1,017 research outputs found
Robust MPC of constrained nonlinear systems based on interval arithmetic
A robust MPC for constrained discrete-time nonlinear systems with additive
uncertainties is presented. The proposed controller is based on the concept of reachable sets, that
is, the sets that contain the predicted evolution of the uncertain system for all possible uncertainties.
If processes are nonlinear these sets are very difficult to compute. A conservative approximation
based on interval arithmetic is proposed for the online computation of these sets. This technique
provides good results with a computational effort only slightly greater than the one corresponding to
the nominal prediction. These sets are incorporated into the MPC formulation to achieve robust
stability. By choosing a robust positively invariant set as a terminal constraint, a robustly stabilising
controller is obtained. Stability is guaranteed in the case of suboptimality of the computed solution.
The proposed controller is applied to a continuous stirred tank reactor with an exothermic reaction.Ministerio de Ciencia y Tecnología DPI-2001-2380-03- 01Ministerio de Ciencia y Tecnología DPI-2002-4375-C02-0
Robust predictive feedback control for constrained systems
A new method for the design of predictive controllers for SISO systems is presented. The proposed technique allows uncertainties and constraints to be concluded in the design of the control law. The goal is to design, at each sample instant, a predictive feedback control law that minimizes a performance measure and guarantees of constraints are satisfied for a set of models that describes the system to be controlled. The predictive controller consists of a finite horizon parametric-optimization problem with an additional constraint over the manipulated variable behavior. This is an end-constraint based approach that ensures the exponential stability of the closed-loop system. The inclusion of this additional constraint, in the on-line optimization algorithm, enables robust stability properties to be demonstrated for the closed-loop system. This is the case even though constraints and disturbances are present. Finally, simulation results are presented using a nonlinear continuous stirred tank reactor model
Min-Max Predictive Control of a Pilot Plant using a QP Approach
47th IEEE Conference on Decision and Control 9-11 Dec. 2008The practical implementation of min-max MPC (MMMPC) controllers is limited by the computational burden required to compute the control law. This problem can be circumvented by using approximate solutions or upper bounds of the worst possible case of the performance index. In a previous work, the authors presented a computationally efficient MMMPC control strategy in which a close approximation of the solution of the min-max problem is computed using a quadratic programming problem. In this paper, this approach is validated through its application to a pilot plant in which the temperature of a reactor is controlled. The behavior of the system and the controller are illustrated by means of experimental results
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Real-time feasibility of nonlinear model predictive control for semi-batch reactors subject to uncertainty and disturbances
This paper presents two nonlinear model predictive control based methods for solving closed-loop stochastic dynamic optimisation problems, ensuring both robustness and feasibility with respect to state output constraints. The first one is a new deterministic approach, using the wait-and-see strategy. The key idea is to specifically anticipate violation of output hard-constraints, which are strongly affected by instantaneous disturbances, by backing off of their bounds along the moving horizon. The second method is a stochastic approach to solve nonlinear chance-constrained dynamic optimisation problems under uncertainties. The key aspect is the explicit consideration of the stochastic properties of both exogenous and endogenous uncertainties in the problem formulation (here-and-now strategy). The approach considers a nonlinear relation between uncertain inputs and the constrained state outputs. The performance of the proposed methodologies is assessed via an application to a semi-batch reactor under safety constraints, involving strongly exothermic reactions
Predictive feedback control using a multiple model approach
A new method of designing predictive controllers for SISO systems is presented. The controller selects the model used in the design of the control law from a given set of models according to a switching rule based on output prediction errors. The goal is to design, at each sample instant, a feedback control law that ensures robust stability of the closed–loop system and gives better performance for the current operating point. The overall multiple model predictive control scheme quickly identifies the closest linear model to the dynamics of the current operating point, and carries out an automatic reconfiguration of the control system to achieve a better performance. The results are illustrated with simulations of a continuous stirred tank reactor
Iterative Nonlinear Control of a Semibatch Reactor. Stability Analysis
This paper presents the application of Iterative
Nonlinear Model Predictive Control, INMPC, to a semibatch
chemical reactor. The proposed control approach is derived
from a model-based predictive control formulation which takes
advantage of the repetitive nature of batch processes. The
proposed controller combines the good qualities of Model
Predictive Control (MPC) with the possibility of learning from
past batches, that is the base of Iterative Control. It uses a
nonlinear model and a quadratic objective function that is
optimized in order to obtain the control law. A stability proof
with unitary control horizon is given for nonlinear plants that
are affine in control and have linear output map.
The controller shows capabilities to learn the optimal trajectory after a few iterations, giving a better fit than a linear
non-iterative MPC controller. The controller has applications in
repetitive disturbance rejection, because they do not modify
the model for control purposes. In this application, some
experiments with a disturbance in inlet water temperature has
been performed, getting good results.Ministerio de Ciencia y Tecnología DPI2004-07444-C04-0
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Economic MPC of Nonlinear Processes via Recurrent Neural Networks Using Structural Process Knowledge
This work discusses three methods that incorporate a priori process knowledge into recurrent neural network (RNN) modeling of nonlinear processes to get increased prediction accuracy and provide information on how the neural network models are structured. The first method proposes a hybrid model that integrates first-principles models and RNN models together. The second method proposes a partially-connected RNN model which its structure is based on a priori structural process knowledge. The third method proposes a weight-constrained RNN model that integrates weight constraints into the training of the RNN model. The proposed RNN models are used in an economic model predictive control system and then applied to a chemical process example to validate the improved approximation performance compared to a fully-connected RNN model that is treated as a black box model
Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints
This paper presents a stochastic model predictive control approach for
nonlinear systems subject to time-invariant probabilistic uncertainties in
model parameters and initial conditions. The stochastic optimal control problem
entails a cost function in terms of expected values and higher moments of the
states, and chance constraints that ensure probabilistic constraint
satisfaction. The generalized polynomial chaos framework is used to propagate
the time-invariant stochastic uncertainties through the nonlinear system
dynamics, and to efficiently sample from the probability densities of the
states to approximate the satisfaction probability of the chance constraints.
To increase computational efficiency by avoiding excessive sampling, a
statistical analysis is proposed to systematically determine a-priori the least
conservative constraint tightening required at a given sample size to guarantee
a desired feasibility probability of the sample-approximated chance constraint
optimization problem. In addition, a method is presented for sample-based
approximation of the analytic gradients of the chance constraints, which
increases the optimization efficiency significantly. The proposed stochastic
nonlinear model predictive control approach is applicable to a broad class of
nonlinear systems with the sufficient condition that each term is analytic with
respect to the states, and separable with respect to the inputs, states and
parameters. The closed-loop performance of the proposed approach is evaluated
using the Williams-Otto reactor with seven states, and ten uncertain parameters
and initial conditions. The results demonstrate the efficiency of the approach
for real-time stochastic model predictive control and its capability to
systematically account for probabilistic uncertainties in contrast to a
nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro
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