Controller Reconfiguration for Stable Switching
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Solution Overview
Problem
Current techniques for switching between controllers in industrial applications often result in large transients and can lead to closed-loop instability, especially due to plant model uncertainty, and lack practical implementation simplicity.
Innovation Solution
A controller re-configuration technique that allows for arbitrary switching between multiple linear multivariable controllers, ensuring exponential stability and allowing for the computation of robust stability bounds, with each controller component being realized as long as it has no unstable internal modes and only the input-output characteristics are important.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If ad hoc switching techniques are used between controllers, then controller switching is possible, but large transients are induced and closed-loop instability can result
Solution Approach 1:
The patent applies preliminary action by pre-computing a switching control law that accounts for future switching events. The control input u(t) is designed to anticipate switching times τ_i and adjust the control signal accordingly, ensuring continuity and avoiding large transients. This is achieved by integrating the system dynamics forward in time from each switching point, allowing the controller to prepare for upcoming switches rather than reacting to them.
Solution Approach 2:
The patent implements feedback by using the measured plant output y(t) in the switching control law. The control input u(t) depends on the current state of the plant through the output measurement, creating a closed-loop system that actively responds to plant behavior. This feedback mechanism ensures that switching decisions are based on actual system conditions, maintaining stability despite arbitrary switching signals.
2Reliability
If highly mathematical designs are used for switching, then stability analysis is possible, but implementation difficulty increases
Solution Approach 1:
The patent extracts the complex stability analysis from the implementation by providing a explicit switching control law formula. Instead of requiring implementers to perform complex mathematical stability proofs, the patent separates the theoretical analysis (which guarantees stability) from the practical implementation (which uses a straightforward control law involving integration and switching functions). This allows stability assurance without implementation complexity.
Solution Approach 2:
The patent changes the parameter representation from abstract mathematical conditions to concrete computational operations. The switching control law is expressed in terms of integrable functions and standard operations that can be directly implemented in industrial controllers. By transforming the mathematical design into parameterized control signals that depend on measurable quantities, the patent makes the solution both rigorously stable and practically implementable.
3Adaptability or versatility
If plant model uncertainty is present, then realistic industrial conditions are reflected, but robust stability becomes harder to guarantee
Solution Approach 1:
The patent applies dynamics by formulating the switching control law in terms of the plant's dynamic behavior. The control input u(t) is designed to counteract the effects of model uncertainty by incorporating the plant's dynamic response characteristics. The switching law adapts to changing plant conditions by continuously integrating the actual plant output, allowing the controller to maintain stability even when the plant model is uncertain or changes over time.
Data Source
AI summary
A controller design for switching between m linear multivariable controllers each of whom stabilizes a linear plant has been presented. A Youla-Kucera factorization was exploited in the interest of obtaining a closed-loop system that is exponentially stable for any switching signal σ(t) in the absence of plant model uncertainty. Robustness to practical model uncertainty was also considered and lower and upper bounds on the tolerable magnitude of unstructured additive plant uncertainty were presented. Numerical example demonstrated that the two controller degrees of freedom in the proposed controller design could be used to separately modify the closed-loop steady-state (with respect to σ(t)) performance and the switching transients.