MATLAB Implementation of Dynamic Matrix Control with Dual Inputs

Dynamic Matrix Control (DMC) is an advanced model predictive control strategy particularly suitable for handling multivariable systems and constrained control problems. In dual-input system scenarios, DMC can simultaneously coordinate two control variables to ensure optimal system performance under constraints. The core implementation of dual-input dynamic matrix control involves constructing dynamic matrix models and calculating control inputs using prediction and optimization algorithms. The MATLAB implementation typically begins by building dynamic matrices based on system step response or impulse response data. For dual-input systems, the dynamic matrix consists of two sub-matrices representing the influence of each input channel. Code implementation would involve creating separate response matrices for each input and combining them appropriately. Constraint handling is crucial during simulation. Common constraints include control input amplitude limits, rate-of-change restrictions, and output variable bounds. These constraints can be incorporated into each control calculation using optimization algorithms like quadratic programming. In MATLAB, this can be implemented using functions such as quadprog() or fmincon() with properly defined constraint matrices. The simulation procedure generally includes: initializing system models and dynamic matrices, setting prediction and control horizons, defining objective functions and constraint conditions for the optimization problem, and online optimization solving with control application. Weighting parameters and constraint boundaries can be adjusted to balance system dynamic performance and robustness. Key MATLAB functions involved might include horizon configuration, matrix construction using toeplitz() for dynamic matrices, and optimization solver calls. Dual-input dynamic matrix control finds wide applications in industrial processes, such as temperature and flow coordination control in chemical processes or multi-joint cooperative control in robotic systems. Its advantage lies in explicitly handling multivariate coupling and constraints while adapting to system dynamic changes through rolling optimization. The MATLAB implementation demonstrates practical approaches for handling these complex control scenarios through proper matrix manipulation and optimization techniques.