Non-linear Controller Design Using Multi-criteria Evolutionary Algorithm
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Solution Overview
Problem
Conventional linear controllers are ineffective for non-linear systems, and existing methods for designing non-linear controllers for local model networks do not adequately account for stability and behavior quality values during the controller design process, leading to complex and costly re-designs.
Innovation Solution
A multi-criteria evolutionary algorithm is used to determine and optimize controller parameters, considering stability and behavior quality values, such as the Lyapunov criterion and tolerance range, to design an optimal non-linear controller for local model networks, allowing for direct determination of characteristic maps for control devices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If conventional linear controllers are used for non-linear systems, then the controller design is simple, but the control performance is unsatisfactory
Solution Approach 1:
The non-linear system is divided into multiple local linear models, each valid in specific operating ranges. Local PID controllers are designed for each local model, and the global controller output is determined by interpolation of local controller outputs. This segmentation allows simple linear controller designs to achieve better overall performance on non-linear systems.
Solution Approach 2:
The controller parameters are optimized using a multi-criteria evolutionary algorithm that adjusts parameters to simultaneously satisfy stability criteria (Lyapunov criterion) and behavior requirements (tolerance range). This parameter optimization transforms a simple controller structure into one that delivers reliable control performance for non-linear systems.
2Reliability
If local model network with local linearizations is used, then control performance improves, but the design process becomes complex and time-consuming
Solution Approach 1:
The stability and behavior quality values are determined and optimized during the controller design stage using a multi-criteria evolutionary algorithm, rather than checking them after design completion. This preliminary optimization of controller parameters ensures that the controller meets stability criteria and behavior requirements from the outset, avoiding time-consuming re-design cycles.
Solution Approach 2:
The multi-criteria evolutionary algorithm uses feedback from stability criteria (Lyapunov criterion) and behavior requirements (tolerance range compliance) to iteratively optimize controller parameters. This feedback mechanism automatically adjusts parameters to achieve both stability and desired behavior, significantly reducing manual design iteration time.
3Adaptability or versatility
If stability and behavior are checked after controller design, then design flexibility is maintained, but optimization is not possible and re-design is costly
Solution Approach 1:
Stability criteria and behavior quality values are determined and integrated into the controller design process from the beginning. The multi-criteria evolutionary algorithm optimizes controller parameters to simultaneously satisfy these criteria during design, rather than checking them afterward. This preliminary optimization maintains design flexibility while eliminating costly re-design cycles.
Solution Approach 2:
Controller parameters are systematically optimized using evolutionary algorithms that adjust parameters to meet stability and behavior requirements. This parameter optimization transforms the design process from a flexible but inefficient trial-and-error approach to a systematic method that achieves both adaptability and design efficiency.
4Manufacturing precision
If characteristic maps are calibrated at test bench, then controller accuracy is ensured, but extensive test runs and calibration time are required
Solution Approach 1:
Characteristic maps for controller parameters are determined directly from the optimized non-linear controller using the multi-criteria evolutionary algorithm, before any test bench calibration. The Pareto front with optimal controller parameters is generated in advance, allowing characteristic maps to be parameterized from simulation results rather than requiring extensive empirical calibration at the test bench.
Solution Approach 2:
The optimized controller parameters and characteristic maps are derived from the mathematical model and optimization results, creating a virtual prototype that can be directly transferred to the physical system. This copying approach from simulation to reality reduces the need for extensive physical calibration while maintaining accuracy.
Data Source
AI summary
For the determination of a non-linear controller for a non-linear system it is proposed that a parameter set (KPID(k)) of the controller (1) is determined by means of an optimization using a multi-criteria evolutionary algorithm, in which algorithm a plurality of parameter sets (KPID(k)), which each represent a possible solution of the optimization, are determined in each evolution step and at least two quality values (fi) are determined for each parameter set (KPID(k)) and the quality values (fi) are optimized by the multi-criteria evolutionary algorithm.