For a special type of DC motor, its transfer function relating the input voltage to the output speed can...

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For a special type of DC motor, its transfer function relating the input voltage to the output speed can be simplified as 1/(1+ st), where t = 0.5. At the initial state, the motor speed and position zero. (a) Explain the physical meaning of t = 0.5 and sketch the steady state motor speed in response to an input voltage v(t) = 5sin (5t). [4] (b) A proportional controller with a control gain of 10 is used to control the motor speed at 10 rad/sec. [1]. Sketch the block diagram of the control system, indicating the input, output, control unit and process of the system, and derive its transfer function. [4] [2]. Express and sketch the input and output signals as the functions of time. [4] [3]. Calculate the steady state error of the motor speed [3] [4]. Propose a control method to eliminate the steady state error and sketch its block diagram. [3]