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[answered] ME 375 - Spring 2013 Homework No. 10 Due: Wednesday, April

The third numerical makes no snese can you please help me provide the solution

ME 375 ? Spring 2013 Homework No. 10 Due: Wednesday, April 17th

Problem No. 1 (30%)

Consider the automobile speed control system depicted in the following figure, where R is the

desired speed, Y is the actual speed of the car, and W is the road grade (in percent) which

represents the slope of the road. The constant K is the control input (the throttle angle), H y is

the gain of the speedometer, and H r is input scaling factor. A

B

and

represent the vehicle

s+a

s+a speed dynamics as a first order system.

(a) Find the transfer functions from W(s) to Y(s) and from R(s) to Y(s).

r0

. Assume that the road

s

is level, so w(t ) = 0 . What are the conditions on the gains K , H r and H y to guarantee that (b) Assume the desired speed is a constant reference r0 , so that R( s ) = lim y (t ) = r0 . Include both the open-loop (assuming H y = 0 ) and feedback ( H y ? 0 ) cases

t ?? in your discussion.

w0

is present in addition to the reference

s

input. Using the same gains as in part (b), what is the steady-state speed of the car lim y (t ) ? (c) Assume that a constant grade disturbance W ( s ) = t ?? Include both the open-loop and feedback cases. Problem No. 2 (40%)

The engine, body and tires of a racing vehicle affect the acceleration and speed attainable. The

speed control of the racing car is represented by the model shown in the figure below. (a) For K = 1, determine the steady-state error and percent overshoot of the car to a step

command in speed.

(b) The system specifications for a unit step input is as follows:

i. settling time ? 1.5 sec.

ii. overshoot ? 25%

Show the permissible area of the poles of the closed loop system.

(c) For K = 2, determine whether the closed loop system meets the performance

specifications given in part B, and a steady-state error less than 10%. (Show the closed

loop system poles in the sketch of part B). Problem No. 3 (30%) Given the above closed loop block diagram:

1

1

Let G ( s ) =

and C( s ) = K P + K I

s( Js + B )

s

(a) Show that the above system will have zero steady state error for step reference input (when

D(s)=0) as well as for step disturbance input (when R(s)=0).

(b) Let J = B = KI = 1 and KP = 0, what about the stability of the closed loop system?

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