2DoF Controller Parameterization for Nonlinear Plant Inversion
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Solution Overview
Problem
Designing and parameterizing a Two Degree of Freedom (2DoF) controller for nonlinear plants is challenging due to the difficulty in inverting nonlinear dynamic models, requiring highly skilled experts and time-consuming tuning processes.
Innovation Solution
The method involves modeling the nonlinear plant with a chosen model structure, separating it into nonlinear static and dynamic parts, and using these parts to approximate the plant's inverse for the feedforward controller, allowing for easier parameterization through testrun data identification and inversion of static maps, while the feedback controller is simplified to compensate for model mismatches.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a Two Degree of Freedom controller with inverse plant model is used for nonlinear plants, then reference tracking performance and disturbance rejection are improved, but the controller cannot be easily designed due to difficulty in inverting nonlinear plant models
Solution Approach 1:
The plant model is segmented into two distinct parts: a nonlinear static part (represented by a static map) and a nonlinear dynamic part (represented by a dynamic model with parameters). This segmentation allows the inverse to be computed more easily by inverting the static map separately while using the dynamic model for the time-varying behavior, avoiding the need to invert the complete nonlinear dynamic model directly.
Solution Approach 2:
A static map is introduced as an intermediary element between the control input and the plant output. This static map captures the nonlinear static relationship and can be inverted more easily than the full nonlinear dynamic model. The static map serves as a mediator that simplifies the inversion process while the dynamic model handles the transient behavior.
2Measurement precision
If traditional controller parameterization methods are used for nonlinear plants, then control accuracy can be achieved, but highly skilled experts and time-consuming tuning processes are required
Solution Approach 1:
The controller parameterization process is made self-service through automated identification procedures. Testrun data from the actual plant is automatically processed to identify the static map and dynamic model parameters. This eliminates the need for manual expert tuning while maintaining control accuracy, as the identification algorithms automatically adapt the controller parameters to the specific plant being controlled.
Solution Approach 2:
The controller parameters are changed from fixed manual tuning values to dynamically identified parameters based on actual plant testrun data. The static map and dynamic model parameters are automatically determined through systematic identification procedures, allowing the controller to adapt to different plants without requiring expert intervention for each specific case.
3Ease of manufacture
If a simple controller design is used, then ease of parameterization is improved, but the controller cannot adequately handle nonlinear plant behavior
Solution Approach 1:
The controller uses local linearization through the static map inversion at the current operating point. By inverting the static map locally around the current state, the controller achieves accurate local control behavior that adapts to nonlinear plant characteristics. This local quality approach allows simple controller structures to handle nonlinear behavior effectively by continuously adapting to the local plant characteristics.
Data Source
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AI summary
To be able to easily control a technical system as plant (1) with a Two Degree of Freedom controller (2) having a feedforward controller (3) and a feedback controller (4) it is provided that the inverse of the plant (1) for the feedforward controller (4) is constituted by a nonlinear dynamic part and a nonlinear static part, whereas an inverted static map (21) of the plant (1) is provided as nonlinear static part and the nonlinear dynamic part is formed as function of the system parameters (K, τ) of a model of the plant (1) and of a desired output variable (ydes) of a desired closed loop behaviour of the plant (1) and the dynamic output (ydyn) of the nonlinear dynamic part and the state variable (x) are fed into the inverted map (21) of the nonlinear static part that outputs the output (uFF) of the feedforward controller (3).