AMME1705 · Introduction to Electromechanical Systems
Control (PID) & Exam Review
This closing chapter of the University of Sydney AMME1705 Introduction to Electromechanical Systems guide turns feedback control into the small set of equations the unit examines. It builds the error signal e(t) = y(t) − y_ref(t) and the PID control law u = Kp·e + Ki·∫e dt + Kd·de/dt, reads the three terms as present, past and future error, and shows how the gains — above all the proportional gain Kp — set the speed of response and the rise time.
It closes with an exam-review section: the sign-convention and unit traps that lose marks, and how to pace the 33% final. The electromechanical control ideas here also tie the course together, since the derivative term is the same rate-of-change idea as a capacitor's I = C·dV/dt.
What this chapter covers
- 01Closing the loop: measure the output, compare to target, act on the difference
- 02The error signal e(t) = y(t) − y_ref(t), and this unit's sign convention
- 03The PID law u = Kp·e + Ki·∫e dt + Kd·de/dt, stated with units
- 04Reading the three terms as present (P), accumulated past (I) and rate-of-change (D) error
- 05Why Kp, Ki and Kd carry different units, and unit-checking each term to the control signal
- 06The gain effect on rise time: a larger Kp gives a faster response (shorter rise time)
- 07Computing the control signal u at an instant from the gains and the error
- 08Exam traps: the sign convention, mismatched gain units, and direction words
- 09Exam-day pacing at about 1.5 minutes per mark, and answering to the stated precision
Worked example: the PID control signal at one instant
- +1Error. Using this unit's convention e = y − y_ref = 1970 − 2000 = −30 rpm (negative because the measured speed is below the setpoint).
- +1Proportional term. P = Kp·e = 0.04 V/rpm × (−30 rpm) = −1.2 V. Units: (V/rpm)(rpm) = V.
- +1Derivative term. D = Kd·(de/dt) = 0.005 V·s/rpm × 80 rpm/s = +0.4 V. Units: (V·s/rpm)(rpm/s) = V.
- +1Integral term. I = Ki·∫e dt = 0.08 V/(rpm·s) × (−25 rpm·s) = −2.0 V. Units: [V/(rpm·s)](rpm·s) = V.
- +1Sum. u = P + I + D = −1.2 + (−2.0) + 0.4 = −2.8 V — every term resolved to volts, so the sum is a valid control signal.
Key terms
- PID controller
- A feedback controller that forms its output from three terms: u = Kp·e + Ki·∫e dt + Kd·de/dt. The letters stand for proportional, integral and derivative — three views of the same error, each scaled by its own gain and added into a single control signal u.
- Error signal e(t)
- The gap the controller acts on. This unit defines it as the measured output minus the reference, e(t) = y(t) − y_ref(t), in the same units as the quantity controlled (rpm, mm, °C, V). e = 0 means the output is exactly on target; some textbooks use the opposite convention y_ref − y, which flips the sign of every term.
- Proportional gain Kp
- Scales the present error: the proportional term is Kp·e(t). Its SI-consistent units are [control unit] per [error unit] (for example V per rpm). A larger Kp turns a given error into a bigger corrective push, giving a faster response.
- Integral gain Ki
- Scales the accumulated past error: the integral term is Ki·∫e dt. Its units are [control unit] per ([error unit]·s). Because it keeps accumulating while any error remains, it works on the error that persists over time rather than the instant value.
- Derivative gain Kd
- Scales the rate of change of the error: the derivative term is Kd·de/dt. Its units are [control unit]·s per [error unit]. It responds to how fast the error is moving — a look-ahead based on the rate of change rather than the present size.
- Rise time
- The time the output takes to climb from its start toward the setpoint. In this unit, raising the proportional gain shortens the rise time (a faster response) and lowering it — for example from 1.0 to 0.5 — lengthens the rise time (a slower response).
- Closed-loop (feedback) control
- Control that drives the actuator from the measured difference between the output and the target, rather than a fixed setting. Unlike open-loop control, which drifts when the load or temperature changes, a closed loop measures y, forms the error and corrects it.
Control (PID) & Exam Review FAQ
What do the three PID terms each respond to?
Read them as present, past and future error. The proportional term Kp·e reacts to the error right now — the bigger the current gap, the harder it pushes. The integral term Ki·∫e dt reacts to the accumulated past error, its running total growing while any error lingers. The derivative term Kd·de/dt reacts to the rate of change of the error, a look-ahead at where it is heading. All three are scaled and added into one control signal u = Kp·e + Ki·∫e dt + Kd·de/dt.
What happens to the response if I increase the proportional gain Kp?
A larger Kp turns a given error into a larger corrective push, so the output moves toward the setpoint faster — the rise time gets shorter. The unit's own example runs the other way: dropping Kp from 1.0 to 0.5 weakens the push, so the response is slower and the rise time increases. When you write this in the exam, make sure the direction words match: higher Kp means shorter rise time, lower Kp means longer.
Can AI help me with PID control in AMME1705?
Yes, as a study aid. AskSia's Sia tutor can explain the error signal and the three PID terms step by step, walk you through why a larger proportional gain shortens the rise time, and check your reasoning on a practice control problem so you understand each move — including unit-checking Kp, Ki and Kd. It is built to help you learn the method and build confidence, not to sit your exam or hand you final answers, and it never promises a particular grade — the working, and the marks, are yours.
Studying with AI? Sia — free AI electrical engineering tutor works through AMME1705 step by step.
Exam move
Make the error your reflex on every control question: write e = y − y_ref first, then handle each term. Compute the proportional (Kp·e), integral (Ki·∫e dt) and derivative (Kd·de/dt) parts separately, unit-check that each collapses to the control unit — volts, say — and only then add them for u; because the three gains carry different units, a term that comes out in the wrong unit is the warning sign of a slip. For the tuning questions, hold one direction firmly: a higher proportional gain gives a faster response and a shorter rise time, while lowering Kp (for example 1.0 to 0.5) slows the response and increases the rise time. Watch the sign convention (this unit uses e = y − y_ref; the reverse flips every term), keep full precision through the working, and round only the final answer to the precision the question states. The final is a paper-based, 2-hour exam (plus 10 minutes' reading) worth 33% of the unit, sat in the University of Sydney Semester 1 formal examination period around June; it is a restricted-materials exam (bring a calculator and, per the exam cover sheet, one A4 double-sided handwritten note sheet), though the assessment table calls it closed book — so confirm the exact date, mark total and permitted materials on your current Canvas assessment page. Pace at about 1.5 minutes per mark (roughly 80 marks across the 2 hours of writing time), so a five-mark control item deserves about seven and a half minutes.
