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  3. 3 the block diagram of the proportionalintegral pi speed control...

Question: 3 the block diagram of the proportionalintegral pi speed control...

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3. The block diagram of the Proportional-Integral (PI) speed control system for maintaining the speed between cars is shown in Figure Q3. The output Y (s) is the relative speed of the two cars and the input R(s) is the desired relative speed between the two cars. The following design specifications are given i) Zero steady-state error for a step input ii) Steady-state error < 25% for a ramp input iii) Maximum overshoot < 5% (Mp-e(-rw1_ ) iv) Settling time <1.5 s (T, =-) wn (a) Identify the type of the system and determine the velocity error constant. (b) Determine the desired region for the poles of the closed-loop transfer function. (c) Determine the range of the controller gains Kp and K, for which the closed-loop system is stable (d) Determine the location of the third pole of the system in terms of Kp and K, such that design specification (iv) is satisfied. Ta (s) Controller Automobile System R(s) Y(s) Ge (s) (s + 2)(s + 8) Figure Q3

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