Machine Design

Adaptive Control

The most recent class of control techniques to be used are collectively referred to as adaptive control. Although the basic algorithms have been known for decades, they have not been applied in many applications because they are calculation-intensive. However, the advent of special-purpose digital signal processor (DSP) chips has brought renewed interest in adaptive-control techniques. The reason is that DSP chips contain hardware that can implement adaptive algorithms directly, thus speeding up calculations.

The main purpose of adaptive control is to handle situations where loads, inertias, and other forces acting on the system change drastically.

A classic example of a system with changing parameters is a guided missile. Missile mass drops as fuel burns, and it encounters differing friction at different altitudes.

Some system changes can be unpredictable, and ordinary closed-loop systems may not respond properly when the system transfer function varies. Sometimes, these effects can be handled by conventional linear-control techniques such as gain scheduling (feed-forward control). Conservative design practices may also enable some systems to remain stable even when subjected to parameter changes or unanticipated disturbances.

The price paid for such stability is suboptimal performance, however. Response to changes may be sluggish. Errors may fail to stay within satisfactory limits, or designs must compensate for loose error tolerances in other ways.

Adaptive control can help deliver both stability and good response. The approach changes the control algorithm coefficients in real time to compensate for variations in the environment or in the system itself. In general, the controller periodically monitors the system transfer function and then modifies the control algorithm. It does so by simultaneously learning about the process while controlling its behavior. The goal is to make the controller robust to a point where the performance of the complete system is as insensitive as possible to modeling errors and to changes in the environment.

Even ordinary feedback-control systems are adaptive in a limited sense, in that they can compensate for changes at their input that are within the system bandwidth. But these changes are comparatively small. Such systems can become unstable for large input swings, or may simply be unable to compensate for sufficiently large input changes.

There are two main approaches to adaptive feedback-control design: model reference adaptive control (MRAC) and self-tuning regulators (STRs). In MRAC, a reference model describes system performance. The adaptive controller is then designed to force the system or plant to behave like the reference model. Model output is compared to the actual output, and the difference is used to adjust feedback controller parameters.

Most work on MRAC has focused on the design of the adaptation mechanism. This mechanism must note the output error and determine how to adjust the controller coefficients. It must also remain stable under all conditions. One problem with the approach is that there is no general theoretical method of designing an adapter. Thus, most adapter functions are specially keyed to some kind of end application.

An advantage of MRAC is that it provides quick adaptations for defined inputs. A disadvantage is that it has trouble adapting to unknown processes or arbitrary disturbances.

Model-reference controllers have an adaptation mechanism. The comparable component in self-tuning regulators is a tuning algorithm. A self-tuning regulator assumes a linear model for the process being controlled (which is generally nonlinear). It uses a feedback-control law that contains adjustable coefficients. Self-tuning algorithms change the coefficients.

These controllers typically contain an inner and an outer loop. The inner loop consists of an ordinary feedback loop and the plant. This inner loop acts on the plant output in conventional ways. The outer loop adjusts the controller parameters in the inner feedback loop. The outer loop consists of a recursive parameter estimator combined with a control design algorithm.

The recursive estimator monitors plant output and estimates plant dynamics by providing parameter values in a model of the plant. These parameter estimates go to a control-law design algorithm that sends new coefficients to the conventional feedback controller in the inner loop.

The above description tends to be abstract because many different types of controllers and schemes are used to estimate parameters. Among the most widely used controllers are PID state controllers, and deadbeat controllers. Recursive parameter estimation techniques include stochastic approximation, least squares, extended Kalman filtering, and the maximum likelihood method.

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