Controller design for parabolic distributed parameter systems using finite integral transform techniques

A procedure is presented for designing a control system for distributed parameter systems of parabolic type based on the reduced-order decoupled state-space model obtained by a finite integral-transform technique. A Kalman filter is used as an observer to estimate the state variables, and state feedback control is performed. The method was applied to a one-dimensional heat conduction process and a moving bed adsorber. Both state estimation and control performances were satisfactory in spite of the model and parameter uncertainties. Following this controller design approach, the searching algorithms for the optimal sensors' and the optimal actuators' allocation problems were solved. These algorithms were applied to a one-dimensional heat conduction process in order to confirm the state estimator and controller performance. The fastest state estimation could be achieved by assigning the sensors at the optimal locations and the desired state distribution was realized with a few actuators located at the optimal positions.