Old spec 4.3 exercise (ENGR5001) - Revisica

Old spec 4.3 exerciseExercise sheetCurrent specThird6 min

ENGR202 (old spec) Control 4.3 Control Objectives, exercise

Develop the Closed Loop Transfer Function for the DC motor speed control system in the figure, where $D$ is the desired motor speed (volts), $C(s)$ the controller, $U$ the input signal (volts), $H(s)$ the motor, $X$ the actual motor speed (volts) and $F(s)$ the feedback elements. Either solve using algebra or (saves time) use the rules of block diagram analysis. What condition gives unity steady state gain, and what is the characteristic equation?

DC motor speed control loop with controller C(s), motor H(s) and feedback elements F(s).

Formulas you may need

Series rule: $G_1 G_2$ ; negative feedback rule: $\dfrac{G_1}{1 + G_1 G_2}$ (learn this)
Steady state gain: set $s = 0$ ; characteristic equation: denominator $= 0$ (learn this)

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