Self-Tuning Regulators
A self-tuning regulator estimates plant parameters online and continually redesigns the controller as if the estimates were exact.
Indirect adaptive control
The self-tuning regulator, or STR, is the indirect counterpart to model-reference adaptive control. Instead of adjusting controller gains directly, it runs a recursive estimator, typically recursive least squares, that identifies the plant parameters from measured inputs and outputs, then computes the controller from those estimates at each step. The name reflects the certainty-equivalence assumption: the current estimate is treated as the truth.
The estimation loop
Recursive least squares updates a parameter vector and a covariance matrix each sample. A forgetting factor below one discounts old data so the estimator tracks slow changes. The controller-design step can be pole placement, minimum variance, or LQG, applied to the freshly estimated model. Minimum-variance self-tuning was the original and remains a canonical form.
Practical concerns
Covariance windup, where the covariance grows without bound when excitation is poor, must be prevented by regularization or covariance resetting. The estimator can also lock onto biased parameters if disturbances are correlated with the input. As with all adaptive schemes, persistent excitation is needed for the estimates to converge, and robustifying modifications guard against unmodeled dynamics.
- Estimate plant parameters recursively, then redesign
- Certainty equivalence: treat estimates as exact
- Forgetting factor tracks slowly varying plants
- Guard against covariance windup and biased estimates
STR is flexible because any linear design method can be dropped into the redesign step, letting engineers reuse familiar synthesis while gaining adaptation. The trade-off is the coupling between estimation and control: aggressive control can reduce excitation and starve the estimator, a dilemma addressed by dual control.
For a design-stage system whose parameters shift with operating conditions, an STR would identify the current model each cycle and retune, all evaluated in simulation. It and MRAC are the two pillars of classical adaptive control.