Closed-Loop Input Design for Sheetmaking CD Model Identification
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Solution Overview
Problem
Current methods for identifying process models in continuous sheetmaking systems, particularly in the cross-direction (CD) process, face challenges due to ill-conditioned processes and large uncertainties, requiring interruptions in normal operations to generate good quality data, which leads to significant profit losses.
Innovation Solution
The method involves converting the non-causal process model into a causal equivalent model to simplify the optimal spatial input spectrum design, allowing for the generation of optimal excitation signals without interrupting normal operations, thereby obtaining reliable process data for model predictive control (MPC) in closed-loop systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If open-loop optimal input design is used to generate good quality process data for model identification, then measurement precision is improved, but productivity deteriorates due to interruption of normal operations
Solution Approach 1:
The patent implements closed-loop optimal input design where the excitation signal is generated based on feedback from the current process model and controller state. The method calculates the optimal input spectrum using the existing closed-loop system information, allowing continuous operation while gathering identification data. This resolves the contradiction by eliminating the need to open the control loop, thus maintaining productivity while achieving measurement precision through optimized excitation signals.
Solution Approach 2:
The patent performs preliminary calculation of the optimal input spectrum using the current process model before applying the excitation signal. By pre-computing the optimal excitation based on existing model information, the system can continuously operate without interruption while the pre-calculated optimal signal ensures high-quality data collection for model identification.
2Measurement precision
If traditional closed-loop optimal input design is applied to CD processes, then device complexity increases due to large matrix operations, but measurement precision is improved
Solution Approach 1:
The patent segments the complex CD process model identification problem by exploiting the spatial structure and assumptions about actuator response behavior. Instead of handling the full large-scale MIMO system directly, the method divides the problem into manageable components by assuming identical temporal and spatial response behavior across actuators, allowing the optimal input spectrum to be computed for each segment independently or with reduced computational burden.
Solution Approach 2:
The patent changes the parameter representation by working in the frequency domain and using spectral representations instead of time-domain matrix operations. By transforming the optimal input design problem into the frequency domain and utilizing the spectral properties of the process, the method reduces computational complexity while maintaining measurement precision for model identification.
Data Source
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AI summary
Sheetmaking cross-directional (CD) control requires a sophisticated model-based controller whose operation requires an accurate model of process behavior, but due to the complexity of the process, identifying these process models is challenging. Current techniques rely on open-loop process experimentation. Using non-causal scalar transfer functions for the steady-state CD process model and controller model avoid the problem of large dimensions associated with the CD process. These non-causal transfer functions can be represented by causal transfer functions that are equivalent to the non- causal ones in the sense of the output spectrum. A closed-loop optimal input design framework is proposed based on these causal equivalent models. CD actuators have responses in both sides along the cross direction which can be viewed as a non-causal behavior. Techniques to perform the non-causal modeling are demonstrated and developed in a closed-loop optimal input design framework based on non-causal modeling of the closed-loop CD process.