Model -based control of nonlinear processes

Model-based control of continuous-time, multivariable, nonlinear processes with input constraints and time delays is studied. Differential geometric control laws are derived for stable processes, whether their delay-free part is minimum- or non-minimum-phase. They are obtained by requesting an approximately linear, input-output response and exploiting the connections between model-predictive control and input-output linearization. Conditions under which the closed-loop system is asymptotically stable are given. The control laws ensure asymptotic tracking of the measured output in the presence of constant model errors and disturbances as long as nominal, closed-loop, asymptotic stability is preserved. There are no limitations on the order, relative order, or number of unstable modes of the zero dynamics of the processes to which the control laws are applicable. To derive control laws that can perform optimally in the presence of input constraints, the connections between model-predictive control and input-output linearization are exploited. The continuous-time control laws are solutions of constrained optimization problems that are solved on-line. They minimize the error between controlled outputs and their reference trajectories, subject to the input constraints. In the absence of input constraints the control laws do not induce a linear, closed-loop, output response when process zero dynamics are unstable. The nonlinearity of the resulting process output response is the price of ensuring closed-loop stability for non-minimum-phase processes. The application and performance of the control laws are illustrated using numerical simulation of several chemical reactors that exhibit non-minimum-phase behavior. The control laws are also implemented in real-time on a pilot-scale, liquid-level process with non-minimum-phase behavior. Real-time implementation issues, and advantages and disadvantages of the control laws are discussed