ENGR202 2022 Q B1 (ENGR5001)

ENGR202 2022 Q B1Past paperOld spec ENGR2022:125 marks30 min

ENGR202 Summer 2022 Q B1[VALID] official answers

An engineering system is represented by the following model:

$\frac{dx}{dt} + 2.5x = 0.7u \qquad (1)$

Formulas you may need

Generalised first order form: $\tau\dfrac{dx}{dt} + x = Ku(t)$ (learn this)
Laplace transform with zero initial conditions: $\dfrac{dx}{dt} \to sX(s)$ (learn this)
First order frequency response: $M = \dfrac{K}{\sqrt{1 + \omega^2\tau^2}}$ , $\phi = -\tan^{-1}(\omega\tau)$ ; corner (break) frequency $\omega = 1/\tau$ (learn this)
Decibels: $20\log_{10}M$ (learn this)
Four control objectives: stability, tracking, transient behaviour, disturbance rejection (learn this)

(a)
What is the order of this model? Convert the model into an appropriate generalised form and state the time constant and steady state gain of the model. Sketch and annotate a Bode diagram for this system. Graph paper is not required for this sketch.
time constant =s
steady state gain =
low-frequency magnitude =dB
corner frequency =rad/s
[6]
(b)
Briefly describe a graphical method of estimating both the time constant and steady state gain of a first order model from step response experimental data. Comment on potential limitations of this approach and suggest an alternative.
[5]
(c)
Develop the Transfer Function form of the model (1). State any assumptions made.
[2]
(d)
An engineer is designing a control system for a constant speed wind turbine. The output is the generator reaction torque. When the wind speed reaches a predetermined value, the wind turbine generates 'rated' power, which is associated with a known value of the generator reaction torque. For active pitch control systems, the pitch angle of the blades is adjusted in real time. The system should minimise load transients and smooth the power generated. State the four standard objectives of control and discuss what these could mean in the context of a control system for generator reaction torque.
[6]
(e)
A wind turbine system shows highly oscillatory dynamics when the pitch angle of the blades is adjusted in open loop. Briefly explain why PID control might be a suitable choice to meet the control objectives developed in part (d). Speculate on any potential limitations of PID control in this context.
[6]