تجزیه و تحلیل حساسیت برای محدودیت های انتخابی و تنظیم تنوع در ارزیابی عملکرد صنعتی MPC
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|25980||2008||21 صفحه PDF||سفارش دهید||محاسبه نشده|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Control Engineering Practice, Volume 16, Issue 10, October 2008, Pages 1195–1215
This paper is concerned with economic performance assessment of industrial model predictive control (MPC) applications for processes with constraints. The interest of this paper is to find sensitive process variables, which are the most contributive to the economic performance of MPC. Optimization algorithms for sensitivity analysis are presented for both constraint and variability tuning of industrial MPC applications. Several new problems related to sensitivity properties of process variables, which arise in the actual MPC economic performance assessment, are addressed. Industrial case studies are included to demonstrate how the proposed sensitivity analysis can be used to provide practical and selective tuning guidelines in industry.
Successful implementations of model predictive control (MPC) can now be seen in a wide variety of industrial application areas, which include pulp and papers, refinery, petrochemical, bio-tech industries, food processing, air and gas plants, power, etc., due to its capabilities and appealing advantages, such as economic optimization, constraints handling, accurate trajectory tracking control, etc. It has been demonstrated as one of the most effective and widely used advanced process control strategies to deal with multivariable systems with input and output constraints. It computes a sequence of predictive manipulated variable (MV) adjustments that optimize the future behavior of a plant with constraints and, among the optimal control moves, only the first one is adopted as the current control law. A receding horizon strategy then applies on-line to repeat the procedure with new measurements obtained from the system at the next sample time. Regarding innovative advancements of this algorithm and its applications, there has been a large amount of work in the literature including survey articles and books (Camacho and Bordons, 1998, Kwon and Han, 2005, Maciejowski, 2002, Morari and Lee, 1999, Qin and Badgwell, 2003 and Rawlings, 2000). Actually, in industries, MPC technology products have been developed by several venders and implemented to many industrial process units (Kassmann et al., 2000, Krishnan et al., 1998 and Sorensen and Cutler, 1998); see the recent industrial MPC survey paper (Qin & Badgwell, 2003). On the other hand, it is noted that less effort has been made on the performance assessment of existing constrained MPC applications, while the performance assessment of conventional unconstrained controllers has been well studied such as in Harris (1989), Harris, Boudreau, and Macgregor (1996), Huang, Shah, and Kwok (1997), Huang and Shah (1999), Xu, Lee, and Huang (2006), Choudhury, Shah, Thornhill, and Shook (2006), Jelali (2006), Salsbury (2007), Srinivasan, Rengaswamy, and Miller (2007) and Bauer and Craig (2008). The MPC scheme has been used to maneuver processes closer to their physical limits in order to obtain a better economic performance according to the external market requirements (Muske, 2003). It is known that the benefit potential comes when the operating point is moved closer to the limit of constraints. Very recently, Xu, Huang, and Akande (2007) studied an MPC performance assessment method with considerations of economic benefit and input and output constraint limits using the back-off approach (Figueroa et al., 1996, Lear et al., 1995, Loeblein and Perkins, 1998, Loeblein and Perkins, 1999 and Seferlis and Grievink, 2001). The MPC economic performance is evaluated by solving linear and quadratic benefit potential problems in Xu et al. (2007). Xu et al. also suggests tuning guidelines for MPC applications via reducing the variability of controlled variables (CVs) or relaxing the constraint limit of CVs and MVs. The applicability of the method has been demonstrated via simulation examples and pilot-scale experiments. It is noted that, unlike reducing the variability of process variables (PVs), adjusting the constraint limits of MPC applications is a simpler tuning method for MPC applications for improving the economic benefit, which can be done without any dynamic controller tuning effort. In this case, the desired benefit potential can be achievable by simply changing the plant operating point with new constraint limits adjusted according to the MPC economic assessment method. The suggestion in Xu et al. (2007) will be useful to industrial processes. However, for the large size of industrial processes, that is, systems with a large number of CVs and MVs, the performance tuning method in Xu et al. (2007) will not be selective in finding PVs of priority. In most cases, the tuning method in Xu et al. (2007) suggests changing many of CVs and MVs to improve economic profit. In industry, process systems are of large size and all variables are not necessary to change. In practice, it is noted that field process and control engineers have made great efforts to minimize risk, which may result from the controller or the plant operation changes. Also, there are cases where some of the constraint limits are not allowed to change simultaneously. It is clear that a more practical and selective method is required in the economic performance assessment and tuning of industrial constrained MPC applications. This paper approaches this MPC constraint and variability tuning problem via sensitivity analysis. That is, it is interested in finding the most sensitive or profitable PVs that contribute to the economic profit. Although Xu et al. (2007) mentioned a heuristic method to find sensitive PVs, it has a limited use and in worst-case, it needs to search the whole variable domain to find sensitive PVs. In this paper, a convex optimization based sensitivity analysis method is developed for the economic performance assessment and tuning of MPC applications as an extension of the method in Xu et al. (2007). New optimization algorithms for sensitivity analysis are presented for both selective constraint and variability tuning of industrial MPC applications. The significant objective of sensitivity analysis should be to provide a quantitative suggestion when some tuning guidelines need to achieve a given desired benefit potential. That is, this paper is interested in providing a suggestion for the questions: Which CV/MV is sensitive or profitable for economic performance? How much does it need to be tuned or changed to achieve a given desired benefit potential? In addition, via the proposed sensitivity analysis, this paper represent an attempt to shed light on several new aspects related to sensitivity properties of PVs, i.e., coupled sensitivity and varying sensitivity, which actually arise in the MPC economic benefit analysis. The sensitivity properties and some difficulties in sensitivity analysis will be discussed in detail in the present paper. The proposed economic optimization problem for sensitivity analysis leads to a convex quadratic programming (QP) problem, which can be solved by QP solvers (Coleman, Branch, & Grace, 1999). The QP problem can also be converted to a semi-definite programming (SDP) problem, which can be solved by SDP solvers (Gahinet et al., 1995, Sturm, 1999 and Vandenberghe and Boyd, 1996). The outline of this paper is as follows. A basic problem formulation for the MPC economic performance assessment is described briefly and the issue of interest in this paper is discussed in Section 2. A convex optimization based sensitivity analysis approach is developed for selective constraint and variability tuning of industrial MPC applications in Section 3. A case study of a diluent recovery unit is included in order to illustrate the economic performance assessment of an MPC application and the proposed sensitivity analysis for constraint and variability tuning in Section 4. An industrial case study of a hydrogen unit is also included in order to demonstrate the validity of the proposed sensitivity analysis and selective tuning guideline in practice in Section 5. Finally, concluding remarks are given in Section 6. Notations used in the paper are summarized in the nomenclature.
نتیجه گیری انگلیسی
This paper has studied economic performance assessment of industrial model predictive control (MPC) applications. A sensitivity analysis approach has been proposed for providing a practical and selective method in the economic performance evaluation and tuning of run-time constrained MPC applications. Via sensitivity analysis, the optimization problem of finding sensitive PVs which are most contributive to the economic performance of MPC applications has been attempted such that controller tuning efforts or plant constraint limit changes are possibly minimized. The proposed economic optimization problems for sensitivity analysis lead to a convex QP problem or a SDP problem, which can be solved in polynomial time by using existing efficient interior-point optimization solvers. In addition, several new sensitivity properties of PVs, which arise in the actual MPC performance assessment, have been discussed in this paper. Through industrial case studies of a diluent recovery unit and a hydrogen unit, the applicability of the proposed sensitivity analysis is demonstrated. The proposed optimization algorithms have been integrated into a plant oriented solution package for industrial MPC economic performance monitoring.