K Hariprasad

Optimal strategies for transitions in simulated moving bed chromatography

Abstract Simulated moving bed chromatography (SMBC) has emerged as a significant separation technology in the process industry. SMB operating parameters are chosen to satisfy various performance objectives such as maximization of purity or productivity and the choice of the objective is generally guided by process economics. From an industrial perspective, the SMB must be operated flexibly, so that the same unit can be operated to satisfy different objectives. Transiting from one objective to another entails large transition periods, resulting in an economic loss. We propose use of optimal transitions as an approach to minimizing transition time, reducing use of feed and desorbent during transition as well as reduction in off-specification product relative to a non-optimal, step change approach. Optimal transitions can also be used in recovering from feed upset scenarios. The above methods are demonstrated using simulations on a benchmark SMBC process for separation of glucose and fructose using Ca++ exchange resin.

Adaptive robust model predictive control of nonlinear systems using tubes based on interval inclusions

This article considers the adaptive robust constrained regulation problem for a class of nonlinear plants with bounded additive disturbances. The nonlinear dynamics of the plant are approximated as an uncertain Quasi-Linear Parameter Varying (Q-LPV) system in which the time varying parameter consist of an on-line adaptation of weights of multiple linear models. The overall multiple model representation consists of a convex combination of the individual models. The uncertainty bounds on the Q-LPV system are “designed” to include the plant-model mismatch in addition to the disturbance bounds. In particular, these uncertainty bounds are computed based on inclusion functions obtained using Bernstein polynomial and interval based bounding. The resulting robust regulation problem of the nonlinear plant is posed as Robust Tube Based Model Predictive Control (RTBMPC) of the uncertain Q-LPV system with “designed” uncertainty bounds. The proposed control strategy is demonstrated for robust regulation of Van de Vusse reactor, a significantly nonlinear system.

A dual-terminal set based robust tube MPC for switched systems

Abstract This article considers the robust regulation problem for a class of constrained linear switched systems with bounded additive disturbances. The proposed solution extends the existing robust tube based model predictive control (RTBMPC) strategy for non-switched linear systems to switched systems. RTBMPC utilizes nominal model predictions, together with tightened sets of state and input constraints, to obtain a control policy that guarantees robust stabilization of the dynamic systems in presence of bounded uncertainties. Similar to RTBMPC for non-switched systems, a disturbance rejection proportional controller is used to ensure that the closed loop trajectories of the switched linear system are bounded in a tube centered on the nominal system. To account for the switching dynamics, the gain of this controller is chosen to simultaneously stabilize all switching dynamics. The RTBMPC for the switched system requires an on-line solution of a Mixed Integer Quadratic Program (MIQP). To reduce the complexity of the MIQP, a sub-optimal design is proposed, which considers the notion of a pre-terminal set in addition to the usual terminal set used to ensure stability. The RTBMPC design with the pre-terminal set aids in tuning the trade-off between the complexity of the control algorithm with the optimal performance of the closed-loop system while ensuring robust stability. Examples are presented to illustrate features of the proposed MPC.

An Efficient and Stabilizing Model Predictive Control of Switched Systems

Model Predictive Control (MPC) of switched systems typically requires an on-line solution of a Mixed Integer Program (MIP). Since the worst case complexity of the optimization problem increases exponentially with respect to the number of integer variables, an on-line implementation of the MPC for problems with large number of sub-systems and/or large horizons is usually expensive. In this technical note, we propose a stabilizing MPC formulation for state-dependent switched systems, that enables a tradeoff between the computational complexity of the MPC controller and the optimal performance of the closed-loop system. The proposed approach uses a pre-terminal set, in addition to the positively invariant terminal set, which aids in reducing the on-line complexity although at the expense of optimality. Examples are presented to illustrate the computational benefits of the proposed MPC strategy over existing MPC for switched systems.

A Computationally Efficient Stabilizing Model Predictive Control of Switched Systems

Abstract Many applications in engineering exhibit switching character due to discrete and continuous aspects in their dynamic behavior. Switching characteristics of hybrid systems bring discontinuity and nonlinearity in their course of operation and pose major challenges in developing stabilizing Model Predictive Control (MPC) for them. For Piecewise Affine (PWA) Systems, the MPC problem requires on-line solution of Mixed Integer Programs (MIPs) for obtaining the input profile. Since, complexity of the optimization problem that needs to be solved in MPC increases combinatorially with respect to the integer variables, on-line computing of MPC control law for large scale problems and/or problems with large horizons is expensive. In this paper we, propose a MPC formulation, under the popular framework of terminal cost - terminal set MPC, which enables tuning the complexity of the control algorithm. The proposed approach introduces an idea of a pre-terminal set, within which the inputs have enough power to trap states inside it. Since the pre-terminal set lies in the terminal mode which contains origin, this eliminates the need for binary decision variables to model mode transitions after the trajectory enters in pre-terminal set, thereby reducing the on-line complexity although at the expense of optimality. Examples are presented to illustrate the computational benefits of the proposed MPC strategy over existing MPC.

Optimal operating strategies for SMBC

Abstract Simulated Moving Bed Chromatography (SMBC) is a technical realization of the counter current adsorption process approximate by sequentially switching the inlet and outlet valves of interconnected columns in the direction of fluid flow. In this work, a systematic, simulation based optimization study is carried out for different operational goals in SMBC to enhance the performance of an existing laboratory setup. The optimization work involves Pareto optimal solution for two different conflicting objective functions. Optimal transition between such operating conditions is a challenging task. The quantitative results obtained by comparing the optimal transition method with a non-optimal, step change method shows that the optimal transition requires less time to achieve the new reference cyclic steady state. All of the above methods are studied on a SMBC process for separation of glucose and fructose using Ca ++ exchange resin.

A Multiple Linear Modeling Approach for Nonlinear Switched Systems

Abstract Many applications in chemical engineering exhibit a switching character due to discrete and continuous aspects in their dynamic behavior. While first principles models of such systems can be constructed with process simulators, they are usually too complex for use in on line applications such as in model based control. The available methods for modeling of such systems mostly use linear models, such as Mixed Logic Dynamical Systems (MLD) and Piece Wise Affine (PWA) models which describe the evolution of states in each discrete mode using linear equations. Here, we present a modeling strategy for nonlinear switched systems, which is well suited for on-line applications. The method involves a trajectory based linearization and employs a model bank with a set of local linear models for each discrete operational mode. The model bank is generated by linearizing the first principles model across a carefully designed trajectory based on its capability of multi-step ahead prediction. The numerous models are clustered and representative models are selected based on the gap metric as the distance measure. The selected linear models are aggregated using Bayesian or Fuzzy approaches to obtain the global model for the nonlinear switched system. A simulation case study of spherical two tank system is presented to validate proposed modeling strategy.