Modern Control Engineering
aa 250 Chapter 5 / Transient and Steady-State Response Analyses A–5–16. Consider the system subjected to the initial condition a ...
aa Example Problems and Solutions 251 Solution.A possible MATLAB program based on Equations (5–58) and (5–60) is given by MAT- L ...
aa 252 Chapter 5 / Transient and Steady-State Response Analyses For stability, we require that From the first and second conditi ...
aa Example Problems and Solutions 253 equation is given by Equation (5–67) is asymptotically stable. Note that exact values of d ...
aa 254 Chapter 5 / Transient and Steady-State Response Analyses The first term in the first column of the Routh array is 1. The ...
aa Example Problems and Solutions 255 For example, if n=4, then Thus it has been shown that the first column of the Routh array ...
aa 256 Chapter 5 / Transient and Steady-State Response Analyses where Similarly, subtracting from the fourth row a 0 /a 1 times ...
aa Example Problems and Solutions 257 From this analysis, we see that The Hurwitz conditions for asymptotic stability reduce to ...
aa 258 Chapter 5 / Transient and Steady-State Response Analyses with the following standard fourth-order characteristic equation ...
aa Example Problems and Solutions 259 A–5–23. The block diagram of Figure 5–67 shows a speed control system in which the output ...
aa 260 Chapter 5 / Transient and Steady-State Response Analyses A–5–24. In the system considered in Problem A–5–23, it is desire ...
aa Example Problems and Solutions 261 With this controller, the block diagram of Figure 5–69 in the absence of the reference inp ...
aa 262 Chapter 5 / Transient and Steady-State Response Analyses If the input is a unit ramp, then the steady-state error is Ther ...
aa Problems 263 Since the system is stable, converges to a constant value. Noting that we have Since we have For a unit-step inp ...
aa 264 Chapter 5 / Transient and Steady-State Response Analyses x m Impulsiveforce k d(t) Figure 5–72 Mechanical system. x 1 T t ...
aa Problems 265 + + R(s) 1 C(s) s 16 s+ 0.8 k R(s) 1 C(s) s K s+ 2 k + + Figure 5–75 Closed-loop system. Figure ...
aa 266 Chapter 5 / Transient and Steady-State Response Analyses B–5–13.Figure 5–77 shows three systems. System I is a po- sition ...
Problems 267 aa B–5–15.Using MATLAB, obtain the unit-step response curve for the unity-feedback control system whose open- loop ...
aa 268 Chapter 5 / Transient and Steady-State Response Analyses Kh K R(s) 20 C(s) (s+ 1) (s+ 4) 1 s + + Figure 5–81 Serv ...
6 269 Control Systems Analysis and Design by the Root-Locus Method 6–1 Introduction The basic characteristic of the transient re ...
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