The self-tuning robust servomechanism problem

In this paper, we consider the problem of designing a selltuning regulator for an unknown, asyrnptotically stable, linear, time-invariant, multivariable plant which will carry out asymptotic error regulation for all constant reference and disturbance signals and all plant initial conditions, while at the same time ensuring that the plant and the controller states remain bounded. In this problem only the plant output and the reference signal are used as controller inputs. It is not assumed that the plant order or the relative degree are known, or that the plant is minimum phase. The only assumptions made are that the plant is open loop asymptotically stable, that there exists a solution to the problem, and that an estimate of the steady-state DC gain matrix (easily obtainable by carrying out a finite number of experiments on the plant) is available when there are more than two outputs. A self-tuning regulator is presented which consists of a multivariable integral compensator together with a tuning mechanism which "tunes" the parameters of this compensator. It is shown that if the reference and disturbance inputs are constant, then the controller and the plant states remain bounded for all t, and asymptotic error regulation occurs. A number of simulation examples are included to illustrate the behaviour of the controller when applied to "unknown" plants.