Modern Control Engineering

630 Chapter 8 / PID Controllers and Modified PID Controllers A–8–10. In some cases it is desirable to provide an input filter as ...

which is the same as Equation (8–15). Hence, we have shown that the systems shown in Figures 8–61(a) and (b) are equivalent. It ...

632 Chapter 8 / PID Controllers and Modified PID Controllers the requirement can be satisfied ifH(s)is chosen to be H(s)=ks beca ...

Example Problems and Solutions 633 MATLAB Program 8–15 t = 0:0.01:5; for K = 50:-1:2; for a = 2:-0.05:0.05; num = [K 2Ka K*a^2]; ...

634 Chapter 8 / PID Controllers and Modified PID Controllers Output t (sec) Unit-Step Response 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 0.5 ...

Example Problems and Solutions 635 32.0000 0.2000 1.0969 2.6400 31.0000 0.2000 1.0890 2.6900 30.0000 0.2000 1.0809 2.7300 29.000 ...

636 Chapter 8 / PID Controllers and Modified PID Controllers From the sorttable, it seems that K=29, a=0.25(max overshoot=9.52%, ...

Example Problems and Solutions 637 Gc 1 (s) Gp(s) Gc 2 (s) Y(s) N(s) U(s) D(s) R(s) B(s) +– ++ ++ ++ Figure 8–66 Two-degrees-of- ...

638 Chapter 8 / PID Controllers and Modified PID Controllers Since we obtain The controller thus becomes (8–17) Then, the closed ...

Example Problems and Solutions 639 (a) t (sec) Response to Unit-Step Reference Input 0.6 0.8 1 1.2 1.4 0.4 0.2 0 0 0.5 1 1.5 2 2 ...

overshoot in the unit-step response is approximately 25%and the settling time is approximately 1.2 sec. The steady-state errors ...

and from Equation (8–17) we obtain (8–19) Equations (8–17) and (8–19) give the transfer functions of the controllers re- spectiv ...

642 Chapter 8 / PID Controllers and Modified PID Controllers B–8–2.Consider the system shown in Figure 8–71. Assume that disturb ...

Problems 643 Obtain the response of the I-PD-controlled system to the unit-step reference input with MATLAB. Compare the unit-st ...

644 Chapter 8 / PID Controllers and Modified PID Controllers B–8–7.Consider the system shown in Figure 8–75. Obtain the closed-l ...

D(s) R(s) Y(s) N(s) Gc 2 +– Gc 1 +–– Gc 3 G 1 G 2 + +–– + + + Problems 645 B–8–9.Show that the control systems shown in Fig- u ...

646 Chapter 8 / PID Controllers and Modified PID Controllers B–8–11.Consider the control system shown in Figure 8–79. Assume tha ...

Problems 647 B–8–14.Consider the system shown in Figure 8–81. The plant is given by Determine the controllers and such that, for ...

9 648 Control Systems Analysis in State Space 9–1 INTRODUCTION* A modern complex system may have many inputs and many outputs, a ...

Section 9–2 / State-Space Representations of Transfer-Function Systems 649 systems, controllability, and observability are prese ...