Figure 4 shows the block diagram of a laser printer with a proportional controller of gain...

 

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Figure 4 shows the block diagram of a laser printer with a proportional controller of gain K, and a system delay of e-ST. (a) For a non-delay condition, where T is zero: (i) Show that the gain Kp should be set to a value of 1 to achieve critical damping of the closed-loop system. (6 marks) (b) (ii) Calculate the phase margin of the system for Kp = 1 based on open-loop frequency response. Hence state whether the system is sufficiently stable at this gain setting. If the system has a delay, where T = 2 seconds: (i) Compute the new phase margin of the system for Kp = 1. (ii) Hence state the effect of dead time on system stability and suggest a way of improving the stability of the system. (2 marks) R(s) E(S) Proportional Controller Kp Device 1 s(s+2) Figure 4 System Delay e-st C(s) Figure 4 shows the block diagram of a laser printer with a proportional controller of gain K, and a system delay of e-ST. (a) For a non-delay condition, where T is zero: (i) Show that the gain Kp should be set to a value of 1 to achieve critical damping of the closed-loop system. (6 marks) (b) (ii) Calculate the phase margin of the system for Kp = 1 based on open-loop frequency response. Hence state whether the system is sufficiently stable at this gain setting. If the system has a delay, where T = 2 seconds: (i) Compute the new phase margin of the system for Kp = 1. (ii) Hence state the effect of dead time on system stability and suggest a way of improving the stability of the system. (2 marks) R(s) E(S) Proportional Controller Kp Device 1 s(s+2) Figure 4 System Delay e-st C(s)

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a i For a nondelay condition where T 0 the open loop transfer function ... View the full answer