Performance bounds for robust quadratic dynamic matrix control with end condition

State estimation is incorporated in a version of Quadratic Dynamic Matrix Control (QDMC) that utilizes nonlinear process models. This formulation enables us to deal with open loop unstable systems as illustrated with simple example. The second part of the paper studies the use of this type of control algorithm for the temperature control of a semibatch polymerization reactor. A model and related control requirements for this problem were recently presented in a session on "Industrial Challenge Problems in Process Control."

ON THE STABILITY OF NONLINEAR QUADRATIC DYNAMIC MATRIX CONTROL

ABSTRACTThis paper addresses the problem of robust stabilisation of nD hybrid systems described by Roesser model. The model is in a descriptor form where all the system matrices are corrupted by uncertainty in a general form as implicit linear fractional representations . Based on the S-procedure technique, robust stability and robust stabilisation conditions are established for hybrid systems. Simulation example is provided in order to illustrate the relevance of our approach.

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.

A decentralized quadratic dynamic matrix control algorithm

ROBUSTNESS AND TUNING OF ON-LINE OPTIMIZING CONTROL ALGORITHMS

This article presents comparative analysis between the classical PI (proportional-integral control) and MPC (model predictive control) techniques for a drying process on spouted beds. The on-line experimental setups were carried out in a laboratory-scale plant of a spouted bed dryer. The main objective was to optimize the plant operation by searching for the best control structure to be used in future scale enlargement. The major drawbacks encountered in this kind of system were high interactivity among variables, a malfunction as a result of calculated variables out of the operational window, and modeling mismatch. Despite the robustness of the operational PI, the control actions of this strategy did not overcome the variable interactions. The DMC (dynamic matrix control) and the QDMC (quadratic dynamic matrix control) algorithms performed satisfactorily over the major drawbacks. Special attention was given to the latter algorithm due to its ability to hold the variables under constrained oscillations. However, the best results were found for the adaptive GPC (generalized predictive control) algorithm whose actions prevailed over the modeling mismatch due to the strong nonlinear behavior intrinsic to the process. The main goal of the present work is to describe a procedure that can be standardized for other types of dryers and different scales. This is especially the case for the adaptive GPC, whose control structure is independent of the dryer nature and scale and whose implementation does not require previous identification procedures (self-tuning) and/or structural changes.

Supervisory Control of High Pressure LDPE Reactors

In this chapter, methodologies are described for the plant-wide optimization and control of nonlinear modular systems for continuous-flow pharmaceutical manufacturing. First-principles models for such modular systems are formulated as partial differential-algebraic equations (PDAEs). The spatial discretization of PDAEs, to enable their numerical solution with standard solvers, usually results in a very high number of states. Quadratic dynamic matrix control (QDMC) is an implementable approach for the real-time control of systems with very high state dimension, by using a linear input-output model so that the resulting optimization does not depend on the number of states. To address the strong nonlinearities in these modular systems, linear input-output model construction methodologies are described that can provide good closed-loop performance. Additionally, dynamic optimization of dynamical plant operations such as startup is formulated as a nonlinear program. The dynamic optimization determines optimal trajectories which are used as setpoints for QDMC to control the plant. Results are presented for a computational case study for the upstream synthesis of atropine in a modular continuous-flow system. Dynamic optimization and closed-loop simulation results are presented for plant operations under various disturbance and time-invariant parametric uncertainty scenarios.

In this paper, we consider generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed time-delays. For fuzzy systems with discrete time-delays, both delay-independent stability conditions and delay-dependent stability conditions have already been obtained. However, no stability condition for fuzzy systems with distributed time-delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed time-delays. With the aid of the stability theorems of linear systems with distributed time-delays, we employ a similar Lyapunov functional for the stability of fuzzy time-delay systems. Then we introduce many free matrices to such a Lyapunov functional, in order to obtain delay-dependent stability conditions. These techniques lead to generalized and less conservative stability conditions. In fact, delay-dependent stability conditions thus obtained are given in linear matrix inequalities(LMIs) and guarantee a wide stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed time-delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we take some examples to illustrate our results.

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steadystates. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.

Using Takagi-Sugeno fuzzy model, feedback linearisation which is widely used in nonlinear control theory can be applied to fuzzy control. If perfect linearization can be obtained, the stability can be analysed by linear system theory. However, since modeling uncertainty and disturbance affect the stability, the robust stability analysis is needed to deal with uncertainty. In this paper, the sufficient L/sub 2/ robust stability condition is derived from the multivariable circle criterion. A simple example illustrates the proposed method.

This paper focuses on the robust stability and the memory feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Especially, the considered time delays depend on the subsystem number. Based on a novel common Lyapunov functional, the aggregation techniques, and the Borne and Gentina criterion, new sufficient robust stability and stabilization conditions under arbitrary switching are established. Compared with existing results, the proposed criteria are explicit, simple to use, and obtained without finding a common Lyapunov function for all subsystems through linear matrix inequalities, considered very difficult in this situation. Moreover, compared with the memoryless one, the developed controller guarantees the robust stability of the corresponding closed-loop system with more performance by minimizing the effect of the delays in the system dynamics. Finally, two numerical simulation examples are shown to prove the practical utility and the effectiveness of the proposed theories.

For a complex hydrologic system with multiple processes and process interactions, global sensitivity analysis is often used to identify important or influential parameters for model development and improvement. The identification is complicated by process model uncertainty, when a system process can be represented by multiple process models. This study develops a new total‐effect process sensitivity index to identify influential processes under model uncertainty. This is done by extending Sobol's total‐effect parameter sensitivity index for one system model to total‐effect process sensitivity index for multiple system models to account for uncertainty in process models and model parameters. The total‐effect process sensitivity index includes not only the first‐order process sensitivity index for measuring the importance of individual processes but also higher‐order indices that account for process interactions. The total‐effect process sensitivity index can identify an influential process that itself and its interactions with other processes influence a model output. The total‐effect process sensitivity index is applied to two numerical examples: (a) Sobol's G*‐functions with analytical solutions of first‐order and total‐effect process sensitivity indices, and (b) groundwater flow models with interactions between recharge, geology, and snowmelt processes. The second evaluation shows that, due to second‐order and higher‐order process interactions, the first‐order and total‐effect process sensitivity indices give different process ranking. It is thus necessary to estimate both first‐order and total‐effect process sensitivity indices to appreciate the difference between the first‐order impact of a process alone and the overall total‐effect impact of the process itself and its interactions with other processes on a model output.

In iterative schemes of identification and control one of the particular and important choices to make is the choice for a model uncertainty structure, capturing the uncertainty concerning the estimated plant model. This is typically done in some norm-bounded form, in order to guarantee robust stability and/or robust performance when re-designing the controller. Structures that are used in the recent literature encompass include the gap metric uncertainty, coprime factor uncertainty, and Vinnicombe gap metric uncertainty. In this paper we study the effect of these choices when our aim is to maximize the (re)tuning freedom for a present controller under conditions of robust stability. Particular attention is given to the representation of plant uncertainty and controller tuning freedom in terms of Youla parameters. This so-called double Youla parametrization provides a norm-bounded set of robustly stabilizing controllers that is larger than corresponding sets that are achieved by using any of the other uncertainty structures.