Design of robust discrete control with desirable quadratic stability

Area of Science:

• Control Systems Engineering
• Systems Theory
• Applied Mathematics

Background:

• Robust control design is crucial for uncertain systems.
• Quadratic stability is a key performance metric in control.
• Extending continuous-time control techniques to discrete-time systems presents challenges.

Purpose of the Study:

• To propose a robust discrete control design for quadratic stability.
• To investigate the influence of sampling time and domain on robustness.
• To demonstrate the algorithm's efficacy on practical systems.

Main Methods:

• An extended discrete version of a continuous robust quadratic stabilization technique was developed.
• The impact of sampling time selection on robustness was analyzed.
• The algorithm was applied to discrete mass-spring and car steering systems.

Main Results:

• The proposed discrete control design achieves desirable quadratic stability.
• Robustness was found to increase as sampling time decreases, up to a certain point.
• The algorithm proved feasible for both mass-spring and car steering systems.

Conclusions:

• The extended discrete robust control design is effective for achieving quadratic stability.
• Sampling time is a critical parameter influencing the robustness of discrete control systems.
• The methodology provides a viable approach for robust control in discrete systems.