ELEC4632 Computer Control Systems
The Complete Exam Bible · T3 2026ELEC4632 Overview
- 6 UoC
- Term 3 2026
- Level 4
- Electrical Engineering
ELEC4632 Computer Control Systems is a fourth-year elective at UNSW Sydney that develops digital control from both input-output and state-space viewpoints.
- Final examination Two-hour written paper with six compulsory questions and approved calculators.
- Core design chain Model the plant, test structure, design feedback, simulate, then verify the implementation.
- Laboratory focus Identification, water-tank modelling, output feedback and PID connect theory to hardware.
- Evidence boundary Use current Moodle materials for plant matrices, case parameters and remaining exam rules.
What you get in the full ELEC4632 Exam Bible
- 7 chapters, 37 pages — every examinable topic, week by week
- 16 original practice questions, each with a model answer in the Final examination format
- 7 worked examples, solved the way ELEC4632 marks
- 8 computed figures, redrawn from the course’s own numbers
- Exam-morning plan for the Final examination (60%) — what to revise last, where marks are lost
Free on this page: assessment table, chapter map, one worked example, key terms, FAQ. The rest is in the full exam bible.
How ELEC4632 is assessed
| Component | Weight | Format |
|---|---|---|
| Laboratory Practical Experiments | 20% | Practical work assessed through preparation, checkpoints, laboratory records, results, understanding and code quality |
| Mid-term test | 20% | Held in Week 5; covers lecture and tutorial material through Week 4 with theoretical, numerical and analytical questions |
| Final examination | 60% | Two-hour written examination with six compulsory questions; approved calculators allowed; theoretical, numerical and analytical questions |
What other students are asking about ELEC4632
- Where can I find lecture notes or study guides for ELEC4632 at UNSW?
- The ELEC4632 study guide in AskSia Library covers Computer Control Systems in 7 chapters, with the assessment table, a chapter-by-chapter topic map, key terms and a worked example, free to read on this page.
- Is there a final exam in ELEC4632, and how much is it worth?
- Yes. In the offering this AskSia Library guide is built from, Final examination carries 60% of the ELEC4632 mark; the full split is Laboratory Practical Experiments 20%, Mid-term test 20%, Final examination 60%.
- What does ELEC4632 cover on discrete-time models and stability?
- In AskSia Library's ELEC4632 guide, the Discrete-Time Models and Stability chapter explains sampled state updates, transition matrices, Cayley-Hamilton and unit-circle tests.
- What does ELEC4632 cover on controllability, observation and pole placement?
- In AskSia Library's ELEC4632 guide, the Controllability, Observation and Pole Placement chapter explains reachability bases, state estimation, desired dynamics and output feedback.
- What does ELEC4632 cover on digital controllers and output feedback?
- In AskSia Library's ELEC4632 guide, the Digital Controllers and Output Feedback chapter explains regulation, set-point control, PID, deadbeat design and real-time verification.
What ELEC4632 covers
The course begins with the matrix and state-space tools needed for discrete-time modelling, then develops stability, controllability, observation, pole placement and digital controller design. It closes with nonlinear and optimal methods, system identification, real-time water-tank control, and biomedical and wind-energy case studies.
Linear Algebra for State-Space Control
Rank, range, null space, inverses, eigenvalues and characteristic polynomialsThe opening tutorials refresh the matrix structure needed for computer control: rank, full-rank status, range, null space, determinants, inverses, eigenvalues and characteristic equations.
- Rank as the number of independent directions preserved by a matrix
- Range bases chosen from pivot columns of the original matrix
- Null-space directions that disappear under the matrix map
- Determinant, invertibility and identity-multiplication checks
- Eigenvalues as modes of a state update
- Characteristic polynomials and companion-form coefficients
Discrete-Time Models and Stability
Sampled state updates, transition matrices, Cayley-Hamilton and unit-circle testsComputer control works through sampled measurements and held inputs, so stability must be read from repeated state updates rather than from a continuous-time shortcut.
- State and input contributions to the next sampled state
- Sampling, computation, input hold and measurement return
- Autonomous evolution through repeated powers of the state matrix
- Matrix exponentials and state-transition structure
- Cayley-Hamilton reduction of higher matrix powers
- Unit-circle classification of discrete-time eigenvalues
Controllability, Observation and Pole Placement
Reachability bases, state estimation, desired dynamics and output feedbackState-feedback design depends on two structural questions: whether the input can reach every modelled state direction and whether the measured output reveals enough information to estimate every relevant mode.
- Controllability matrix and full-state reachability
- Coordinate transformation using a controllability basis
- Similarity transforms that preserve eigenvalues
- Desired characteristic polynomials and pole assignment
- Observability as state inference from output history
- Observer correction and estimation-error dynamics
Digital Controllers and Output Feedback
Regulation, set-point control, PID, deadbeat design and real-time verificationThe laboratory distinguishes regulation from set-point control and then implements both observer-based state feedback and digital PID on the water-tank process. This chapter treats controller choice as a requirements decision.
- Regulation as return to an equilibrium point
- Set-point control as tracking a desired physical level
- Deviation variables and restoration of input-output offsets
- Reference scaling and closed-loop steady-state mapping
- Digital PID error actions and integral windup risk
- Deadbeat response and sensitivity to model or actuator limits
Optimal, Nonlinear and Predictive Control
Linearisation, Lyapunov reasoning, dynamic programming, LQ control and MPCThe advanced-design block moves from nonlinear discrete-time systems and singular-point stability to linearisation, Lyapunov functions, dynamic programming, linear-quadratic control and model-predictive control.
- Equilibrium verification for nonlinear sampled systems
- Local linearisation in deviation coordinates
- Lyapunov candidates and one-step change
- Bellman optimality and backward recursion
- Linear-quadratic trade-offs between state and input
- Model-predictive control over a receding horizon
System Identification and Water-Tank Control
Least squares, coupled-tank modelling, signal paths and laboratory evidenceThe laboratory uses a coupled water-tank process to connect data, modelling, design and real-time evidence.
- Computer, acquisition board, driver, pump and pressure-sensor signal path
- Pump command and level-measurement voltage ranges
- Least-squares regression matrix and parameter vector
- Residual analysis and validation on separate data
- Coupled-tank flows, levels and nonlinear MIMO description
- SISO selection using Pump 1 and Tank 1 level
Biomedical and Wind-Energy Case Studies
Blood-pump, hemodialysis, heart-rate, wind smoothing and storage decisionsThe course outline names five research-facing applications: blood-pump flow estimation and deadbeat control, predictive control during hemodialysis, heart-rate modelling with LQ or deadbeat control, wind-power smoothing with battery storage, and wind-plant income maximisation through dynamic programming.
- Non-invasive estimation and deadbeat blood-pump control
- Predictive regulation of circulatory variables during dialysis
- Heart-rate response modelling with LQ or deadbeat control
- Wind-power smoothing using battery storage and MPC
- Wind-plant income maximisation using dynamic programming
- Application-specific inputs, outputs, objectives and constraints
The current outline begins with mathematical models of discrete-time systems and stability analysis, then moves through controllability, observability, pole placement, state estimation, output feedback, digital PID and deadbeat control. It also introduces nonlinear discrete-time systems, linearisation, Lyapunov functions, dynamic programming, linear-quadratic control and model-predictive control.
Practical implementation is a central thread rather than an appendix. The laboratory sequence starts with linear least-squares system identification, identifies a water-tank model, designs observer-based state feedback for regulation and set-point control, implements output feedback in real time, and concludes with a real-time PID controller.
Assessment combines Laboratory Practical Experiments worth 20%, a Mid-term test worth 20%, and a Final examination worth 60%. The mid-term is held in Week 5 and covers lecture and tutorial material through Week 4, including theoretical, numerical and analytical work. The written final lasts two hours and requires attempts at all six questions; an approved calculator may be used.
Confirm every remaining permitted-material rule on Moodle. Laboratory attendance must reach at least 80%, and the practical marking criteria include preparation, task completion, understanding, code quality and topic knowledge. The course finishes with biomedical and wind-energy cases that connect estimation, deadbeat control, LQ design, MPC and dynamic programming to research-facing systems.
This guide follows the current outline, tutorial problems and laboratory guide. Where those materials name a method without supplying plant coefficients or case data, the discussion remains symbolic and directs numerical work back to current course materials.
Worked example · free
Read a controllability basis before placing poles
- +1Form T = [b, Ab, A squared b]. Independence gives rank three, so T is invertible and the input reaches every state direction represented by the model.
- +1Use the coordinate change x = Tz. In these coordinates the input aligns with the first basis direction and its influence shifts through the remaining directions.
- +1Full controllability permits pole assignment for the model, but the desired poles must still be chosen against response speed, control effort and robustness requirements.
- +1If the complete state is not measured, also test observability, design an observer and verify the combined controller and estimator in simulation before hardware implementation.
Key terms
- State-space model
- A model that updates a vector of internal states from the current state and input, then maps those states to measured outputs.
- Discrete-time stability
- A property describing whether modes of a sampled system decay, persist or grow under repeated state updates.
- Controllability
- The ability of an input to reach every state direction represented by the model over successive updates.
- Observability
- The ability to reconstruct internal state behaviour from the available input and output history.
- Pole placement
- A state-feedback design method that selects a gain so the controllable closed-loop characteristic roots match desired locations.
- State observer
- A dynamic estimator that propagates a model and corrects its state estimate using measured output.
- Deadbeat control
- A discrete-time design objective that drives the modelled response to its target in a finite number of samples.
- Digital PID
- A sampled controller that combines proportional, accumulated-error and error-change actions.
- Lyapunov function
- A scalar candidate used to certify stability by showing positive state measure and a suitable decrease along system motion.
- Dynamic programming
- A staged optimisation method that combines current return or cost with the optimal value of the resulting future state.
- Model-predictive control
- A controller that repeatedly solves a finite-horizon constrained problem and applies the first action before resolving.
- System identification
- The process of estimating a dynamic model from measured input-output data and validating it on separate behaviour.
ELEC4632 FAQ
How is the course assessed?
The current outline assigns 20% to Laboratory Practical Experiments, 20% to the Mid-term test and 60% to the Final examination. The mid-term occurs in Week 5 and covers material through Week 4. Laboratory attendance must reach at least 80%, and practical marking considers preparation, completion, understanding and code quality.
What is the final examination format?
The written final lasts two hours and requires an attempt at each of six questions. An approved calculator may be used, and the paper includes theoretical, numerical and analytical work from the course unless the lecturer announces an exclusion. Confirm every remaining permitted-material rule on Moodle.
Why can this course be demanding?
The work moves repeatedly between matrix structure, controller design and physical implementation. A calculation can be algebraically correct yet incomplete if controllability, observability, signal range or actuator limits are ignored. The laboratory also expects preparation and reproducible code, so steady work on tutorials and practical records matters more than last-minute formula memorisation.
What attendance condition applies?
The published assessment rows do not mark a weighted component as a hurdle. The course outline does state a positive attendance condition: students must attend at least 80% of laboratories. Treat that requirement as operational course information and check Moodle for any current clarification rather than inferring a component pass mark.
What background knowledge is expected?
The outline lists ELEC3114 as the prerequisite and says familiarity with a standard introductory undergraduate control-engineering course is essential. The opening tutorials revisit rank, null space, determinants, inverses, eigenvalues and characteristic equations before state-space controller design, so refreshing linear algebra is a high-value first step.
What practical system is used in the laboratories?
The laboratory sequence uses a coupled water-tank process. Students identify a linear model, design state feedback with an observer, implement output feedback for set-point control, and implement a PID controller. The setup links computer commands, data-acquisition hardware, pumps, pressure-based level measurements and real-time verification.
Where should students find official practice papers?
The practice in this guide is newly authored around the tutorial methods and current laboratory sequence. Use Moodle and the UNSW Library for any officially released paper, and confirm current examination guidance through course announcements.
Questions students ask in each ELEC4632 chapter
- Why must range bases use the original columns?
- Row operations change the columns while preserving row-equivalent equations. Pivot locations reveal which original columns are independent, but the reduced columns belong to a different matrix. Selecting the original pivot columns keeps the basis tied to the original range. Chapter 01 · Linear Algebra for State-Space Control
- Why is a negative pole not automatically stable in discrete time?
- Discrete-time stability depends on eigenvalue magnitude rather than sign alone. A pole at negative one keeps its magnitude and alternates sign, while a pole below negative one in value can have magnitude above one and produce a growing oscillation. Chapter 02 · Discrete-Time Models and Stability
- Why check controllability before choosing poles?
- A feedback gain acts through the input channel. If a state direction is unreachable, its associated mode cannot be moved by that gain. Full controllability establishes feasibility; pole selection then addresses the desired response and control-effort trade-off. Chapter 03 · Controllability, Observation and Pole Placement
- How do regulation and set-point control differ?
- Regulation removes a deviation and returns the process to equilibrium. Set-point control moves the process to a specified reference and must address steady-state tracking. The same plant can perform both tasks, but the reference handling and performance evidence differ. Chapter 04 · Digital Controllers and Output Feedback
- What does local stability mean for a nonlinear system?
- A local result describes behaviour near the analysed equilibrium, where the linear approximation or Lyapunov conditions are valid. It does not automatically describe trajectories that begin far away, because neglected nonlinear terms may become important. Chapter 05 · Optimal, Nonlinear and Predictive Control
- Why is the water-tank system described as MIMO?
- The physical setup has multiple inlet flows, valve-dependent transfer and outlet flows, and two tank levels. Those interacting inputs and outputs form a nonlinear coupled plant even when the laboratory selects one input-output path for a simpler experiment. Chapter 06 · System Identification and Water-Tank Control
- Why does the blood-pump case include estimation?
- The case pairs non-invasive estimation with deadbeat control, indicating that the controlled flow is not treated as a directly available state. The estimate therefore becomes part of the feedback evidence and must be validated as well as the controller. Chapter 07 · Biomedical and Wind-Energy Case Studies
How to study for the exam
Begin with the tutorial linear algebra because every later state-space method depends on rank, characteristic equations and eigenvalue reasoning. For each matrix problem, write the structural conclusion beside the arithmetic: full rank, singular direction, stable mode or reachable basis. Next, organise controller design as a sequence rather than a formula list.
State the plant model and objective, test controllability or observability, choose poles or an optimisation objective, simulate, and then identify what hardware evidence would support the claim. Keep a separate laboratory notebook trail for model version, signal channels, offsets, controller settings, input and output plots, and checkpoint feedback.
The mid-term tests material through Week 4, so solve the published tutorial types early and practise explaining each result in one sentence. For the final, rehearse six compact answer shapes because every question is compulsory: matrix structure, stability classification, feedback feasibility, estimator architecture, optimal-method comparison, and application mapping.
Where the outline names advanced methods without numerical data, use current Moodle lecture materials for the assigned matrices, weights, horizons and constraints. Do not fill those gaps from memory. On the water-tank work, compare simulation with real-time behaviour and diagnose sensing, operating-point, timing and saturation differences before retuning.
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