ME2142E Exam Solution Hints

ME2142E: Module Report December 2014 Question 1

The purpose of this question is to test the student on his/her basic understanding of transfer functions that the transient response of control systems. (a)

This part of the question tests on the student’s ability to derive the differential equations of motion of a simple spring-mass-damper mechanical system and, thereby, the transfer function of the system. Those students who did poorly on this part were those who had a weak foundation on the dynamics of simple mechanical systems.

(b)

This part of the question tests the student’s ability to identify a simple first -order response. This was covered in the lectures and also demonstrated in one of the two experiments that students had to go through. Most students were able to identify the response as that for a first-order system although some had difficulties determining the exact form of the transfer function with appropriate parameters.

(c)

This part of the question tests the student understanding of the transient response of a simple second-order system and the dynamic parameters governing such a response. Most students did quite well.

Question 2

The purpose of this question is to test the student on his/her basic understanding of feedback control system stability and how the parameters affecting this. (a)

This part of the question tests on the student’s understanding of how the characteristic equation and its roots affect system stability. Most students generally answered well although some did not provide sufficient details.

(b)

This part of the question tests the student’s ability to use Routh’s Stability Criterion to determine the stability of a given system. Students generally did well on this part.

(c)

This part of the question tests the student on his/her understanding of a system’s steadysteadystate characteristics and requires the derivation of a given system’s steady-state steady-state error for two common test inputs. This is a straightforward question, especially given that students are allow a page of personal notes/formulae students generally gave the correct answers.

Question 3

The purpose of this question is to test a student on his/her basic understanding of Frequenc y Response.

(a)

This part of the question tests tests on the student’s ability to sketch the Bode plots (both magnitude (or gain) versus frequency and phase versus frequency) for a given transfer function. Most students were able to sketch these plots. plots. However, there there were a few students who were unable to sketch these plots.

(b)

This part of the question tests the student’s ability to read off the gain and phase margins from the plots of part (a). Most students were able able to deduce the gain and phase margins.

(c)

This part of the question tests the student on the effect of increasing gain on the Bode  plots of part (a). Only the gain plot changes: It is shifted vertically by the gain amount in dB. The phase plot remains unchanged. Therefore, one can compute the new gain and  phase margins without re-plotting the plots of part (a). Most students understand that the  phase plot will remain unchanged. However, this does not mean the phase margin will remain the same as in part (a).

(d)

This part of the question tests the student on the output response of a system whose transfer function and its input sinusoidal are given. given. Most students were able able to calculate the gain and phase of the system at the frequency of the input and then re-constituting the output response with these values.

Question 4

The purpose of this question is to test a student’s understanding of the Nyquist Stability Criterion. (a)

This part of the question tests the student on the sketching of the Nyquist plot for a given transfer function.

(b)

This part of the question tests the student on the application of the Nyquist Stability Criterion. This requires requires the student student to calculate the negative negative real axis intercept. intercept. The student then has to determine the value of the gain such that the negative real axis intercept is greater than -1. Generally most students were able to do the above. However, there are a few who have left this part of the question unanswered.

(c)

This part of the question requires the student to calculate the imaginary axis intercept for a gain of K=10. Since imaginary axis intercepts are are complex conjugate pairs, the student student has to identify the appropriate of these conjugate pairs as the positive imaginary axis intercept. Most students were were able to do this.

(d)

This part of the question tests the student on the calculation of the gain margin when K=1. For this part of the question, the definition of gain margin requires the student student to compute the reciprocal of the negative real axis intercept. Most students were able to do this.