ELEC4632 Chap.6 System Identification and Water-Tank Control
System Identification and Water-Tank Control
The laboratory uses a coupled water-tank process to connect data, modelling, design and real-time evidence. Students first apply linear least squares, then identify a plant model, design observer-based state feedback, implement output feedback and compare it with PID control.
This chapter maps the physical signal path, explains the SISO reduction inside a larger coupled plant, and shows how residuals and validation protect controller design from a poor model.
What this chapter covers
- 01
Computer, acquisition board, driver, pump and pressure-sensor signal path
- 02
Pump command and level-measurement voltage ranges
- 03
Least-squares regression matrix and parameter vector
- 04
Residual analysis and validation on separate data
- 05
Coupled-tank flows, levels and nonlinear MIMO description
- 06
SISO selection using Pump 1 and Tank 1 level
- 07
Laboratory notebook, checkpoints, code and report evidence
Worked example · free
Set up a least-squares identification study
- +1Write y approximately equal to Phi theta with named, aligned regressors.
- +1Choose theta hat to minimise the squared residual norm.
- +1Inspect residual magnitude and structure instead of reporting only fitted parameters.
- +1Validate predicted output on separate data under the same physical configuration and operating region.
Key terms
- Least Squares
- Least squares estimates model parameters by minimising the sum of squared prediction residuals.
- Regression Matrix
- A regression matrix collects the measured or constructed predictors associated with unknown parameters.
- Residual
- A residual is the difference between a measured output and the output predicted by the fitted model.
- Coupled Tanks
- Coupled tanks exchange flow so one tank level can influence the dynamics observed in the other.
- Validation Data
- Validation data test model prediction on measurements that were not used to estimate the parameters.
System Identification and Water-Tank Control FAQ
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.
What does the SISO laboratory model include?
The selected input is associated with Pump 1 and the controlled output is Tank 1 level, while Pump 2 is set to zero and the valve configuration is held. Coupling remains part of the physical dynamics rather than disappearing.
What evidence should appear in the laboratory report?
Record the objective, configuration, model version, signal paths, controller parameters, reference, measured output, estimate and actual input. Compare simulation with real-time results, identify limitations and state whether the requirement was met under the tested conditions.
Why validate on data not used for fitting?
A model can reproduce the data that determined its parameters while failing on new behaviour. Separate validation tests whether the chosen regressors and dynamics generalise to another record and helps reveal overfitting, operating-point limits or structured residual error.
What should be checked before retuning a real-time controller?
Verify channel selection, units, signs, equilibrium offsets, sample timing and command limits. Compare the test with the identification conditions and inspect observer behaviour. Retuning first can hide a sensing, saturation, file-version or model-validity problem.
Why retain code and model versions between laboratories?
Later tasks reuse earlier identification and controller work, so an untracked change can alter every subsequent result. A versioned record lets the response, parameters, offsets and checkpoint feedback be reconstructed before a discrepancy is attributed to the plant.
Exam move
Draw the instrument chain and label input and output units before fitting a model. Rehearse least squares as model structure, regression matrix, parameter estimate, residual and independent validation. For the coupled tanks, list every flow and level, then state exactly what is fixed when the experiment becomes SISO. Prepare laboratory records before each session and save code versions because later tasks reuse earlier work.
Diagnose signal, offset and saturation problems before changing controller gains. Turn the laboratory sequence into a traceability ledger. For each session, record the model version, sample interval, configured valve and pump conditions, signal channels, equilibrium offsets, controller settings and file names.
Pair every plot with the input that produced it and label whether the trace belongs to fitting, validation, regulation or set-point tracking. When least squares returns parameters, check regressor independence and inspect residual patterns rather than reporting only a vector. When the tank experiment is treated as SISO, explain which physical paths are fixed and which coupling effects may remain as disturbances.
Before hardware operation, verify the driver and sensor ranges separately because they use different voltage spans. After implementation, compare the measured output and actual command with simulation on the same time basis. If they differ, test sensing, units, timing, operating region, saturation and observer behaviour in that order.
Close the lab record with a reproducible decision about whether the stated requirement was met and which evidence supports it. Before each checkpoint, ask a partner to reconstruct the experiment from the ledger without verbal help. Missing units, offsets or file versions will become obvious. Keep the identification and validation plots separate and annotate the operating range on both.
When a controller is added, preserve the open-loop or identification record so improved tracking cannot erase evidence about model quality. This habit strengthens both the demonstrator explanation and the final report.
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