 EXAMPLE 5–3 Consider the following system: Obtain the unit-step res ...
aa 186 Chapter 5 / Transient and Steady-State Response Analyses To: Y2 1.5 2 1 0.5 0 04812 Time (sec) 1.5 2 1 0.5 0 04812 To: Y1 ...
aa Section 5–5 / Transient-Response Analysis with MATLAB 187 MATLAB Program 5–2 % ***** In this program we plot step-response cu ...
aa 188 Chapter 5 / Transient and Steady-State Response Analyses Step-Response Plots: Input =u2 (u 1 = 0) Time (sec) Amplitude 01 ...
aa Section 5–5 / Transient-Response Analysis with MATLAB 189 MATLAB Program 5–3 wn = 5; damping_ratio = 0.4; [num0,den] = ord2(w ...
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