Implementation of Single-Input Single-Output Model Predictive Control Algorithm with Code Examples

The implementation of Single-Input Single-Output (SISO) Model Predictive Control (MPC) algorithm is a mathematical model-based control methodology that predicts future system behavior and regulates system operations in real-time using predictive information. This algorithm features three primary implementation approaches, including standard implementation, inverse response handling, and linear programming techniques. The standard implementation represents the fundamental approach, typically suitable for simple control systems. In code implementation, this involves basic prediction models and control horizon calculations using difference equations or transfer functions, often implemented through recursive prediction loops and constraint handling functions. Inverse response implementation constitutes a more sophisticated approach that excels in managing system time delays, enabling more accurate predictions of future system behavior. Programmatically, this requires specialized delay compensation algorithms and non-minimum phase system handling, frequently implemented using advanced filtering techniques and modified prediction equations to address inverse response characteristics. Linear programming represents an advanced implementation method designed for complex systems, providing enhanced precision in predicting and controlling system behavior. This approach typically involves formulating the control problem as an optimization task with linear constraints, solved using simplex methods or interior-point algorithms. Key implementation elements include constraint matrix construction, objective function definition, and real-time optimization solvers. Therefore, when selecting a SISO MPC implementation approach, careful consideration of practical application scenarios and system complexity is essential. Code implementation should correspondingly prioritize computational efficiency for standard systems, delay compensation mechanisms for inverse response scenarios, and robust optimization frameworks for linear programming applications.