Adaptive Control of Systems with Unknown Physical Element Values

This paper considers the indirect adaptive control of systems with physical element values as the unknown parameters. Conventionally, both direct'-3 and controllers for linear, time-invariant, finite-order systems presuppose a complete lack of knowledge about the unknown system, aside sometimes from the order and relative order. Consequently, they implicitly estimate the numerator and denominator coefficients of the system transfer function, having assumed them all to be unknown. Often, the only unknowns in a system are a small number of physical parameter values. Thus all parts of a mechanical system may be known a prior i , except perhaps the value of a moment of inertia, a frictional coefficient or the like. Accordingly, in the underlying parametrization of this paper the unknown parameters have direct physical significance. In any given system, usually such parameters are few in number, certainly fewer than the transfer function coefficients. Thus adaptive algorithms involving such parametrizations can be expected to comprise fewer update equations. When most parts of a linear, time-invariant, finite-dimensional system are known but certain physical parameters are unknown, Dasgupta and Anderson6 have shown the numerator and