Modern Control Engineering

570 Chapter 8 / PID Controllers and Modified PID Controllers Kp Plant r(t) u(t) c(t) Figure 8–4 +– Closed-loop system with a pro ...

Section 8–2 / Ziegler–Nichols Rules for Tuning PID Controllers 571 Pcr 0 t c(t) Figure 8–5 Sustained oscillation with period ( i ...

572 Chapter 8 / PID Controllers and Modified PID Controllers Gc(s) PID controller 1 s(s+ 1)(s+ 5) R(s) C(s) + Figure 8–6 PID-co ...

Section 8–2 / Ziegler–Nichols Rules for Tuning PID Controllers 573 PID controller 1 s(s+ 1)(s+ 5) 6.3223 (s+ 1.4235)^2 s R(s) C( ...

574 Chapter 8 / PID Controllers and Modified PID Controllers Next, let us examine the unit-step response of the system. The clos ...

Section 8–2 / Ziegler–Nichols Rules for Tuning PID Controllers 575 Unit-Step Response Amplitude 0 0.6 1.2 0.8 0.4 0.2 1 Time (se ...

576 Chapter 8 / PID Controllers and Modified PID Controllers the root-locus analysis. Figure 8–11 shows the root-locus diagram f ...

Section 8–3 / Design of PID Controllers with Frequency-Response Approach 577 1 K s(s+ 1)(s+5) (s+ 0.65)^2 s jv j 8 j 6 j 4 j 2 ...

Since the static velocity error constant Kvis specified as 4 sec–1, we have Thus Next, we plot a Bode diagram of MATLAB Program ...

Section 8–3 / Design of PID Controllers with Frequency-Response Approach 579 MATLAB Program 8–3 num = [20 4]; den = [1 0.0000000 ...

Based on the Bode diagram of Figure 8–15, we choose the value of b.The term (bs+1)needs to give the phase margin of at least 50° ...

Section 8–3 / Design of PID Controllers with Frequency-Response Approach 581 Therefore, the designed system satisfies all the re ...

582 Chapter 8 / PID Controllers and Modified PID Controllers Output c( t) t (sec) Unit-Step Response of Compensated System 1.4 1 ...

Section 8–4 / Design of PID Controllers with Computational Optimization Approach 583 8–4 DESIGN OF PID CONTROLLERS WITH COMPUTAT ...

584 Chapter 8 / PID Controllers and Modified PID Controllers To sort out the solution sets in the order of the magnitude of the ...

Section 8–4 / Design of PID Controllers with Computational Optimization Approach 585 sortsolution = 2.0000 0.5000 0.9002 2.2000 ...

586 Chapter 8 / PID Controllers and Modified PID Controllers Amplitude Time (sec) Step Response 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 0. ...

Section 8–4 / Design of PID Controllers with Computational Optimization Approach 587 To plot the unit-step response curve of the ...

588 Chapter 8 / PID Controllers and Modified PID Controllers In this problem, we choose the step sizes to be reasonable, — say 0 ...

Section 8–4 / Design of PID Controllers with Computational Optimization Approach 589 3.0000 1.0000 1.1469 2.7700 5.0000 0.8000 1 ...