Applications of hysteresis switching in parameter adaptive control

The hysteresis switching algorithm of R.H. Middleton et al. (ibid., vol.33, no.1, p.50-8, Jan. 1988) is reexamined in a broader context. To demonstrate its utility, the algorithm is applied to various families of identifier-based parameterized controllers of both the direct and indirect control types. Application to the direct control type results in a model reference adaptive controller capable of stabilizing, without excitation, any SISO process which can be modeled by a minimum phase linear system whose transfer function has relative and McMillan degrees not exceeding prescribing integers m and n, respectively. It is shown that such processes can also be adaptively stabilized with indirect adaptive controllers and hysteresis switching. A simple numerical example involving a non-minimum-phase process model is used to illustrate how hysteresis switching might be applied to implicitly tuned parameterized controllers to realize an adaptive controller with capabilities which might prove very difficult, if not impossible, to achieve without hysteresis switching or some other form of discontinuous control