Modern Control Engineering

590 Chapter 8 / PID Controllers and Modified PID Controllers 8–5 Modifications of PID Control Schemes Consider the basic PID con ...

Section 8–5 / Modifications of PID Control Schemes 591 Notice that in the absence of the disturbances and noises, the closed-loo ...

592 Chapter 8 / PID Controllers and Modified PID Controllers 1 Tis Gp(s) Y(s) N(s) R(s) B(s) B(s) U(s) D(s) Kp 1 Tds + +– + ...

Section 8–6 / Two-Degrees-of-Freedom Control 593 For this system, three closed-loop transfer functions Y(s)/R(s)=Gyr, Y(s)/D(s)= ...

594 Chapter 8 / PID Controllers and Modified PID Controllers Hence, we have In this case, ifGydis given, then Gynis fixed, but G ...

Section 8–7 / Zero-Placement Approach to Improve Response Characteristics 595 Hence, Clearly, ifGydis given, thenGynis fixed, bu ...

596 Chapter 8 / PID Controllers and Modified PID Controllers where A(s)=As+z 1 BAs+z 2 BpAs+zmB B(s)=sNAs+pN±1BAs+pN±2BpAs+pnB w ...

The response y(t)to a step disturbance input will have the general form shown in Figure 8–32. Note that Y(s)/R(s)andY(s)/D(s)are ...

598 Chapter 8 / PID Controllers and Modified PID Controllers Determination of Gc 2. Now that the coefficients of the transfer fu ...

Section 8–7 / Zero-Placement Approach to Improve Response Characteristics 599 we have (8–6) The two controllers Gc1andGc2can be ...

600 Chapter 8 / PID Controllers and Modified PID Controllers Second, note that Notice that the characteristic equation for Y(s)/ ...

Section 8–7 / Zero-Placement Approach to Improve Response Characteristics 601 and the remaining closed-loop pole is real and is ...

602 Chapter 8 / PID Controllers and Modified PID Controllers Since the denominators of Y(s)/D(s)andY(s)/R(s)are the same, the de ...

Section 8–7 / Zero-Placement Approach to Improve Response Characteristics 603 As noted above, 23 sets of variables a, b,andcsati ...

604 Chapter 8 / PID Controllers and Modified PID Controllers By equating the coefficients of equal powers ofson both sides of th ...

Section 8–7 / Zero-Placement Approach to Improve Response Characteristics 605 Hence Then can be written as The closed-loop trans ...

606 Chapter 8 / PID Controllers and Modified PID Controllers our problem becomes that of designing to satisfy the requirements o ...

Section 8–7 / Zero-Placement Approach to Improve Response Characteristics 607 tor of the closed-loop transfer function Y(s)/R(s) ...

608 Chapter 8 / PID Controllers and Modified PID Controllers The response to the unit-ramp reference input and that to the unit- ...

Section 8–7 / Zero-Placement Approach to Improve Response Characteristics 609 Assume also that the controller is of PID type. Th ...