Continuous-discrete interactions in chemical processing plants

Hybrid system is a dynamic system that involves continuous, discrete behaviors, and the interactions between continuous physical components and discrete controllers. In this paper a hybrid modeling language (called HML) for hybrid systems is extended with templates to achieve code reuse. For the formal analysis of the corresponding hybrid system models in this modeling language, these models are translated into SMT (satisfiability modulo theories) formulas as the input to an SMT solver dReal which retains the capability of bounded reachability analysis for non-linear hybrid systems. Moreover, dReal can produce data for potential traces of hybrid systems, thus it can be employed to simulate on hybrid systems. In this paper the simulation and reachability analysis are integrated in a prototype tool (open source). We present a case study for an inverted pendulum with PID (Proportional-Integral-Derivative) controllers and a rod reactor system for temperature control, both are verified to demonstrate the efficiency of the prototype tool. We conclude that, this modeling language is capable of modeling and verification of hybrid systems based on simulation and bounded reachability analysis.

It is challenging to provide students studying in chemical engineering, biotechnology and other related fields with an opportunity to tour and interact with a full-scale chemical processing plant. To address this challenge, an open-sourced virtual reality (VR) chemical processing plant was designed and built to provide students with an experiential learning opportunity. The VR plant is modelled after an ampicillin processing facility complete with a piping and instrumentation diagram (P&ID). The initial student experience inside the VR plant is a tour of the plant, various plant features and unit operations. The tour enables students to freely tour the plant but also engages them in a “Quest” style experience where they need to search for specific areas and components within the plant. An EngPad was designed to provide learners with a help tool to assist their navigation and strengthen their understanding during the VR experience. Experiential learning theory was used to guide the design of the VR application and take students through the four learning modes of concrete experience, reflective observation, abstract conceptualization, and active experimentation. A focus group provided feedback on the design and user interaction of the VR experience. This paper will outline how design features and enhancements were selected based on their connection to experiential learning theory.

Current synthesis methodologies for chemical process plants assume all design and operating conditions are constant values and thus overlook controllability issues. The controllability measures presented in this paper are intended to assess the controllability of a chemical process plant, through a simple and comprehensive methodology that allows an easy screening to determine a more controllable plant and state of operating conditions. In this paper, we address the controllability issues of two chemical plants, an HDA plant and an acrylic acid plant.

Modeling and Optimization for Short-term Scheduling of Multipurpose Batch Plants

This is paper proposes a new particle swarm optimization (NPSO) algorithm to short-term scheduling of single-stage batch plants with parallel units using the continuous-time domain representation. The model is formulated as a mixed-integer linear programming (MILP) problem. The key to the improvement of the algorithm is the introduction of mutation operators, crossover operators and some heuristic rules which can get better initialization population and no effect on the optimality of the scheduling problem. Computational examples show that NPSO are clearly more appropriate than GA and PSO algorithm in resolution for batch plants to minimize earliness for scheduling problems with due date constraints, and NPSO becomes more effective after involving heuristic rules

Optimal scheduling of batch plants satisfying multiple product orders with different due-dates

Control of liquid level in Interacting Two Tank Hybrid System (ITTHS) is highly challenging due to variation in the area of cross section. The modelling of such hybrid systems is different from the convention modelling techniques. Modelling and designing controllers for hybrid systems is an upcoming research area. This paper describes the modelling and control of such a highly non-linear system and also implementation of PID controller. The modelling of such hybrid systems is different from the convention modelling techniques. PID controller has been designed for this process application. Piecewise linearization technique was applied for linearizing non-linear system output. For all the five regions, separate PID controller has been designed and simulated using MATLAB. The performance measures of the system are tabulated.

Summary of the Basic StepsThe basic steps in the suggested procedure for the optimal design of multi-purposebatch plants can be summarized as follows:1. List the candidate product groups.2. Obtain the super-structure that contains the candidate groups.3. Derive the horizon constraints..4. Examine the horizon constraints. If at least one horizon constraintimplicitly contains all the time periods, complete the merged formulationand solve the MINLP given in Equations (38) to (44) with the correspondinghorizon constraints. Otherwise, go to step 5.5. Select a product(s) that breaks the loop(s) in the super-structure. Treat thechosen product(s) as two or more artificial products.6. Revise the super-structure to include the additional products. Verify thatthe loop is broken. If this condition is met, go to step 7. Otherwise,return to step 5 and modify the products chosen for splitting.7. Derive the multi-period form of the constraints for the product(s) that aresplit into its (their) values for the time periods in which it (they) appear.Formulate the merged representation of the model for the rest of theproducts, including the horizon constraints. At least one horizonconstraint will contain implicitly all the time periods.Example 2The seven product, ten stage example problem of Suhami and Mah (1982) has beensolved to illustrate the design of a large multi-purpose batch plant. From the super-structure of this problem (Figure 4), the horizon constraints shown in Table II arederived.Using these constraints, the example has been solved with the merged formulation.Data for this problem appears in Table III. In addition, the following specificationshave been used: H = 6200 hr, a = 250 SFr, fi = 0.6, 1 < N <, 3, and 250 < V£ 10,000. As seen in Table IV, the MINLP formulation involves 48 variables and 67constraints. MINOS/Augmented (Murtagh and Saunders, 1980) required 16.09 secondsof CPU-time on a DEC-20 computer to solve the relaxed nonlinear program.

The increasing interest in multipurpose batch plants is evident, because of their inherent flexibility to cope with an ever changing market environment. These plants are easily reconfigured for product modifications, to cover a wide range of operating conditions. They are also suitable for producing different products within the same facility. In spite of this advantage, the design, synthesis, and scheduling of multipurpose batch plants can be a challenging task. This paper addresses design, synthesis, and scheduling simultaneously. It is known that the scheduling platform employed has a significant impact on the computational performance of the overall model in the design and synthesis of batch plants. The recent scheduling model that results in better computational efficiencies is extended to incorporate design and synthesis. Computational studies are presented to illustrate the effectiveness of the proposed model. A comparison with earlier formulations showed that better computational times and objective functions were obtained by this work.

Hybrid dynamical systems contain both time-driven continuous dynamics and event-driven discrete dynamics that interact with each other, and their interactions determine the behavior of the system over time. To fully understand the tight interactions between discrete and continuous dynamics, we need a unified modeling framework. Various models have been developed for hybrid systems; they can be broadly classified into two groups according to their origins. On the one hand, computer scientists look at hybrid systems primarily as discrete (computer) programs interacting with the continuous environment. They extend their computational models, such as finite state machines, automata, and Petri nets, from discrete systems to hybrid systems by embedding the continuous-variable dynamics into these discrete models. On the other hand, researchers from the areas of dynamical systems and control regard hybrid systems as a collection of differential/difference equations with discontinuous or multi-valued variables. They extend the models and methodologies for traditional continuous-variable systems, such as those described by ordinary differential/difference equations, by including discrete variables to describe the jumping or switching phenomena. Both approaches have their own strengths. For instance, the first group of approaches has traditionally been able to deal with complex discrete dynamics emphasizing analysis results (verification) and simulation methodologies, while the second group typically deals with complex continuous-variable dynamics and mainly concerns itself with stability, robustness, optimality, and synthesis issues.

Design, synthesis and scheduling of multipurpose batch plants via an effective continuous-time formulation

This paper presents a hybrid system approach in the design of a singularityless task level controller. To achieve a singularityless motion control in the neighborhood of singularity, the hybrid system approach is used to integrate the task level controller and joint level controller. First, a hybrid system model is developed for the singularityless task level controller. A max-plus dynamic model is used to integrate the discrete switching control and continuous motion control in the controller. Based on this model, a smooth trajectory and control command for the hybrid system can be obtained. The Lyapunov theory was used to prove the stability of the singularityless controller. The new singularityless task level controller has been experimentally implemented and tested on a PUMA 560 robot manipulator. Experimental results have been employed to verify the theoretical conclusions, thus clearly demonstrating the advantages of the new task level control method.

The analysts and design of process topology is an important factor to ensure safety during the design and operation of chemical production plants as well as to support other lifecycle activities. This paper presents topology analysis mechanism, which is integrated within computer-aided engineering environment and used to support the design and operation of chemical production plants with considerations of process safety assessment. The proposed topology analysis is based on robust modeling methodology, which enabled the structuring of the accumulated design knowledge where fault propagation models are defined and mapped to process topology. A case study chemical production plant is used to illustrate the proposed solution

A survey of modeling and control of hybrid systems

Interval-based Solving of Hybrid Constraint Systems