Efficient sensitivity analysis of large-scale differential-algebraic systems

Feehery, William F.; Tolsma, John; Barton, Paul I.

doi:10.1016/s0168-9274(97)00050-0

Cited by 191 publications

(142 citation statements)

References 9 publications

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“…where is the parameter covariance matrix, and is the jacobian computed using the nominal parameters and estimated states: (14) Equation (13) provides an easily implementable way to estimate the process noise covariance matrix, since the parameter covariance matrix is usually available from parameter estimation, and the sensitivity coefficients in can be computed by finite differences or via sensitivity equations (Feehery et al, 1997). Note that the above approach leads to a time-varying, full covariance matrix, which has been shown to provide better estimation performance for batch processes than the classically used constant, diagonal ( Valapil and Georgakis, 2000;Nagy and Braatz, 2003).…”

Section: State Estimationmentioning

confidence: 99%

Nonlinear Model Predictive Control of Batch Processes: An Industrial Case Study

Nagy

Mahn²,

Franke³

et al. 2005

IFAC Proceedings Volumes

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Batch processes play a significant role in the production of most modern highvalue added products. The paper illustrates the benefits of nonlinear model predictive control (NMPC) for the setpoint tracking control of an industrial batch polymerization reactor. Real-time feasibility of the on-line optimization problem from the NMPC is achieved using an efficient multiple shooting algorithm. A real-time formulation of the NMPC that takes computational delay into account is described. The control relevant model used in the NMPC is derived from the complex first principles model and is fitted to the experimental data using maximum likelihood estimation. A parameter adaptive extended Kalman filter (PAEKF) is used for state estimation and on-line model adaptation. The performance of the NMPC implementation is assessed via simulation and experimental results.

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Section: State Estimationmentioning

confidence: 99%

Nonlinear Model Predictive Control of Batch Processes: An Industrial Case Study

Nagy

Mahn²,

Franke³

et al. 2005

IFAC Proceedings Volumes

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show abstract

“…An important conclusion is that trajectory sensitivities are defined for complex event driven behaviour. Furthermore, it is shown that the sensitivities can be calculated efficiently as a by-product of using an implicit numerical integration technique, such as trapezoidal integration, to produce the nominal system trajectory [3,9].…”

Section: Trajectory Sensitivitiesmentioning

confidence: 99%

Iterative computation of marginally stable trajectories

Hiskens

2004

Intl J Robust & Nonlinear

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Stability limits place restrictions on the economic operation of power systems. Calculation of these limits is therefore very important, but has traditionally been quite difficult. This paper proposes an iterative algorithm for determining parameter values that result in marginal stability of a system. (A system is marginally stable for a particular disturbance if the postdisturbance trajectory lies on the stability boundary.) The algorithm is based on GaussNewton solution of a nonlinear least-squares problem. Gradient information is provided by trajectory sensitivities.

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“…For the sequential method, it also increases the cost of computing the sensitivity information by introducing extra sensitivity equations to the dynamic model. The integration of sensitivity equations can be a computationally dominant task despite the significant progress made so far regarding their efficient calculation (see [9][10][11]). This is especially true when the number of optimization variables is large, and can be a potentially limiting factor in applying dynamic optimization to large-scale processes.…”

Section: Introductionmentioning

confidence: 99%

Efficient Control Discretization Based on Turnpike Theory for Dynamic Optimization

Sahlodin

Barton

2017

Processes

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Dynamic optimization offers a great potential for maximizing performance of continuous processes from startup to shutdown by obtaining optimal trajectories for the control variables. However, numerical procedures for dynamic optimization can become prohibitively costly upon a sufficiently fine discretization of control trajectories, especially for large-scale dynamic process models. On the other hand, a coarse discretization of control trajectories is often incapable of representing the optimal solution, thereby leading to reduced performance. In this paper, a new control discretization approach for dynamic optimization of continuous processes is proposed. It builds upon turnpike theory in optimal control and exploits the solution structure for constructing the optimal trajectories and adaptively deciding the locations of the control discretization points. As a result, the proposed approach can potentially yield the same, or even improved, optimal solution with a coarser discretization than a conventional uniform discretization approach. It is shown via case studies that using the proposed approach can reduce the cost of dynamic optimization significantly, mainly due to introducing fewer optimization variables and cheaper sensitivity calculations during integration.

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Efficient sensitivity analysis of large-scale differential-algebraic systems

Cited by 191 publications

References 9 publications

Nonlinear Model Predictive Control of Batch Processes: An Industrial Case Study

Nonlinear Model Predictive Control of Batch Processes: An Industrial Case Study

Iterative computation of marginally stable trajectories

Efficient Control Discretization Based on Turnpike Theory for Dynamic Optimization

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