Research ArticleController design approach based on linear programming

- We proposed an approach to solve observer gains by linear programming.
- The constraints can be obtained by the Routh-Hurwitz stability criterion.
- The object function can be obtained by the final-value theorem.
- The effectiveness of the proposed method is confirmed by simulations and experimental results with a DC motor.

This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor.