Symbolic model order reduction: a new state feedback approach for simplified control and verification

Abstract

Abstract Symbolic model order reduction (SMOR) is an efficient technique for simplifying high dynamics models with a large number of states into fewer states by eliminating states with minimal impact and focusing the control design process on the dominant states. The reduction process facilitates the control design, and the resulting controller is verified using both the full and reduced models. In this study, a new symbolic model order reduction (SMOR) methodology is proposed, based on a state-feedback technique. The model is derived symbolically, and the contribution of each state to the input signal, along with the corresponding gains, is calculated symbolically as a function of the model’s physical parameters. Ultimately, the dominant and non-dominant states are identified, and the non-dominant states are eliminated. It is important to note that the physical parameters of the system remain in the reduced model to maintain a one-to-one correspondence, ensuring that both the inputs and outputs of the reduced model match those of the original model. The gains are calculated based on the reduced model, and the control law is verified using both the full and reduced models in the proposed algorithm and the Model Reducer Tool from MATLAB to ensure the effectiveness of the proposed methodology.

Keywords

• Symbolic control
• Symbolic model order reduction
• State-feedback
• High dynamics systems
• Inverted pendulum system
• Aircraft longitudinal autopilot