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If the integral term K is zero, the corresponding controller is known as a proportional-derivative (or PD) controller. By setting K0 and equating coefficients, show that the two PD controllers above have equivalence to the mechanical systems to the mechanical systems shown in Figure 1 and from this make interpretations of the functions of the P and D terms of a PID controller. x(t) yCt) (a) Damper in the forward path xCt) yCt) M ㄧㄧㄒㄧ- m (b) Damper in the return path Figure 1 R(S) x(s) PID controller Hardware gain Plant (a) PID in Forward Path R(s)+ x(s) (b) PI in Forward Path, in the return path Figure 2: A mass whose position is controlled by a PID compensator If the integral term K is zero, the corresponding controller is known as a proportional-derivative (or PD) controller. By setting K0 and equating coefficients, show that the two PD controllers above have equivalence to the mechanical systems to the mechanical systems shown in Figure 1 and from this make interpretations of the functions of the P and D terms of a PID controller.
x(t) yCt) (a) Damper in the forward path xCt) yCt) M ㄧㄧㄒㄧ- m (b) Damper in the return path Figure 1
R(S) x(s) PID controller Hardware gain Plant (a) PID in Forward Path R(s)+ x(s) (b) PI in Forward Path, in the return path Figure 2: A mass whose position is controlled by a PID compensator
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