Lyapunov-based optimizing control of nonlinear blending processes

Blending processes consisting of linear dynamics and a static nonlinearity are considered. We propose a control law that optimizes the equilibrium point of the process and regulates the output to the corresponding equilibrium state. A control Lyapunov function (CLF) is used to derive a stable optimizing update law for the equilibrium point, in combination with a linear quadratic (LQ) feedback law for tracking the optimized equilibrium point. The analysis and design also incorporates the use of an observer for state and bias estimation. Experimental results using a laboratory scale colorant blending process illustrate the efficiency of the method.