SISO and MIMO Generalized Predictive Control Algorithm Programming with Implementation Details

Generalized Predictive Control (GPC) represents an advanced control strategy widely applied in industrial process control. It achieves precise system control by establishing predictive models of controlled objects combined with optimization techniques. Based on system input-output configurations, GPC can be categorized into Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) types.

For SISO systems, the GPC algorithm implementation is relatively straightforward. Key implementation steps include: constructing system prediction models using difference equations or transfer functions, defining control objectives and constraints through cost function formulation, and solving optimization problems using quadratic programming algorithms to obtain optimal control sequences. During implementation, developers must handle system dynamics and external disturbances through recursive least-squares parameter estimation and incorporate disturbance observers to ensure stable and reliable control performance.

MIMO GPC systems present greater complexity due to multiple input and output variables with potential coupling effects. Algorithm implementation requires careful consideration of inter-variable interactions, necessitating decoupling strategies such as diagonal dominance design or centralized control approaches. The computational burden increases significantly for multivariate systems, particularly in prediction model construction involving matrix operations and constrained optimization solving, demanding efficient numerical algorithms like active-set methods or interior-point solvers for real-time applications.

In practical programming implementations for both SISO and MIMO systems, several critical issues must be addressed: prediction model accuracy through proper system identification techniques, optimization algorithm effectiveness via appropriate solver selection, and real-time computational capability achieved through code optimization. These factors directly impact control system performance and stability, requiring careful attention to numerical robustness and computational efficiency in code development.