A methodology for the simultaneous design and control of large-scale systems under process parameter uncertainty

https://doi.org/10.1016/j.compchemeng.2010.05.010Get rights and content

Abstract

This work presents a simultaneous design and control methodology for large-scale systems. The approach is based on the identification of an uncertain model from a first-principle process model. Using the identified uncertain model, a Structured Singular Value (SSV) analysis is used to estimate the realizations in the disturbance set that generates the worst-case variability and constraint violations. Then, simulations of the first-principle process model are performed with the critical disturbance profile as input to estimate the actual worst-case output variability and the worst-case variations in the process constraints. Since the proposed methodology is formulated as a nonlinear constrained optimization problem, it avoids the computationally expensive task of solving dynamic optimization problems, making it suitable for application to large-scale systems. The proposed methodology was tested on the Tennessee Eastman process to show that a redesign of the major process units in the process could significantly reduce the costs of this plant.

Introduction

Chemical processes are complex dynamic systems that are subject to external disturbances and uncertainty in the system parameters. The design of a chemical process has been traditionally performed using steady-state models which parameters are accurately known a priori. It is only at the later stages of the design that the dynamics of the system and the ability of the plant to reject disturbances are generally analyzed. It has been widely recognized that this sequential approach may not return an optimal design since control decisions are not considered in the specification of the process units (Luyben, 2004, Shiskey, 1982). Therefore, an integrated design and control strategy is needed to design a feasible plant that satisfies the design goals during both steady states and transients in the presence of external perturbations and process parameters’ uncertainties.

The calculation of the optimal design that simultaneously considers process design and control decisions is a complicated task since it involves trade-offs between the optimal steady-state operation of the plant and the dynamic operability of the plant under the effect of disturbances and in the presence of process parameter uncertainties. The optimal process design and control configuration must provide optimal performance for all possible combinations of the disturbance and the uncertain process variables, including those combinations that return the largest variability in the process output variables and in those variables that are required to be within constraints. The scenario that result in worst-case variability in either process output variables or alternatively it results in variables being at constraints is referred heretofore as worst-case scenario. Then, the final design must remain stable and feasible in the presence of any magnitude-bounded realizations in the disturbance variables and process parameter uncertainties.

Although several methodologies have been proposed to perform integration of design and control, e.g. Luyben and Floudas (1994), Kookos and Perkins (2001), Fuente and Flores-Tlacuahuac (2009), Malcolm, Polan, Zhang, Ogunnaike, and Linninger (2007), Sakizlis, Perkins, and Pistikopoulos (2004), Schweiger and Floudas (1998), Swartz (2004), Grosch, Monnigmann, and Marquardt (2008), Altimari and Bildea (2009), Chawankul, Ricardez-Sandoval, Budman, and Douglas (2007), Ricardez-Sandoval, Budman, and Douglas (2008), and Ricardez-Sandoval, Budman, and Douglas (2009), only a few methodologies have been applied to large-scale chemical systems, e.g. Alhammadi and Romagnoli (2004), Monnigmann and Marquardt (2005), and Ramirez and Gani (2007). A review of the current methodologies available to perform the integration of design and control can be found in Seferlis and Georgiadis (2004), Sakizlis et al. (2004) and Ricardez-Sandoval, Budman, and Douglas (2009b).

The present work presents a robust approach-based methodology that performs the simultaneous design and control of large-scale chemical processes under disturbances and process model parameter uncertainties. The proposed methodology expands upon a previous methodology introduced by the authors (Ricardez-Sandoval, Budman, & Douglas, 20009c). In that study, uncertain dynamic models of the process, obtained from the true mechanistic nonlinear dynamic closed-loop process model, were used to estimate analytical bounds on the worst-case variability and the process feasibility constraints. The bounds were computed using a formulation introduced by the authors based on a Structured Singular Value (μ) analysis. This methodology is referred heretofore as the Analytical Bounds Worst-case Approach (BWA).

The current work introduces two key novel features as compared to the previous study as follows: (i) Uncertainty in model parameters of the first-principle model is explicitly considered whereas in the earlier study this first-principle model was considered to be exact. (ii) The BWA methodology used analytical bounds on variability and constrained variables calculated from SSV analysis leading to an overall conservative design. Instead, in this work, the SSV analysis is used to calculate a worst disturbance whereas the corresponding worst-case variability in the output variables is calculated from simulations of the closed-loop first-principle process model. Although the use of simulation increases the computational demand, it leads to an overall less conservative design as compared to the previous work (Ricardez-Sandoval et al., 2009c) that calculated variability from analytical bounds. Because the proposed approach is based on a combination of analytical calculations and simulations it will be referred to as the Hybrid Worst-case Approach (HWA) to differentiate it from the analytical bounds based approach to be referred as BWA used in the earlier study.

To test the potential of the proposed methodology, the present work applies the method to an isothermal liquid storage tank and to the Tennessee Eastman (TE) process (Downs & Vogel, 1993). The first case study is used as a motivating example to illustrate the application of the methodology. The second case is used to demonstrate the application of the methodology to a large-scale chemical process such as the TE chemical plant. Studies on this plant have shown that the original design of the TE process units may imposed limitations on the performance of this system (Ramirez and Gani, 2007, Wu and Yu, 1997).

This paper is organized as follows: Section 2 presents the proposed mathematical formulation to assess the simultaneous design and control of large-scale systems under process parameter uncertainty. Section 3 shows the application of the proposed methodology to an isothermal liquid storage tank. Section 4 introduces the TE process. Section 5 presents the application of the proposed methodology to the reactor section of the TE process. A comparison in terms of the design and the computational time required by the HWA method proposed in the current study and the analytical bound-based approach (BWA) proposed in an earlier study is presented at the end of this section. Section 6 presents the integration of design and control of the complete TE plant. A comparison with an optimal set-point/controller tuning problem is presented at the end of this section. Concluding remarks are given in Section 7.

Section snippets

Simultaneous design and control methodology

This section discusses the two novel features presented in this work with respect to the previous work (Ricardez-Sandoval et al., 2009c) regarding uncertainty in process parameters and simulation-based calculations of largest output variability. Additional details regarding the basic method can be found in Ricardez-Sandoval et al. (2009c).

Motivating case study: an isothermal liquid storage tank

To illustrate the application of the methodology, the formulation presented in the previous section was used to simultaneously design and control an isothermal liquid storage tank. Fig. 2 presents the process flow-sheet for this system. The process involves an inlet and an outlet water flow-rate. The system is assumed to be at constant temperature and density. The material balance for this system is as follows:Adhdt=FinFoutFout=KCv1.45×104βg0hwhere A and h are the area and the height of the

The Tennessee Eastman process

The HWA methodology presented in the previous section was applied to the simultaneous design and control of the Tennessee Eastman (TE) plant (Downs & Vogel, 1993). This chemical process involves the production of two liquid products, G and H, and one by-product, F, from four reactants, A, C, D and E, and one inert, B. The process involves five unit operations: a two-phase exothermic reactor, a partial condenser, a liquid–vapour separator, a compressor and a stripper column. The irreversible

Scenario A: simultaneous design and control of the reactor section of the TE plant

The operation of the reactor has a significant effect on the stability and performance of the TE process. The reactions shown in (9) that produce products G and H occur in this unit. Thus, the reactor's nominal operating conditions determine the conversion and the yield of the products of this system. Since the reaction that produces G is temperature sensitive, there is a possibility of a thermal runaway if sudden changes in the reactor temperature occur. Therefore, the HWA formulation was

Scenario B: simultaneous design and control of the TE plant

The formulation presented in problem (16) was extended to consider the simultaneous design and control of the complete TE plant. That is, the capacities of the reactor, the flash unit and the stripper column were considered as optimization variables in this scenario. Also, the nine adjustable set points available in the plant, set points for loops 8–16 in Table 3, and the 17 PI controller tuning parameters were considered for optimization. Thus, the vector of decision variables is composed for

Conclusions

This paper presented a simultaneous design and control methodology for large-scale systems under disturbances and process parameter uncertainty. At each calculation step, an uncertain FIR model is identified from simulations of the dynamic first-principle process model. The identified uncertain model is used to calculate, based on a Structured Singular Value norm, the worst-case realization in the disturbance set and the critical value in the uncertain process parameters that generates the

Acknowledgements

The financial support provided by the Mexican National Council for Science and Technology (CONACYT) and the Natural Science and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.

References (24)

  • C.L.E. Swartz

    The use of controller parametrization in the integration of design and control

  • N. Chawankul et al.

    Integration of design and control: A robust control approach using MPC

    Canadian Journal of Chemical Engineering

    (2007)
  • Cited by (57)

    • Integration of design and control for industrial-scale applications under uncertainty: a trust region approach

      2020, Computers and Chemical Engineering
      Citation Excerpt :

      However, in the current trust region method, the critical disturbance profile is specified a priori and remains unchanged during the calculations. That is, the critical disturbance is not estimated at each step of the iterations as it is performed in (Ricardez-Sandoval et al., 2011). To make a fair comparison, a similar disturbance profile to the critical time-dependent profile found at the optimal solution by (Ricardez-Sandoval et al., 2011) for the TE plant is considered in this work.

    • Design and Control of a Vapour Recompression C<inf>3</inf> Splitter

      2020, Chemical Engineering Research and Design
    View all citing articles on Scopus
    View full text