1,252 research outputs found

    On the convergence of stochastic MPC to terminal modes of operation

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    The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that guarantee closed-loop performance bounds and boundedness of the state, but convergence to a terminal control law is typically not shown. In this work we use results on general state space Markov chains to find conditions that guarantee convergence of disturbed nonlinear systems to terminal modes of operation, so that they converge in probability to a priori known terminal linear feedback laws and achieve time-average performance equal to that of the terminal control law. We discuss implications for the convergence of control laws in stochastic MPC formulations, in particular we prove convergence for two formulations of stochastic MPC

    Vibration suppression in multi-body systems by means of disturbance filter design methods

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    This paper addresses the problem of interaction in mechanical multi-body systems and shows that subsystem interaction can be considerably minimized while increasing performance if an efficient disturbance model is used. In order to illustrate the advantage of the proposed intelligent disturbance filter, two linear model based techniques are considered: IMC and the model based predictive (MPC) approach. As an illustrative example, multivariable mass-spring-damper and quarter car systems are presented. An adaptation mechanism is introduced to account for linear parameter varying LPV conditions. In this paper we show that, even if the IMC control strategy was not designed for MIMO systems, if a proper filter is used, IMC can successfully deal with disturbance rejection in a multivariable system, and the results obtained are comparable with those obtained by a MIMO predictive control approach. The results suggest that both methods perform equally well, with similar numerical complexity and implementation effort

    Robust model predictive control for dynamics compensation in real-time hybrid simulation

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    Hybrid simulation is an efficient method to obtain the response of an emulated system subjected to dynamic excitation by combining loading-rate-sensitive numerical and physical substructures. In such simulations, the interfaces between physical and numerical substructures are usually implemented using transfer systems, i.e., an arrangement of actuators. To guarantee high fidelity of the simulation outcome, conducting hybrid simulation in hard real-time is required. Albeit attractive, real-time hybrid simulation comes with numerous challenges, such as the inherent dynamics of the transfer system used, along with communication interrupts between numerical and physical substructures, that introduce time delays to the overall hybrid model altering the dynamic response of the system under consideration. Hence, implementation of adequate control techniques to compensate for such delays is necessary. In this study, a novel control strategy is proposed for time delay compensation of actuator dynamics in hard real-time hybrid simulation applications. The method is based on designing a transfer system controller consisting of a robust model predictive controller along with a polynomial extrapolation algorithm and a Kalman filter. This paper presents a proposed tracking controller first, followed by two virtual real-time hybrid simulation parametric case studies, which serve to validate the performance and robustness of the novel control strategy. Real-time hybrid simulation using the proposed control scheme is demonstrated to be effective for structural performance assessment

    Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints

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    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

    The State of the Art in Model Predictive Control Application for Demand Response

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    Demand response programs have been used to optimize the participation of the demand side. Utilizing the demand response programs maximizes social welfare and reduces energy usage. Model Predictive Control is a suitable control strategy that manages the energy network, and it shows superiority over other predictive controllers. The goal of implementing this controller on the demand side is to minimize energy consumption, carbon footprint, and energy cost and maximize thermal comfort and social welfare.  This review paper aims to highlight this control strategy\u27s excellence in handling the demand response optimization problem. The optimization methods of the controller are compared. Summarization of techniques used in recent publications to solve the Model Predictive Control optimization problem is presented, including demand response programs, renewable energy resources, and thermal comfort. This paper sheds light on the current research challenges and future research directions for applying model-based control techniques to the demand response optimization problem
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