A straightforward way to design nonlinear controllers for nonlinear processes by means of process discretization (Q1088625)

This paper is concerned with controller design for systems described by nonlinear ordinary differential equations. The controller should be designed so that the system exhibits the desired speed of response to a large input signal. It is assumed that a scalar performance index J is given. A reference trajectory vector \(r\) whose elements correspond to the state variables is specified such that \(J\) is minimized. A controller depending nonlinearly on the state variables but linear on a parameter vector \(p_ c\) is chosen such that the deviation of the state vector from the reference vector \(r\) is minimized. \(p_ c\) is determined by discretizing the differential equations by a suitable numerical integration formula (e.g. the trapezoidal rule). A set of algebraic equations is then obtained and \(p_ c\) is calculated by solving a least squares problem. If \(r\) is not optimal, a second level of optimization is employed to find the best specified trajectories. The design method is demonstrated for a nonlinear chemical reactor. As is shown by simulation results the nonlinear controller is superior to linear controllers.