Perfect control for nonminimum-phase unstable systems defined in the multivariable continuous-time state-space...

Area of Science:

• Control Systems Engineering
• Systems Theory
• Robotics

Background:

• Nonminimum-phase unstable Linear Time-Invariant (LTI) Multiple-Input Multiple-Output (MIMO) systems present significant control challenges.
• Existing control strategies often struggle with ensuring stability for these complex systems.

Purpose of the Study:

• To propose a new perfect control law for continuous-time LTI MIMO systems.
• To ensure structural stability for nonminimum-phase unstable systems.
• To extend the applicability of inverse model control to a broader class of plants.

Main Methods:

• Development of a novel perfect control law based on inverse model control principles.
• Investigation of two distinct algorithms for control law implementation.
• Application of generalized inverses to guarantee structural stability.
• Validation using theoretical examples and practical simulations in Matlab/Simulink.

Main Results:

• One of the investigated algorithms proved to be highly accurate.
• The proposed control law is applicable to any right-invertible plants with more inputs than outputs.
• The perfect control procedure successfully guarantees structural stability, even for unstable systems.
• The study demonstrates that the nonminimum-phase property can be managed across the entire class of LTI MIMO continuous-time plants.

Conclusions:

• The newly introduced perfect control approach is feasible and effective for nonminimum-phase unstable LTI MIMO systems.
• The method provides a robust solution for achieving structural stability in complex control scenarios.
• This work expands the theoretical and practical understanding of control for challenging system dynamics.