Cross-Directional MPC Weighting Matrix for Actuator Picketing Prevention
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Solution Overview
Problem
Current CD-MPC systems face challenges in achieving robust spatial control performance due to parametric model uncertainty, leading to actuator picketing and instability, with a lack of easy-to-use techniques for tuning controllers to handle spatial and temporal aspects independently.
Innovation Solution
A CD-MPC design that explicitly accounts for parametric model uncertainty by determining the worst-case cutoff frequency, designing a weighting matrix to penalize high-frequency actuator variability, and adjusting a multiplier in the MPC cost function to ensure robust spatial stability, using a systematic automated procedure to tune the weighting matrix and ensure robust stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional CD-MPC control is implemented without explicit parametric uncertainty consideration, then the control system can be simpler to design, but actuator picketing occurs and spatial robustness is compromised
Solution Approach 1:
The patent applies preliminary action by determining the worst-case cutoff frequency before designing the weighting matrix. The method calculates the worst-case cutoff frequency based on parametric uncertainty bounds, then uses this pre-determined frequency to design the weighting matrix that penalizes high-frequency actuator variability. This preliminary determination of uncertainty bounds and cutoff frequency prevents actuator picketing before it occurs, rather than reacting to it afterward.
Solution Approach 2:
The patent applies parameter changes by modifying the weighting matrix parameters in the MPC cost function based on the worst-case cutoff frequency. Specifically, the weighting matrix is designed with frequency-dependent weights that increase penalty on actuator variability at frequencies above the worst-case cutoff frequency. This parameter adjustment ensures robust stability margins are maintained across all possible parametric variations within the uncertainty bounds.
2Object-generated harmful factors
If weighting matrix is designed to penalize high frequency actuator variability, then actuator picketing is prevented, but the tuning procedure becomes more complex
Solution Approach 1:
The patent applies self-service by providing an automated procedure that calculates the worst-case cutoff frequency and designs the weighting matrix without requiring manual trial-and-error tuning. The system automatically determines the uncertainty bounds from process models, computes the worst-case cutoff frequency, and generates the appropriate weighting matrix parameters. This automated self-service approach eliminates the need for complex manual tuning while still achieving the goal of preventing actuator picketing.
3Reliability
If robust stability is guaranteed under parametric uncertainty, then spatial control performance is improved, but the controller requires more sophisticated tuning techniques
Solution Approach 1:
The patent applies parameter changes by systematically adjusting the weighting matrix parameters based on the worst-case cutoff frequency derived from parametric uncertainty analysis. The method transforms the complex robust control tuning problem into a parameter optimization problem where the weighting matrix elements are explicitly determined as functions of the worst-case cutoff frequency and uncertainty bounds. This makes the tuning process more systematic and less dependent on operator expertise.
Solution Approach 2:
The patent applies feedback by using the worst-case cutoff frequency information to continuously adjust the weighting matrix parameters. The method incorporates feedback from the uncertainty analysis and stability margin requirements into the weighting matrix design, ensuring that the controller automatically adapts to maintain robust stability. This feedback mechanism eliminates the need for manual iterative tuning by providing direct guidance on appropriate parameter values.
Data Source
AI summary
Automated parameter tuning techniques for cross-directional model predictive control for paper-making under user-specified parametric uncertainties to reduce variability of the actuator and measurement profiles in the spatial domain is proposed. Decoupling properties of the spatial and temporal frequency components permit separate controller design and parameter tuning. CD-MPC design that explicitly accounts for parametric model uncertainty while finding MPC cost function weighing matrices that prevent actuator picketing and guarantee robust stability of the spatial CD profile. Picketing refers to periodic variation patterns in the actuator array. The inventive technique includes: (i) determining the worst case cutoff frequency of all process models, given parametric uncertainty, (ii) designing a weighing matrix to penalize high frequency actuator variability based on the process model and worst case cutoff frequency, and (iii) finding a multiplier for the spatial frequency weighted actuator variability term in the MPC cost function that assures robust spatial stability.