The design of suboptimal linear regulators using reduced order aggregated models

An approach to the design of suboptimal linear regulators is developed. Two techniques are proposed for obtaining a reduced order aggregated model for a constant coefficient dynamic system. This model is then used to determine a suboptimal control law to solve an output regulator problem.

The research is developed by first examining the problems involved when the design and implementation of the optimal regulator is attempted. The idea of using a reduced order model to overcome some of these problems is discussed and a set of criteria that the reduced model must satisfy is presented. Two methods for determining a reduced order model that satisfies the criteria are then developed and used to design controllers for two example systems.

The methods are based on using gradient descent to minimize the error between the exact system output and the output of an observer dependent aggregated model. The use of a stochastic input to serve as the test function for this minimization is proposed and shown to be quite useful. The procedure developed is applicable to multi-input systems and to systems with unstable modes. In addition, there is no requirement that the exact model be in any special form.