Alejandro H. González

Model predictive control suitable for closed-loop re-identification

The main problem of a closed-loop re-identification procedure is that, in general, the dynamic control and identification objectives are conflicting. In fact, to perform a suitable identification a persistent excitation of the system is needed, while the control objective is to stabilize the system to a given equilibrium point. In this work, a generalization of the concept of stability, from punctual stability to (invariant) set stability, is studied to avoid the conflict between these objectives. Furthermore, a persistent excitation scheme is proposed to properly perform a closed-loop re-identification. Simulation results show the propose controller formulation properties.

A gradient-based strategy for integrating Real Time Optimizer (RTO) with Model Predictive Control (MPC)

Abstract In the process industries it is often desirable that advanced controllers, such as model predictive controllers (MPC), control the plant ensuring stability and constraints satisfaction, while an economic criterion is minimized. Usually the economic objective is optimized by an upper level Real Time Optimizer (RTO) that passes steady state targets to a lower dynamic control level. The drawback of this structure is that the RTO employs complex stationary nonlinear models to perform the optimization and has a sampling time larger than the controller one. As a consequence, the economic setpoints calculated by the RTO may be inconsistent for the dynamic layer. In this paper an MPC that explicitly integrates the RTO structure into the dynamic control layer is presented. To overcome the complexity of this one-layer formulation a first order approximation of the RTO cost function is proposed, which provides a low-computational-cost suboptimal solution. It is shown that the proposed strategy ensures convergence and recursive feasibility under any change of the economic function. The strategy is tested in a simulation on a subsystem of a fluid catalytic cracking (FCC) unit.

Robust Model Predictive Control for Time Delayed Systems with Optimizing Targets and Zone Control

Model Predictive Control (MPC) is frequently implemented as one of the layers of a control structure where a Real Time Optimization (RTO) algorithm laying in an upper layer of this structure defines optimal targets for some of the inputs and/or outputs (Kassmann et al., 2000). The main scope is to reach the most profitable operation of the process system while preserving safety and product specification constraints. The model predictive controller is expected to drive the plant to the optimal operating point, while minimizing the dynamic error along the input and output paths. Since in the control structure considered here the model predictive controller is designed to track the optimal targets, it is expected that for nonlinear process systems, the linear model included in the controller will become uncertain as we move from the design condition to the optimal condition. The robust MPC presented in this chapter explicitly accounts for model uncertainty of open loop stable systems, where a different model corresponds to each operating point of the process system. In this way, even in the presence of model uncertainty, the controller is capable of maintaining all outputs within feasible zones, while reaching the desired optimal targets. In several other process systems, the aim of the MPC layer is not to guide all the controlled variables to optimal targets, but only to maintain them inside appropriate ranges or zones. This strategy is designated as zone control (Maciejowski, 2002). The zone control may be adopted in some systems, where there are highly correlated outputs to be controlled, and there are not enough inputs to control all the outputs. Another class of zone control problems relates to using the surge capacity of tanks to smooth out the operation of a process unit. In this case, it is desired to let the level of the tank to float between limits, as necessary, to buffer disturbances between sections of a plant. The paper by Qin and Badgwell (2003), which surveys the existing industrial MPC technology, describes a variety of industrial controllers and mention that they always provide a zone control option. Other example of zone control can be found in Zanin et al, (2002), where the authors exemplify the application of this

Model Predictive Control for Changing Economic Targets

Abstract The objective of this paper is to present recent results on model predictive control for tracking in the context of economic operation of a industrial plants. The well-established hierarchical economic control is based on a Real Time Optimizer that calculates the economic target to the advanced controller, in this case model predictive controllers. The change of the economic parameters or constraints, or the existence of disturbances and modelling errors make that this target may change throughout the plant evolution. The MPC for tracking is an appealing formulation to deal with this issue since maintain the recursive feasibility and convergence under any change of the target. Thus, this MPC formulation is summarized as well as its properties. In virtue of these properties, it is demonstrated how the economic operation can be improved by integrating the Steady State Target Optimizer in the MPC. Then it is also shown how the proposed MPC can deal with practical problems such us zone control or distributed control. Finally, the economic control of the plant can be enhanced by adopting an economic MPC approach. A formulation capable to ensure economic optimality and target tracking is also shown.

Stable MPC with reduced representation for linear systems with multiple input delays

It is well known that MPC recursive feasibility and asymptotic stability is related to the so called stabilizing elements, namely: (i) terminal cost, (ii) terminal stabilizing control law, and terminal constraint. For systems with multiple delays, it is commonly used an augmented representation, which avoid the use of input delays. However, although the augmented description permits an easy inclusion of the stabilizing elements, the control problem dimension could be prohibitively enlarged (mainly from a computational point of view). In this paper it is shown that a stable MPC with enlarged domain of attraction can be easily applied to control open-loop stable systems with multiple input delays by considering the original (reduced) representation. Stabilizing conditions are presented and a modified cost function is proposed in order to avoid the augmented representation. A simulation example is presented to illustrate the simplicity of the proposed approach.

One-layer robust MPC: a multi-model approach

Abstract In this paper, an MPC that explicitly integrates the RTO structure into the dynamic control layer is presented. In particular, a robust MPC is proposed, which takes into account the uncertainties that arise from the difference between nonlinear and linear models, by means of a multi-model approach: a finite family of linear models is considered, which operate appropriately in a moderate-to-large region around a given operating point. In this way, each linear model provides an enough accurate description of the system. Feasibility and stability conditions are preserved. Moreover, the real plant converges to the optimal point that optimizes the economic cost function.

Impulsive zone model predictive control with application to type I diabetic patients

In this work the problem of regulating glycemia in type I diabetic patients is studied by means of a novel impulsive zone model predictive control. According to the control objective of steering the system to an arbitrary desired target set, weak stability is demonstrated based on a novel dynamic characterization of two underlying discrete-time subsystems of the original impulsive system. To evaluate the proposed strategy, a new patient model is used. A long-term scenario - including meals - is simulated, and the results appear to be satisfactory as long as every hyperglycemia and hypoglycemia episodes are suitably controlled/minimized.

Probabilistic Invariant Sets for Closed-Loop Re-Identification

Recently, a Model Predictive Control (MPC) suitable for closed-loop re-identification was proposed, which solves the potential conflict between the persistent excitation of the system and the stabilization of the closed-loop by extending the equilibrium-point-stability to the invariant-set-stability. The proposed objective set, however, derives in large regions that contain conservatively the excited system evolution. In this work, based on the concept of probabilistic invariant sets, the controller target sets are substantially reduced ensuring the invariance with a sufficiently large probability (instead of deterministically), giving the resulting MPC controller the necessary flexibility to be applied in a wide range of systems.

On Economic Optimality of Model Predictive Control

Model Predictive Control (MPC) is the most used advanced control strategy in the industries, mainly due to its capability to fulfill economic objectives, taking into account a dynamic simplified model of the plant, constraints, and stability requirements. In the last years, several economic formulations of MPC have been presented, which get over the standard setpoint-tracking formulation. The goal of this work is to provide, by means of application to a highly nonlinear plant, a comparison of different strategies, focusing mainly on economic optimality, computational burden, and economic performance.

Iterative Learning - MPC: an Alternative Strategy

A repetitive system is one that continuously repeats a finite-duration procedure (operation) along the time. This kind of systems can be found in several industrial fields such as robot manipulation (Tan, Huang, Lee & Tay, 2003), injection molding (Yao, Gao & Allgower, 2008), batch processes (Bonvin et al., 2006; Lee & Lee, 1999; 2003) and semiconductor processes (Moyne, Castillo, & Hurwitz, 2003). Because of the repetitive characteristic, these systems have two count indexes or time scales: one for the time running within the interval each operation lasts, and the other for the number of operations or repetitions in the continuous sequence. Consequently, it can be said that a control strategy for repetitive systems requires accounting for two different objectives: a short-term disturbance rejection during a finite-duration single operation in the continuous sequence (this frequently means the tracking of a predetermined optimal trajectory) and the long-term disturbance rejection from operation to operation (i.e., considering each operation as a single point of a continuous process1). Since in essence, the continuous process basically repeats the operations (assuming that long-term disturbances are negligible), the key point to develop a control strategy that accounts for the second objective is to use the information from previous operations to improve the tracking performance of the future sequence.