Reference no: EM131552204

a) A continuous time control system is described by Figure 1. C(s) is a linear controller transfer function Consider a plant with the following first order transfer function: G(s) = b/s+a

Figure 1: Block diagram of a continuous time control system

i) Prove that a proportional plus integral controller is sufficient to achieve zero steady state error for this system with a step input.

ii) If a=2 and b=1, calculate the proportional and integral gains of C(s) to make the closed loop damping ratio equal to 0.8 and natural frequency equal to 2 radis.

b) A continuous time control system is described by Figure 1. Consider a plant with the following second order transfer function:

G(s) = c/(s²+as+b)

C(s) represents a PID controller. Prove that the PID controller achieves zero steady state error for this system with a step input.

c) A continuous time control system is described by Figure 1. Design a PID controller by applying the Reaction Curve method. The process unit step response is shown in Figure 2.

Figure 2: The process unit step response