Coursework - C1 [40 marks]

Coursework - C1 [40 marks]

Question 1.1 (10 marks)

To investigate the effect of the P controller on the response of the conveyor control system, perform the tests described below.

P Controller

In MATLAB/Simulink, having constructed the system block diagram, determine the step response of the system for gains = 250, and 500 . Record the percentage overshoot and rise times for each response, and take a screenshot of results in the space provided below. (The zoom in/out and scale functions can be used in the scope window for facilitating the observation of results).

Screenshot of results:

For P Controller:

= 250 Overshoot = Rise time =

= 500 Overshoot = Rise time =

[7 marks]

What effect does the proportional gain have on the speed of response and the degree of oscillation?

[3 marks]

Question 1.2 (10 marks)

Motor Currents

In most servo systems, it is desirable to have as fast a response as possible. However, increasing the speed of response has repercussions in terms of the current consumed by the motor.

In practice, the amplifier will limit the maximum current applied to the motor (a maximum current of about 2 A in this case). This avoids damaging the motor by overheating the windings. However, in limiting the current, the response of the system is not as good for large gains or steps. Consequently, the control system designer must choose a proportional gain that generates a fast-enough response without causing excessive motor currents.

In MATLAB/Simulink, attach a second Scope to the output of the amplifier gain block.

For the same gain values = 250 and 500 run the simulation and determine the maximum current being fed to the motor. Record the values below.

For gain values = 500 , apply step inputs of different sizes (0.04 m and 0.08 m). Record the maximum current in each case.

Step input 0.02 m:

= 250 Maximum motor current =

= 500 Maximum motor current =

Step input 0.04 m:

= 500 Maximum motor current =

Step input 0.08 m:

= 500 Maximum motor current =

[4 marks]

What effect does increasing have on the motor current, and what form does the relationship between gain and motor current take?

[3 marks]

What effect does increasing the step size have on the motor current, and what form does the relationship between step size and motor current take?

[3 marks]

Question 1.3 (20 marks)

PI controller

In practice, disturbances will exist in a servo system and this will affect the performance of the system. A proportional-integral (PI) controller can be used to ensure that the actual table position is precisely controlled at the desired value.

In MATLAB/Simulink, create a constant voltage disturbance by dragging a constant block and a sum element from the commonly used blocks tree.

Delete the link connected between the output of the PID controller and the input of the amplifier gain ().

Connect the output of the PID controller and the constant block to the added sum element, then connect the output of the added sum element to the amplifier gain.

For gain value = 250 , with the constant block, set the magnitude of the voltage disturbance by setting the value of the constant block to 0.5 V, 1 V, then apply the step input of 0.02 m. Answer the question in the space provided below.

For gain value = 250 , 0.5 V disturbance, with the PID controller, set the integral gain value (KI) to 50, 200, and 1000, then apply step input of 0.02 m. Answer the questions in the space provided below.

In step 4, estimate the steady-state errors between the actual and desired table positions with different disturbances. What effect does increasing the magnitude of disturbances have on the steady-state errors of table positions?

[4 marks]

In step 5, by observing the result, what is the advantage of enabling the integral gain?

[4 marks]

In step 5, what effect does increasing the magnitude of integral gain have on the system's response?

[4 marks]

Derive the transfer function Y(s)/R(s) of the block diagram in the figure below, and sketch the time domain response with Kp=250, KI= 50.

[8 marks]