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Design of an optimal preview controller for linear discrete-time descriptor noncausal multirate systems
1School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China ; School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China.
Thescientificworldjournal
|March 5, 2014
Summary
A new method designs optimal preview control for linear discrete-time descriptor noncausal multirate systems. This approach transforms complex systems into simpler forms for deriving effective control laws.
Area of Science:
- Control Theory
- System Engineering
- Signal Processing
Background:
- Linear discrete-time descriptor noncausal multirate systems present unique control challenges.
- Existing control methods may not directly address the noncausal and multirate characteristics simultaneously.
- Optimal preview control is crucial for systems requiring future information.
Purpose of the Study:
- To present a novel design approach for optimal preview control.
- To develop a systematic method for handling linear discrete-time descriptor noncausal multirate systems.
- To derive an optimal preview controller for these complex systems.
Main Methods:
- Transformation of noncausal systems into causal closed-loop systems.
- Conversion of descriptor causal systems into normal systems using elementary transformations.
- Application of the discrete lifting technique to convert multirate systems to single-rate systems.
- Construction of a descriptor augmented error system using standard preview control methods.
Main Results:
- A new single-rate system is obtained with a derived optimal control law.
- The quadratic performance index for the multirate system is adapted for the single-rate system.
- The optimal preview controller for the original system is successfully derived.
- Stabilizability and detectability of the lifted single-rate system are analyzed.
Conclusions:
- The proposed method provides an effective framework for optimal preview control design.
- The techniques successfully simplify complex noncausal multirate systems for control.
- Simulation results validate the effectiveness of the derived optimal preview control techniques.
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