ME or MEng Master of Engineering Control Systems and Dynamics 1 — Questions and Answers
Question 1: How is the transfer function of a linear time-invariant system formally defined?
- The ratio of output to input in the time domain
- The ratio of the Laplace transform of output to input with zero initial conditions (Correct answer)
- The ratio of input to output in the frequency domain
- The convolution of the input and output signals
Correct answer: The ratio of the Laplace transform of output to input with zero initial conditions
The transfer function is the Laplace transform of the output divided by the Laplace transform of the input, assuming all initial conditions are zero.
Question 2: In a closed-loop control system, what is the primary purpose of feedback?
- To increase the system's open-loop gain
- To compare the output with the desired input and reduce error (Correct answer)
- To eliminate the need for a controller
- To increase system bandwidth without affecting stability
Correct answer: To compare the output with the desired input and reduce error
Feedback compares the actual output with the reference input to generate an error signal, which the controller uses to drive the error toward zero.
Question 3: A PID controller combines which three control actions?
- Proportional, Integral, and Derivative (Correct answer)
- Position, Inertia, and Damping
- Phase, Impedance, and Damping
- Proportional, Impedance, and Differential
Correct answer: Proportional, Integral, and Derivative
PID stands for Proportional, Integral, and Derivative — actions that reduce error magnitude, eliminate steady-state offset, and improve transient response, respectively.
Question 4: What is the steady-state error to a step input for a Type 1 control system?
- Zero (Correct answer)
- A constant non-zero value
- Infinite
- Dependent on system gain
Correct answer: Zero
A Type 1 system contains one open-loop integrator, which drives the steady-state error to zero for a step (position) input.
Question 5: In the s-domain, what is the transfer function of an ideal differentiator?
- 1/s
- s (Correct answer)
- 1/s²
- s²
Correct answer: s
Differentiation in the time domain corresponds to multiplication by s in the Laplace domain, so the transfer function of a differentiator is simply s.
Question 6: What information does a Bode plot provide about a control system?
- Root locations as open-loop gain varies
- Magnitude and phase of the frequency response versus frequency (Correct answer)
- Time-domain step response of the closed-loop system
- Nyquist contour mapping in the complex plane
Correct answer: Magnitude and phase of the frequency response versus frequency
A Bode plot consists of two graphs: the magnitude (in dB) and the phase (in degrees) of the open-loop frequency response plotted against logarithmic frequency.
Question 7: The characteristic equation of a control system is obtained by setting which expression to zero?
- The numerator of the open-loop transfer function
- The numerator of the closed-loop transfer function
- The denominator of the closed-loop transfer function (Correct answer)
- The gain of the proportional controller
Correct answer: The denominator of the closed-loop transfer function
The characteristic equation is found by setting the denominator of the closed-loop transfer function to zero; its roots (poles) determine stability and transient behavior.
ME or MEng Master of Engineering Control Systems and Dynamics 1
How is the transfer function of a linear time-invariant system formally defined?