Gaussian Process PID Tuning for Multivariable Control
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Solution Overview
Problem
Tuning multiple, coupled PID controllers in industrial applications can be tedious due to their complexity, especially in multivariable systems, where existing methods require significant a priori knowledge and are not efficient for optimal control.
Innovation Solution
A method using a Gaussian process model to optimize PID control policies by representing multivariable PID controllers as parametrized static state feedback laws, allowing for gradient-based optimization of a cost function without prior knowledge of system dynamics, and incorporating state augmentations to track errors and their derivatives for improved prediction and control.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If traditional PID tuning methods are used for multivariable systems, then the control structure remains simple and widely available, but the tuning process becomes tedious and requires significant a priori knowledge
Solution Approach 1:
The patent transforms the PID tuning problem from a manual parameter adjustment task into an automated optimization problem by changing the parameters from traditional PID gains to cost function weights (Q, R, S matrices) that can be optimized using systematic methods without requiring deep system knowledge
Solution Approach 2:
The patent replaces the manual mechanical tuning process with an automated computational optimization system using gradient-based methods and Gaussian process models, eliminating the need for expert intervention and a priori system knowledge
2Productivity
If gradient-based optimization is used to optimize PID control policies, then the tuning efficiency is improved and a priori knowledge is not required, but the computational complexity increases
Solution Approach 1:
The patent introduces a Gaussian process model as an intermediary that approximates the complex system dynamics and cost function gradients, enabling efficient optimization without requiring direct computation of complex derivatives from first principles
Solution Approach 2:
The patent performs preliminary system identification and Gaussian process model training before the actual PID optimization, preparing the computational framework in advance to enable faster subsequent optimization iterations
Data Source
AI summary
A method for devising an optimum control policy of a controller for controlling a system includes optimizing at least one parameter that characterizes the control policy. A Gaussian process model is used to model expected dynamics of the system. The optimization optimizes a cost function which depends on the control policy and the Gaussian process model with respect to the at least one parameter. The optimization is carried out by evaluating at least one gradient of the cost function with respect to the at least one parameter. For an evaluation of the cost function a temporal evolution of a state of the system is computed using the control policy and the Gaussian process model. The cost function depends on an evaluation of an expectation value of a cost function under a probability density of an augmented state at time steps.