Adaptive control

Adaptive control involves modifying the control law used by a controller to cope with the fact that the parameters of the system being controlled are slowly time-varying or uncertain. For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; we need a control law that adapts itself to such changing conditions. Adaptive control is different from robust control in the sense that it does not need a priori information about the bounds on these uncertain or time-varying parameters; robust control guarantees that if the changes are within given bounds the control law need not be changed, while adaptive control is precisely concerned with control law changes.

Classification of adaptive control techniques

In general one should distinguish between:

1. Feedforward Adaptive Control
2. Feedback Adaptive Control

There are several broad categories of feedback adaptive control (classification can vary):

• Dual Adaptive Controllers [based on Dual control theory]
  • Optimal Dual Controllers [difficult to design]
  • Suboptimal Dual Controllers
• Nondual Adaptive Controllers
  • Gain scheduling
  • Model Reference Adaptive Controllers (MRACs) [incorporate a reference model defining desired closed loop performance]
    

    

    MRAC
    

    

    MIAC
    • Gradient Optimization MRACs [use local rule for adjusting params when performance differs from reference. Ex.: "MIT rule".]
    • Stability Optimized MRACs
  • Model Identification Adaptive Controllers (MIACs) [perform System identification while the system is running]
    • Cautious Adaptive Controllers [use current SI to modify control law, allowing for SI uncertainty]
    • Certainty Equivalent Adaptive Controllers [take current SI to be the true system, assume no uncertainty]
      • Nonparametric Adaptive Controllers
      • Parametric Adaptive Controllers
        • Explicit Parameter Adaptive Controllers
        • Implicit Parameter Adaptive Controllers

Some special topics in adaptive control can be introduced as well:

1. Adaptive Control Based on Discrete-Time Process Identification
2. Adaptive Control Based on the Model Reference Technique
3. Adaptive Control based on Continuous-Time Process Models
4. Adaptive Control of Multivariable Processes
5. Adaptive Control of Nonlinear Processes

Applications

When designing adaptive control systems, special consideration is necessary of convergence and robustness issues.

Typical applications of adaptive control are (in general):

• Self-tuning of subsequently fixed linear controllers during the implementation phase for one operating point;
• Self-tuning of subsequently fixed robust controllers during the implementation phase for whole range of operating points;
• Self-tuning of fixed controllers on request if the process behaviour changes due to ageing, drift, wear etc;
• Adaptive control of linear controllers for nonlinear or time-varying processes;
• Adaptive control or self-tuning control of nonlinear controllers for nonlinear processes;
• Adaptive control or self-tuning control of multivariable controllers for multivariable processes (MIMO systems);

Usually these methods adapt the controllers to both the process statics and dynamics. In special cases the adaptation can be limited to the static behavior alone, leading to adaptive control based on characteristic curves for the steady-states or to extremum value control, optimizing the steady state. Hence, there are several ways to apply adaptive control algorithms.

See also

• Nonlinear control
• Intelligent control

References

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External Links and Further Reading

• K. J. Astrom and B. Wittenmark, Adaptive Control, Addison-Wesley, 1989, 2d ed. 1994.
• Shankar Sastry and Marc Bodson, Adaptive Control: Stability, Convergence, and Robustness, Prentice-Hall, 1989-1994 (book)
• K. Sevcik: Tutorial on Model Reference Adaptive Control (Drexel University)