Efficient Model Predictive Control Algorithm Research Articles

Distributed power system coordination via parametric optimization and ADMM

In this paper we present an efficient model predictive control algorithm for distributed coordination of an electrical power system comprising many spatially distributed controllable units. The coordination problem is formulated using parametric solutions of local optimization problems corresponding to individual subsystems leading to favorable problem structure which can be split across all subsystems and nodes in the network. The structure of the obtained coordination problem is exploited to develop a very efficient solution algorithm based on an ADMM technique. The key features of the overall approach are: (i) private data of individual subsystems are protected, (ii) simple and efficient on-line computations, (iii) parallelization of computation across all subsystems and all nodes in the network. Efficiency of the proposed control strategy is demonstrated on a number of numerical case studies of varying size.

Set-based fast gradient projection algorithm for model predictive control of grid-tied power converters

Model Predictive Control (MPC) has attracted much attention and is widely used in power electronics. However, implementing the MPC algorithm is still a difficult task due to the fast dynamics of power converters and strict time constraints. In this paper, a computationally efficient MPC algorithm for grid-tied power converters based on the fast gradient projection method and invariant set theory is proposed. The algorithm is implemented and tested through hardware-in-the-loop simulations using Texas Instruments digital signal processors and Xilinx Field Programmable Gate Arrays platforms.

An efficient MPC algorithm for switched systems with minimum dwell time constraints

This paper presents an efficient suboptimal model predictive control (MPC) algorithm for nonlinear switched systems subject to minimum dwell time constraints (MTC). While MTC are required for most physical systems due to stability, power and mechanical restrictions, MPC optimization problems with MTC are challenging to solve. To efficiently solve such problems, the on-line MPC optimization problem is decomposed into a sequence of simpler problems, which include two nonlinear programs (NLP) and a rounding step, as typically done in mixed-integer optimal control (MIOC). Unlike the classical approach that embeds MTC in a mixed-integer linear program (MILP) with combinatorial constraints in the rounding step, our proposal is to embed the MTC in one of the NLPs using move blocking. Such a formulation can speedup on-line computations by employing recent move blocking algorithms for NLP problems and by using a simple sum-up-rounding (SUR) method for the rounding step. An explicit upper bound of the integer approximation error for the rounding step is given. In addition, a combined shrinking and receding horizon strategy is developed to satisfy closed-loop MTC. Recursive feasibility is proven using a l-step control invariant (l-CI) set, where l is the minimum dwell time step length. An algorithm to compute l-CI sets for switched linear systems off-line is also presented. Numerical studies show significant speed-up and comparable control performance of the proposed MPC algorithm against the classical approach, though at the cost of significant solution quality degradation especially when the MTC are large.

An efficient model predictive control for Markovian jump systems with all unstable modes

This paper is concerned with the efficient model predictive control (EMPC) problem for a class of Markovian jump systems (MJSs) with unstable modes under polytopic uncertainties and hard constraints. The transition probability matrix and a dual-mode control strategy in the framework of EMPC are co-designed. To achieve a nice tradeoff among the computation burden, the initial feasible region, and the control performance, the EMPC is proposed, whose main idea is two-fold: (1) the terminal constraint set, the corresponding feedback gain, and proper switching rules (i.e. the transition probability) are designed simultaneously by solving an off-line “min–max” problem related to subsystem modes; and (2) a fairly large initial feasible region is obtained off-line by adjusting the dimension of the control perturbation sequence, meanwhile such a perturbation sequence is designed online to steer the system state belonging to initial feasible region into the terminal constraint set within the pre-determined steps. Furthermore, sufficient conditions are presented to rigidly guarantee the feasibility of the proposed EMPC algorithm and the mean-square stability of the underlying MJS. Finally, an illustrative example regarding the economic system is provided to verify the feasibility and effectiveness of the developed algorithm.

Efficient model predictive control for Markovian jump systems with Lur'e nonlinear term: A dual‐mode control scheme

AbstractIn this article, the efficient model predictive control (MPC) problem is investigated for a class of Markovian jump Lur'e systems (MJLSs) subject to parameter uncertainties and input constraints, where each subsystem is described by the combination of a linear part and a nonlinear Lur'e term. The main purpose of the addressed problem is to design a set of dual‐mode feedback controllers in the framework of efficient MPC to make a nice tradeoff among the online computation burden, the initial feasible region, and the control performance. To this aim, the following two tasks need to be fulfilled: 1) for the terminal constraint set, the corresponding fixed feedback gain that is composed of a linear part and a nonlinear part is designed with aid of the Lur'e‐type Lyapunov‐like function related to the modes of subsystems; and 2) a fairly large initial feasible region is obtained off‐line by adjusting the dimension of the control perturbation sequence. Then, an online optimization problem is put forward to design this perturbation sequence with the determined dimension to steer the system state into the terminal constraint set within the pre‐determined steps. Sufficient conditions are presented to guarantee the recursive feasibility of the proposed efficient MPC algorithm and the mean‐square stability of the underlying MJLSs. Finally, a simulation example with regards to the DC motor device system is provided to demonstrate the effectiveness of our proposed MPC strategy.

Model Predictive Control of Phase Shift Full-Bridge DC–DC Converter Using Laguerre Functions

The real-time computational load of an optimization problem plays a major role in the application of model predictive control (MPC) to fast switching power electronic converters. It is, therefore, highly desired to alleviate the computational burden of the MPC to render it feasible for these applications. In this brief, an efficient MPC algorithm based on Laguerre functions is proposed for a phase shift full-bridge (PSFB) dc–dc converter, in which the main control objective is to maintain the converter’s load voltage at the desired set point while fulfilling multiple physical constraints, including the nonlinear peak input current constraint. It is shown in this work that the Laguerre functions’ parameterization of MPC offers a promising solution to the high computational requirement associated with the conventional MPC without compromising on the dynamic closed-loop performance. The efficacy of the proposed control algorithm is tested on 60-W experimental hardware for 40- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{s}$ </tex-math></inline-formula> sampling time. Experimental results are also compared with the conventional proportional-integral (PI) control structure in order to illustrate different aspects of the proposed control scheme.

Efficient Model-Predictive Control for Nonlinear Systems in Interval Type-2 T-S Fuzzy Form Under Round-Robin Protocol

This article is concerned with the efficient model-predictive control (EMPC) problem for interval type-2 Takagi–Sugeno (IT2 T-S) fuzzy systems with hard constraints. By applying the round-robin (RR) protocol, all controller nodes are activated in a pregiven order such that the occurrence of network congestion or data collisions can be effectively reduced. The aim of the proposed problem is to design a fuzzy controller in the framework of EMPC so as to obtain a good balance among the computation burden, the initial feasible region, and the control performance. With respect to the RR protocol and IT2 T-S fuzzy nonlinearities, a unified representation is modeled for the underlying system, and then, an augmentation state comprising of the system state, the token-dependent perturbation, and the previous input under the RR protocol is put forward; correspondingly, objective functions are constructed for the controller design. Subsequently, by using the min–max strategy, some token-dependent optimizations are established to facilitate the formation of the EMPC algorithm, where the feedback gain is designed offline, and the perturbation is calculated by solving an online optimization dependent of the token. Moreover, with the help of the matrix partition technique, the feasibility of the proposed EMPC algorithm and the stability of the underlying IT2 T-S fuzzy system are rigidly guaranteed. Finally, two numerical examples are utilized to illustrate the validity of the proposed EMPC strategy.

Explicit nonlinear predictive control algorithms for Laguerre filter and sparse least square support vector machine-based Wiener model

In this paper, three computationally proficient model predictive control (MPC) algorithms for least square support vector machine (LSSVM)-based Wiener model are described. A Wiener model with Laguerre filter as dynamic linear part and LSSVM approximator as nonlinear static part is considered. Even though having excellent approximation abilities, LSSVM suffers from lack of sparseness. A pruning algorithm for LSSVM model is proposed and its comparison is made with classical pruning algorithm. The proposed pruning algorithm is able to remove 99% of support vectors with no remarkable drop in modelling accuracy. Using pruned Wiener model, three computationally efficient MPC algorithms are described. In the first algorithm, linearization of Wiener model is performed at every sampling interval and therefore control vector is determined by carrying out a quadratic optimization task. In the second algorithm, control signal is determined by an explicit control law and parameters of this control law are computed by performing lower-upper (LU) factorization of a matrix and solving linear equations without any online optimization. In the third algorithm, the parameters of explicit control law are calculated directly by another LSSVM approximator, which is trained offline. The advantages and effectiveness of proposed methods are demonstrated on the benchmark pH neutralization reactor. The control performance and computational efficiency of proposed algorithms are compared with computationally complex nonlinear MPC, which repeats a nonlinear optimization task at every sampling interval. The impact of pruning on model accuracy, computational efficiency and control accuracy is also discussed.

Efficient Model-Predictive Control for Networked Interval Type-2 T–S Fuzzy System With Stochastic Communication Protocol

In this article, the efficient model-predictive control (EMPC) problem of a class of nonlinear systems in the framework of interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy is investigated. In order to improve the reliability of the data transmission while reducing the network communication burden, a so-called stochastic communication protocol (SCP) governed by a Markov chain is adopted to orchestrate the data transmission order from the controller to the actuator. The purpose of the addressed problem is to design a set of desired EMPC controllers so as to guarantee the mean-square system stability and obtain a good balance among the computation burden, initial feasible region, and the control performance. A novel control model is established for the SCP and IT2 T-S fuzzy nonlinearities in a unified representation by using a fuzzy periodic switching related to the transmission token and the membership function. Then, the system state, the SCP-based control perturbation, and the previous input under the SCP are fully taken into consideration for constructing the objective function. By virtue of the “min-max” strategy, a few optimizations are formulated, and the corresponding EMPC algorithm is provided, where the feedback gain is designed offline, while the control perturbation is obtained online. Furthermore, by means of the matrix partition technique, sufficient conditions are presented to rigidly guarantee the feasibility of the proposed EMPC algorithm and the mean-square stability of the underlying IT2 T-S fuzzy system. Finally, two illustrative examples are utilized to demonstrate the validity of the proposed EMPC strategy.

New results on semi-explicit and almost explicit MPC algorithms

Abstract New results on a particular type of state-dependent parameterization for model predictive control (MPC) are presented. Based on such parameterizations efficient MPC algorithms can be formulated, which combine the advantages of explicit and online optimization-based MPC. The new results comprise an offline stability check for the parameterizations to decide if a closed-loop MPC scheme applying the parameterizations is asymptotically stabilizing. Second, a novel way of computing the parameterizations with improved scalability in the state space dimension is included. Furthermore, new results and simplifications of almost explicit MPC schemes based on univariate parameterizations are contributed. The results are presented in a common framework and are illustrated in numerical examples including an almost explicit controller for an eight-dimensional spring-damper system.

Modelling and predictive control of a neutralisation reactor using sparse support vector machine Wiener models

This paper has two objectives: (a) it describes the problem of finding a precise and uncomplicated model of a neutralisation process, (b) it details development of a nonlinear Model Predictive Control (MPC) algorithm for the plant. The model has a cascade Wiener structure, i.e. a linear dynamic part is followed by a nonlinear steady-state one. A Least-Squares Support Vector Machine (LS-SVM) approximator is used as the steady-state part. Although the LS-SVM has excellent approximation abilities and it may be found easily, it suffers from a huge number of parameters. Two pruning methods of the LS-SVM Wiener model are described and compared with a classical pruning algorithm. The described pruning methods make it possible to remove as much as 70% of support vectors without any significant deterioration of model accuracy. Next, the pruned model is used in a computationally efficient MPC algorithm in which a linear approximation of the predicted output trajectory is successively found on-line and used for prediction. The control profile is calculated on-line from a quadratic optimisation problem. It is demonstrated that the described MPC algorithm with on-line linearisation based on the pruned LS-SVM Wiener model gives practically the same trajectories as those obtained in the computationally complex MPC approach based on the full model with on-line nonlinear optimisation repeated at each sampling instant.

Explicit efficient constrained model predictive control

A more efficient model predictive control algorithm is algebraic model predictive control. The efficiency is improved by forming the prediction horizon with a non-uniform distribution of points. The most efficient case reduces the problem down to a single prediction point, defining the horizon length as well as removing any redundant control calculations. This paper shows that for this single prediction point case, the constrained control can be easily evaluated explicitly, thus making the control calculation deterministic and more efficient. We also show that because an explicit control can be determined for the system, the closed-loop constrained stability bounds can be evaluated a priori. Using the key constraint of the peak location of the response also allows the system to meet the constraints while still being explicit and deterministic. The proposed explicit algorithm is applied to two numerical simulation examples with the performance, computational efficiency and stability analysed.

Simulation and experimental demonstration of model predictive control in a building HVAC system

This article presents the framework and results of implementing optimization-based control algorithm for building HVAC systems and demonstrates its benefits through reduced building energy consumption as well as improved thermal comfort along with lessons learned. In particular, a practically effective and computationally efficient model predictive control algorithm is proposed to optimize building energy usage while maintaining thermal comfort in a multi-zone medium-sized commercial building. This article has two themes. Driven by the challenge of fully evaluating the benefit of the proposed model predictive controller against baseline control, a model predictive control design framework is first presented with its performance benchmarked based on a high-fidelity building HVAC simulation environment to verify its effectiveness and feasibility. Following the same model predictive control design framework, the experimental results from the same building located at the Philadelphia Navy Yard are then presented. For the simulation study, the performance of the model predictive control algorithm was estimated relative to baseline days with exactly the same internal loads and outdoor conditions, and it was estimated that model predictive control reduced the total electrical energy consumption by around 17.5%. For the subsequent experimental demonstration, the performance of the model predictive control algorithm was estimated relative to baseline days with similar outdoor air temperature patterns during the cooling and shoulder seasons, and it was concluded that model predictive control reduced the total electrical energy consumption by more than 20% on average while improving thermal comfort in terms of zone air temperature.