Approximating automata and discrete control for continuous systems - Two examples from process control

A standard problem in hybrid control systems theory is to design discrete, or symbolic, feedback for a given continuous plant. When specifications are discrete, this problem can be solved by first approximating the continuous plant model by a (nondeterministic) automaton, and then synthesizing discrete (supervisory) control for the automaton. A necessary condition is that the approximation behaviour contains the behaviour of the underlying continuous plant model. Then, any controller forcing the approximation to obey the specifications will arise force the continuous model to satisfy the specifications. We use a version of this approach which allows adjustment of approximation accuracy to address two simple process control problems: supervisory control of a three-tank laboratory experiment; md safety enforcement for an evaporator. In both cases, the entire design process is carried through: we first determine a suitable abstraction, compute the minimally restrictive supervisor, and then present examples for closed loop trajectories.