1,721,202 research outputs found
Robust Disturbance Modeling for Model Predictive Control with Application to Multivariable Ill-conditioned Processes
Full text linkIn this paper the disturbance model, used by MPC algorithms to achieve offset-free control, is optimally designed to enhance the robustness of single-model predictive controllers. The proposed methodology requires the off-line solution of a min-max optimization problem in which the disturbance model is chosen to guarantee the best closed-loop performance in the worst case of plant in a given uncertainty region. Application to a well-known ill-conditioned distillation column is presented to show that, for ill-conditioned processes, the use of a disturbance model that adds the correction term to the process inputs guarantees a robust performance, while the disturbance model that adds the correction term to the process outputs (used by industrial MPC algorithms) does not. (C) 2003 Elsevier Ltd. All rights reserved
Robust Model Predictive Control with Guaranteed Setpoint Tracking
No full textIn this paper a novel robust model predictive control (RMPC) algorithm is proposed, which is guaranteed to stabilize any linear time-varying system in a given convex uncertainty region while respecting state and input constraints. Moreover, unlike most existing RMPC algorithms, the proposed algorithm is guaranteed to remove steady-state offset in the controlled variables for setpoints (possibly) different from the origin when the system is unknown linear time-invariant. The controller uses a dual-mode paradigm (linear control law plus free control moves to reach an appropriate invariant region), and the key step is the design of a robust linear state feedback controller with integral action and the construction of an appropriate polyhedral invariant region in which this controller is guaranteed to satisfy the process constraints. The proposed algorithm is efficient since the on-line implementation only requires one to solve a convex quadratic program with a number of decision variables that scale linearly with the control horizon. The main features of the new control algorithm are illustrated through an example of the temperature control of an open-loop unstable continuous stirred tank reactor. © 2004 Elsevier Ltd. All rights reserved
Offset-free Tracking: There and Back Again
No full textFeedback is necessary to reduce the effect of disturbances and to cope with unavoidable modeling errors. Nonetheless, the way in which feedback is used to achieve offset-free tracking in the presence of persistent errors or non-zero mean disturbances appears to be often a question of personal preference among possible different, sometimes ad-hoc, methods. As a matter of fact, this aspect of controller design is typically overlooked in academic papers but is often fundamental for successful implementation.
After a preliminary introduction to linear offset-free Model Predictive Control (MPC) design principles based on disturbance models, explaining how the integral action is achieved in spite of modeling errors, we address the following results.
1. We propose an observer-based Internal Model Control (IMC) struc- ture which extends the simple IMC design principles to integrating and unstable plants, showing the conditions for internal stability and offset-free property. A connection with the Youla-Kucera parameter- ization is also established as a special case.
2. We show that several known alternative offset-free MPC algorithms (using velocity models) are special cases of the general disturbance models.
3. We extend the concepts of offset-free estimation to design an eco- nomic MPC algorithm that is able to cope with persistent errors while still achieving the optimal ultimate economic performance
Offset-free tracking MPC: A tutorial review and comparison of different formulations
Full text linkOffset-free Model Predictive Control formulations refer to a class of algorithms that are able to achieve output tracking of reference signals despite the presence of plant/model mismatch or unmeasured nonzero mean disturbances. The general approach is to augment the nominal system with disturbances, i.e. to build a disturbance model, and to estimate the state and disturbance from output measurements. Some alternatives are available, which are based on a non augmented system with state disturbance observer, or on velocity form representations of the system to be controlled. In this paper, we review the disturbance model approach and two different approaches in a coherent framework. Then, differently from what is reported in the literature, we show that the two alternative formulations are indeed particular cases of the general disturbance model approach
Ottimizzazione e controllo della terapia farmacologica: applicazione ai casi di HIV e diabete di tipo I
No full textConsistency of property estimators in distillation column control
No full textThis paper addresses the problem of input selection in inferential control of multicomponent distillation columns by introducing the concept of consistency. An estimator is consistent when a feedback (multivariable) control system that uses the estimates of the controlled variables guarantees low closed-loop steady-state offset in the true unmeasured controlled variables when disturbances enter the system (and/or set-point changes are considered). A definition of this property is given, and the relations between the estimator consistency and the closed-loop steady-state offset are derived for both single-input-single-output and multi-input-multioutput systems. A multicomponent distillation column case study is presented to show that the selection of the most "precise" inputs does not necessarily guarantee the lowest closed-loop offset in the presence of disturbances, whereas the use of less precise but more "consistent" inputs leads to a well-designed estimator that guarantees a lower closed-loop steady-state offset
Disturbance Models for Offset-free Model Predictive Control
No full textModel predictive control algorithms achieve offset-free control objectives by adding integrating disturbances to the process model. The purpose of these additional disturbances is to lump the plant-model mismatch and/or unmodeled disturbances. Its effectiveness has been proven for particular square cases only. For systems with a number of measured variables (p) greater than the number of manipulated variables (m), it is clear that any controller can track without offset at most m controlled variables. One may think that m integrating disturbances are sufficient to guarantee offset-free control in the m controlled variables. We show this idea is incorrect and present general conditions that allow zero steady-state offset. In particular, a number of integrating disturbances equal to the number of measured variables are shown to be sufficient to guarantee zero offset in the controlled variables. These results apply to square and nonsquare, open-loop stable, integrating and unstable systems
A Predictor Form PARSIMonious Algorithm for Closed-loop Subspace Identification
No full textIn this paper, we present a novel subspace identification algorithm in which all non-causal terms are removed, and the specific Toeplitz structure of the Markov parameter's matrices is fully exploited in the spirit of the so-called PARSIMonious algorithms. We use the state-space formulation in predictor form, and we show that consistent estimates of the Markov parameters are granted both for open-loop and closed-loop data. Furthermore, we propose to evaluate the system matrices (B(K) = B - KD, D, K) and the initial condition by a single Least Squares problem, which is well conditioned even for unstable systems. We present identification results for two multi-variable systems to show the main features of the proposed method, and to assess its performance against that achieved by other subspace methods. Furthermore, we compare the performance of Model Predictive Controllers, based on models identified from closed-loop data using the different subspace algorithms, in the control of the Wood-Berry distillation column. Results indicate that the proposed method is suitable for MPC design purposes, and compares favorably with the other subspace algorithms. (C) 2010 Elsevier Ltd. All rights reserved
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