Applications of S-Functions in MATLAB

In the MATLAB simulation environment, S-functions (system functions) serve as powerful tools for modeling and simulating custom dynamic systems. They enable users to programmatically describe system differential equations, difference equations, or discrete-event logic, particularly useful for implementing complex algorithms that are difficult to construct with standard Simulink blocks.

Active Disturbance Rejection Control (ADRC), as a model-independent control strategy, frequently utilizes S-functions to implement its core algorithms. Key advantages include: Flexibility: S-functions support C/MEX language programming, allowing complete implementation of ADRC's nonlinear tracking differentiator, extended state observer (ESO), and nonlinear feedback combination logic. Real-time capability: Through discrete or continuous S-functions, ADRC's real-time estimation and compensation processes for system disturbances can be accurately simulated. Integration: S-functions can be directly embedded into Simulink models, seamlessly connecting with other control modules (e.g., PID controllers, plant models) for comparative testing.

Critical implementation considerations: Callback function design: Use `mdlInitializeSizes` to define input/output ports and `mdlDerivatives` for continuous state equations. Disturbance observation: Dynamically compute extended state observer outputs within the S-function to estimate total system disturbances. Discretization: For digital control implementations, implement discrete-time state updates in the `mdlUpdate` function.

ADRC modules built using S-functions can be further encapsulated as custom library components, enhancing efficiency and reusability in complex control system simulations. The implementation typically involves structuring the S-function to handle multiple sample rates and implementing the ESO algorithm using difference equations for discrete-time systems.