A novel anti-windup framework for cascade control systems: an application to underactuated mechanical systems

Area of Science:

• Control Systems Engineering
• Nonlinear Control Theory
• System Stability Analysis

Background:

• Actuator saturation in cascade control systems leads to performance degradation and instability.
• Existing anti-windup compensator (AWC) designs often lack comprehensive solutions for both stable and unstable cascade plants.

Purpose of the Study:

• To develop novel anti-windup compensator (AWC) design methodologies for stable and unstable cascade plants with actuator saturation.
• To introduce two full-order decoupling AWC architectures ensuring closed-loop system equivalence.
• To provide a comparative analysis of the proposed AWC architectures for practical implementation.

Main Methods:

• Development of two novel full-order decoupling AWC architectures based on closed-loop system equivalence.
• Formulation of AWC synthesis using assured equivalence between coupled and decoupled architectures.
• Design of global AWC methodologies using linear matrix inequalities (LMIs), Lyapunov theory, global sector condition, and ℒ2 gain reduction.
• Derivation of an LMI-based local AWC design for unstable cascade plants using a local sector condition and quadratic Lyapunov function.

Main Results:

• Two distinct AWC architectures are proposed, addressing windup effects in cascade systems.
• One architecture offers computational efficiency, while the other is tailored for unstable cascade systems.
• Global and local AWC design methodologies based on LMIs are successfully developed.
• Effectiveness demonstrated through simulations and practical implementation on a ball-and-beam system.

Conclusions:

• The proposed AWC design methodologies effectively mitigate windup effects in stable and unstable cascade plants under actuator saturation.
• The developed decoupling architectures offer flexible solutions with trade-offs in computational complexity and suitability for unstable systems.
• LMI-based approaches provide a systematic framework for synthesizing robust anti-windup compensators, validated by experimental results.