Analysis of Equilibrium Point and Genetic Algorithm Design of Observer-Based PID Controller for Membrane Bioreactor

Abstract

The operation of most wastewater treatment systems is an open-loop system. There is limited feedback control of membrane bioreactors (MBR) which makes it impossible to regulate the quality of the treated water. The objectives of this paper are twofold. First, we analyze the equilibrium point of the MBR nonlinear model. Second, we utilize output feedback control with state observer and design optimal PID controllers. We determine the optimum equilibrium point and derive a linearized model of MBR. Then, we design the state observer to estimate the non-measurable state using the pole placement method. Both the measurable output and estimated state are fed back through PID controller. The objectives of PID control consist of stabilization and performance improvement. Genetic Algorithm is applied to find the optimal PID parameters that minimize the integral of absolute error and satisfy the specified time-domain criteria. We apply the observer-based PID controller to the linearized model of MBR. Numerical results demonstrate the design of PID controller and the improvement of the closed-loop response and quality of the treated water.