How do you choose the sliding surface and the switching function for sliding mode control?

My Top 5 Tips: #1: Define the Sliding Surface Select a sliding surface that ensures stability and reflects system behavior. #2: Select the Switching Function Ensure the switching function allows effective convergence to the sliding surface. #3: Utilize AI Tools Use AI tools like ChatGPT Plus and Taplio to enhance calculations and simulations. #4: Mitigate Chattering Reduce chattering with saturation functions or boundary layers for smoother transitions. #5: Implement Automation Incorporate AI agents for real-time adjustments, improving responsiveness in control systems.

The sliding surface in a control system ensures the system behaves as desired. It must meet three needs: stability (system stays on the surface and doesn’t drift away), performance (achieves goals like reducing errors or following targets), and robustness (handles uncertainties or disturbances without major issues). This makes the system reliable, accurate, and effective in varying conditions.

To choose the sliding surface for sliding mode control, select a function that ensures system stability and convergence to the desired state. The surface is often defined by a linear combination of state variables that reflects the system's dynamics. For the switching function, choose one that drives the system towards the sliding surface while minimizing chattering. The function should ensure fast reaching of the sliding surface and smooth control action. Typically, this involves a design that balances system robustness with performance, considering factors like system uncertainties and disturbances.

The switching function controls when and how the system switches to keep it on the desired path. It must meet two key needs: existence (once on the sliding surface, the system stays there) and reachability (the system quickly reaches the surface from any initial state). This ensures the system follows the desired behavior efficiently and remains stable.

The linear-quadratic (LQ) approach is a popular choice for sliding mode control (SMC). Here, the sliding surface is a weighted combination of system states, balancing performance trade-offs. The switching function is a sign function of the sliding surface, scaled by a constant to control switching speed and robustness. This method is simple and works well, offering optimal performance and robustness for linear or easily adjustable nonlinear systems.

The integral-sliding mode (ISM) approach is another popular SMC method. The sliding surface is based on the integral of system states, weighted for performance balance. The switching function uses a sign function of the sliding surface, scaled by a constant to control switching speed and robustness. This approach is flexible and adapts well to unknown or changing uncertainties, making it effective for handling disturbances in dynamic systems.

While SMC has many benefits, it also faces challenges. For nonlinear systems, it can be hard to design a sliding surface that ensures stability and reachability. Another issue is chattering, where control inputs oscillate rapidly, reducing performance and causing wear on actuators. Additionally, SMC requires quick and accurate measurements of system states, which might not always be possible, limiting its use in some applications.