Kalman filter-based centralized controller design for non-square multi-input multi-output processes

In this paper, a simple and effective centralized controller is presented to control non-square multi-input multi-output industrial processes with heavy interactions and significant time-delays. The control objective is to achieve a good load disturbance rejection and set point tracking. The controller and process model equations are represented in a stochastic state-space. Also, the state and measurement equations respectively use general random walk model and finite impulse response model of the plant. To design the controller, a quadratic cost function including the control error vector as well as the input vector and its changes is introduced. A Kalman filter algorithm is used to solve the discrete algebraic Riccati equation and to estimate the state vector of the controller recursively. This novel use of Kalman filter combines the observer and controller in a block. No square down/up, pairing and pseudo-inversing, is required for the proposed control structure. This leads to the simplicity of controller design. To evaluate the performance of the proposed control strategy, it is applied to a simulation example and an industrial case study with heavy interactions and significant time delays, an atmospheric distillation column with 7 inputs and 4 outputs. Simulation results show that the proposed controller has a good performance in both load disturbance rejection and setpoint tracking.