Controlling a non-linear process

Abstract

System and method for modeling a nonlinear process. A combined model for predictive optimization or control of a nonlinear process includes a nonlinear approximator, coupled to a parameterized dynamic or static model, operable to model the nonlinear process. The nonlinear approximator receives process inputs, and generates parameters for the parameterized dynamic model. The parameterized dynamic model receives the parameters and process inputs, and generates predicted process outputs based on the parameters and process inputs, where the predicted process outputs are useable to analyze and / or control the nonlinear process. The combined model may be trained in an integrated manner, e.g., substantially concurrently, by identifying process inputs and outputs (I / O), collecting data for process I / O, determining constraints on model behavior from prior knowledge, formulating an optimization problem, executing an optimization algorithm to determine model parameters subject to the determined constraints, and verifying the compliance of the model with the constraints.

Description

PRIORITY AND CONTINUATION DATA[0001]This application is a divisional application of U.S. application Ser. No. 10 / 842,157, titled “Parametric Universal NonLinear Dynamics Approximator and Use”, filed May. 10, 2004, whose inventors were Bijan Sayyar-Rodsari, Edward Plumer, Eric Hartman, Kadir Liano, and Celso Axelrud, which claims benefit of priority to U.S. Provisional Application 60 / 545,766 titled “Parametric Universal Nonlinear Dynamics Approximator and Use”, filed Feb. 19, 2004, whose inventors were Bijan Sayyar-Rodsari, Edward Plumer, Eric Hartman, Kadir Liano, and Celso Axelrud, and which is a Continuation-In-Part of U.S. application Ser. No. 10 / 730,835, titled “System and Method of Adaptive Control of Processes with Varying Dynamics”, filed Dec. 9, 2003, whose inventors were Bijan Sayyar-Rodsari, Eric Hartman, Celso Axelrud, and Kadir Liano, which issued as U.S. Pat. No. 7,039,475, and which claims benefit of priority to U.S. Provisional Application 60 / 431,821 titled “Parametri...

AI Technical Summary

Benefits of technology

[0043]The PUNDA model disclosed herein allows the empirical information and / or the first-principles knowledge available about the process to be systematically used in building a computationally efficient model of the physical process that is suitable for online optimization and control of the process, i.e., substantially in real time. Additionally, such a model may be capable of approximating the nonlinear physical process with any desired degree of accuracy.

Problems solved by technology

However, the complexity of most real world systems generally precludes the possibility of arriving at such solutions analytically, i.e., in closed form.

Each of these two approaches has substantial strengths and weaknesses when applied to real-world complex systems.

2. First-principles information is often incomplete and / or inaccurate, and so the model and thus its outputs may lack the accuracy required.

4. FP models may be computationally expensive and hence useful for real-time optimization and control only in slower processes.

5. When the process changes, modification of the first principles model is generally expensive.

Regarding empirical models:

1. Since data capture the non-idealities of the actual process, where data are available, an empirical model can often be more accurate than a first-principles model.

2. The available data are often highly correlated and process data alone is not sufficient to unambiguously break the correlation. This is particularly apparent when process operation is recipe-dominated. For example, in a linear system with 2 inputs and 1 output, a recipe may require two inputs to move simultaneously, one to increase by one unit and the other to decrease by one unit. If the output increases by one unit, the sign and value of the gain from the two inputs to the output cannot be uniquely determined based on these data alone.

3. Additional designed experiments are often needed in order to produce the necessary data for system identification; however, designed experiments disrupt the normal operation of the plant and hence are thus highly undesirable.

4. Certain regions or regimes of operation are typically avoided during plant operation, and hence the representative data for that region may not be available.

1. When the FP model does not fully describe the process. For example, if FP information for only a part of the process is known, a combined model of the process that is appropriate for optimization and control cannot be built based on the prior art techniques (e.g., using the system of FIG. 2), even if representative measurements of all the relevant process variables are available.

2. When the FP model only implicitly describes the relationship between inputs / states / parameters / outputs. The prior art approaches do not address the issue of training a neural network that models the parameters of an implicit FP model.

3. When higher-order fidelity of the input / output mapping (such as first or second order derivatives of the outputs with respect to the inputs) is critical to the usability of the combined model for optimization and control. Prior art does not address the imposition of such constraints in the training of neural network models in the context of combined models as depicted in FIG. 2.

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