MPC Optimization Research Articles

Fault Tolerant Control for MIMO Nonlinear Systems via MPC Based on MIMO ARX-Laguerre Multiple Models

In this article, we propose a fault tolerant control for multiple-input multiple-output (MIMO) nonlinear systems via model predictive control. The MIMO nonlinear systems are approximated by MIMO ARX-Laguerre multiple models. The latter is obtained by expanding a discrete-time MIMO ARX multiple model parameters on Laguerre orthonormal bases. The resulting model ensures an efficient complexity reduction with respect to the classical MIMO ARX multiple models. This parametric complexity reduction still subjects to an optimal choice of the Laguerre poles defining Laguerre bases. The parameter and structure identifications of the MIMO ARX-Laguerre multiple models are achieved by the recursive method and a metaheuristic algorithm, respectively. The proposed model is built from the system input/output observations and is used to synthesize a MIMO nonlinear fault tolerant control algorithm via MPC. So, we develop a fault detection and isolation (FDI) scheme based on the proposed model. The scheme of the fault detection is applied at every step of MPC control calculation, where we determine the actuator faults and we use it in the MPC optimization problem to determine the new control with respect to the actuator faults. The proposed strategy is tested on numerical simulation and validated on the real system.

Coordinated Energy Dispatch of Autonomous Microgrids With Distributed MPC Optimization

With the increased penetration of renewable energy sources (RESs) and plug-and-play loads, Microgrids (MGs) bring direct challenges in energy management due to the uncertainties in both supply and demand sides. In this paper, we present a coordinated energy dispatch based on Distributed Model Predictive Control (DMPC), where the upper level provides an optimal scheduling for energy exchange between Distribution Network Operator (DNO) and MGs, whereas the lower level guarantees a satisfactory tracking between supply and demand. With the proposed scheme, not only we maintain a supply–demand balance in an economic way, but also improve the renewable energy utilization of distributed MG systems. To describe the dynamic process of energy trading, a novel conditional probability distribution model is introduced, which can characterize randomness of charging/discharging and uncertainties of energy dispatch. Moreover, we formulate a two-layer optimization problem and the corresponding algorithm is given. Finally, simulation results show the effectiveness of the proposed method.

Predictive Control for Networked Interval Type-2 T–S Fuzzy System via an Event-Triggered Dynamic Output Feedback Scheme

In this paper, the problem of event-triggered dynamic output feedback model predictive control (OFMPC) for nonlinear networked control systems (NCSs) with packet loss and bounded disturbance is studied. Interval type-2 (IT2) Takagi–Sugeno fuzzy model is exploited to represent the nonlinear plant with parameter uncertainties, which can be captured by the lower and upper membership functions. Whether or not the measured output should be released into unreliable network links is determined by the error between the current measured output and the latest event-triggered output. The Bernoulli random binary distribution is used to describe the process of packet loss in NCSs. This paper proposes the following: 1) the synthesis approach, including the design of the parameter-dependent dynamic output feedback controller by solving an online MPC optimization problem, which minimizes the upper bound of an infinite time horizon quadratic objective function respecting input and state constraints; 2) the guarantee of recursive feasibility and quadratical stability of the closed-loop system by applying the quadratic boundedness technique. Moreover, an algorithm of tightening the ellipsoidal bounds of state error is added to improve the control performance. The simulation and comparison studies are performed to demonstrate the usefulness and availability of the presented new techniques.

Fast predictive control algorithm based on an FPAA analog neural network

A fast predictive control algorithm was developed for simpler, faster MPC optimization based on an FPAA analog neural network. An FPAA analog circuit provides the quadratic programming using a continuous neural network which avoids the convergence problem of discrete neural networks in a fast, simple and flexible algorithm that uses less computational resources than previous methods. The signal constraint of the FPAA analog circuit is solved by translation and scaling. The software and hardware design of the FPAA analog neural network predictive control is presented and verified in tests that show that the algorithm is effective. 摘要 针对模型预测控制 (model predictive control, MPC) 优化求解中占用资源较多、实时性较低且实现相对复杂的问题, 该文提出了一种基于现场可编程模拟阵列 (field programmable analog array, FPAA) 模拟神经网络的快速模型预测控制算法。通过FPAA模拟电路来实现基于连续神经网络的二次规划求解, 有效规避了离散神经网络的收敛性问题, 具有求解速度快、占用资源小、简单易实现的特点; 通过平移变换和尺度变换方法, 解决FPAA模拟电路的信号限制。最后该文给出了FPAA模拟神经网络预测控制软硬件设计方案并通过实验验证了该算法的有效性。

An offset-free MPC formulation for nonlinear systems using adaptive integral controller

This paper investigates a novel offset-free control scheme based on a multiple model predictive controller (MMPC) and an adaptive integral action controller for nonlinear processes. Firstly, the multiple model description captures the essence of the nonlinear process, while keeping the MPC optimization linear. Multiple models also enable the controller to deal with the uncertainty associated with changing setpoint. Then, a min–max approach is utilized to counter the effect of parametric uncertainty between the linear models and the nonlinear process. Finally, to deal with other uncertainties, such as input and output disturbances, an adaptive integral action controller is run in parallel to the MMPC. Thus creating a novel offset-free approach for nonlinear systems that is more easily tuned than observer-based MPC. Simulation results for a pH-controller, which acts as an example of a nonlinear process, are presented to demonstrate the usefulness of the technique compared to using an observer-based MPC.

Honeywell's Multivariable Predictive Control for Pulp Process Optimization and Life Cycle Management of MPC

近年になって国内紙パルプ産業においてもパルプ製造装置への多変数モデル予測制御の導入が始まっている。多変数モデル予測制御は導入した装置全体を安定して制御するとともに，最適化機能により自動的に最適運転を継続して実現する。このような目に見える収益改善効果があることにより，多変数モデル予測制御は国内を含めた世界中の装置産業の主要な装置で広く用いられている。国内装置産業ですでに長年に渡って使用され，海外のパルプ製造装置でも多数使用されているハネウェルが提供する多変数モデル予測制御「Profit Controller」について，コントローラそのものの技術的特長を簡単に説明するとともに，導入後の運用やモニタリングなどをサポートする機能や，将来のさらに大きなスコープの最適化への拡張性について紹介する。

A Real-time MPC-based Energy Management of Hybrid Energy Storage System in Urban Rail Vehicles

The most challenges for the hybrid energy storage system made up of the battery and super capacitor (SC) are the reasonable energy management strategy (EMS) and real-time implementation. Therefore, a variable-step multistep prediction MPC-based energy management strategy is proposed in this paper, which minimizes the system energy losses of the whole operating process and ensures the battery current and SC SOC in a suitable range. In addition, the neural networks (NN) are applied in this paper for real-time implementation, which are trained by using MPC optimization results. To do this, the loss models of the battery, SC and DC/DC converter are built and Simulation is carried out in MATLAB/Simulink, which shows that the proposed EMS can keep the SC SOC in a suitable range. At the same time, the proposed online energy management method can achieve excellent results of MPC optimization.

Approximation techniques for dynamic real-time optimization (DRTO) of distributed MPC systems

A dynamic real-time optimization (DRTO) strategy has recently been proposed for coordination of distributed MPC systems. The scheme utilizes a prediction model that accounts for the impact of the distributed controllers on the plant response. Two techniques are presented for approximating the closed-loop prediction within the DRTO formulation - a hybrid closed-loop and an input clipping formulation. The hybrid formulation generates closed-loop predictions for a limited number of time intervals along the DRTO prediction horizon, followed by an open-loop optimal control formulation for the rest of the horizon. The input clipping formulation utilizes an unconstrained MPC optimization formulation for each distributed MPC, coupled with an input saturation mechanism. The performance of the approximation techniques is evaluated through application to case studies based on linear and nonlinear dynamic plant models respectively. The approximation techniques are demonstrated to be more computationally efficient than the rigorous counterpart without significant loss in performance.

Stochastic self-triggered model predictive control for linear systems with probabilistic constraints

A stochastic self-triggered model predictive control (SSMPC) algorithm is proposed for linear systems subject to exogenous disturbances and probabilistic constraints. The main idea behind the self-triggered framework is that at each sampling instant, an optimization problem is solved to determine both the next sampling instant and the control inputs to be applied between the two sampling instants. Although the self-triggered implementation achieves communication reduction, the control commands are necessarily applied in open-loop between sampling instants. To guarantee probabilistic constraint satisfaction, necessary and sufficient conditions are derived on the nominal systems by using the information on the distribution of the disturbances explicitly. Moreover, based on a tailored terminal set, a multi-step open-loop MPC optimization problem with infinite prediction horizon is transformed into a tractable quadratic programming problem with guaranteed recursive feasibility. The closed-loop system is shown to be stable. Numerical examples illustrate the efficacy of the proposed scheme in terms of performance, constraint satisfaction, and reduction of both control updates and communications with a conventional time-triggered scheme.

Economic Coordination of Distributed Nonlinear MPC Systems using Closed-loop Prediction of a Nonlinear Dynamic Plant

A coordination scheme for nonlinear MPCs is presented using a dynamic real-time optimization (DRTO) formulation with a nonlinear dynamic plant model. By considering the control action of constrained nonlinear MPCs, the nonlinear DRTO formulation generates the predicted closed-loop response of the plant and computes optimal set-point trajectories based on an economic objective. The set-point trajectories are assigned to lower-level nonlinear MPCs for tracking. Due to the inclusion of nonlinear MPC regulation, the DRTO formulation results in a multi-level optimization problem. The solution strategy applied is to transform the nonlinear MPC optimization subproblems into sets of algebraic equations using the Karush-Kuhn-Tucker (KKT) optimality conditions, and to embed these equations in the DRTO formulation to yield a single-level optimization problem. The performance of proposed formulation is evaluated through application to a case study, with comparisons made against its counterpart that utilizes linear DRTO and MPC formulations.

Distributed Model Predictive Control of linear discrete-time systems with local and global constraints

This paper proposes a Distributed Model Predictive Control (DMPC) approach for a family of discrete-time linear systems with local (uncoupled) and global (coupled) constraints. The proposed approach is based on the dual problem of a MPC optimization problem involving all systems. This dual problem is then distributedly solved, based on the Alternating Direction Multiplier Method (ADMM) with several known simplifications. When the network of systems is large or sparsely connected, the computation of the optimal control using ADMM can be expensive. The proposed approach mitigates this problem by allowing early termination of the ADMM process. This is made possible via a finite-time consensus algorithm that determines the satisfaction of the termination condition and by appropriate tightening of the coupled constraints. Under reasonable assumptions, the approach is guaranteed to converge to a small neighborhood of the optimal so long as the network is connected. Recursive feasibility and exponential stability of the closed-loop system are shown. The performance of the proposed approach is demonstrated by a numerical example.

Assessing plant design with regard to MPC performance

Model Predictive Control is ubiquitous in the chemical industry and offers great advantages over traditional controllers. Notwithstanding, new plants are being projected without taking into account how design choices affect the MPC’s ability to deliver better control and optimization. Thus a methodology to determine if a certain design option favours or hinders MPC performance would be desirable. This paper presents the economic MPC optimization index whose intended use is to provide a procedure to compare different designs for a given process, assessing how well they can be controlled and optimised by a zone constrained MPC. The index quantifies the economic benefits available and how well the plant performs under MPC control given the plant’s controllability properties, requirements and restrictions. The index provides a monetization measure of expected control performance. This approach assumes the availability of a linear state-space model valid within the control zone defined by the upper and lower bounds of each controlled and manipulated variable. We have used a model derived from simulation step tests as a practical way to use the method. The impact of model uncertainty on the methodology is discussed. An analysis of the effects of disturbances on the index illustrates how they may reduce profitability by restricting the ability of a MPC to reach dynamic equilibrium near process restrictions, which in turn increases product quality giveaway and costs. A case of study consisting of four alternative designs for a realistically sized crude oil atmospheric distillation plant is provided in order to demonstrate the applicability of the index.

Event-Driven Robust Output Feedback Control for Constrained Linear Systems via Model Predictive Control Method

This paper considers the problem of event-driven robust output feedback model predictive control for constrained linear systems subject to bounded disturbances. The proposed output feedback controller involves designing a Luenberger state estimator and an event-driven robust model predictive controller. The state estimation error is bounded by a robust positively invariant set, and a constraint tightening method is utilized to formulate the robust output feedback MPC optimization problem. Based on input-to-state stability theory, the event-triggering condition with respect to the error between the system output and the observer output is derived. At each sampling instant, the optimization problem is required to be solved only when the triggering condition is violated. Otherwise, a candidate control law is constructed and applied to system. Moreover, both the feasibility of the optimization problem and the convergence of closed-loop system are proved. Finally, a simulation example is given to show that the proposed approach can reduce the solving frequency of optimization problems while guaranteeing that the system state converges to a neighborhood of the equilibrium.

Fast Model Predictive Control for Multilevel Cascaded H-Bridge STATCOM with Polynomial Computation Time

To solve the issue of exponentially increasing computational burden of finite control set model predictive control (FCS-MPC) for multilevel converters, a fast MPC scheme for multilevel cascaded H-bridge STATCOM is presented. The proposed approach consists of three steps. First, with the partially stratified optimization approach, the multiobjective programming of MPC is divided into two suboptimization problems, i.e., current-control MPC and voltage-balancing MPC. Second, a dynamic programming algorithm is proposed for the optimization of current-control MPC. Third, a mixed algorithm, which combines dynamic programming and greedy algorithm (0-1 programing), is proposed to select the optimal switching combination from all the redundant switching combinations for the voltage balancing MPC achieving a global optimization. Through the analysis of the time complexity, with the proposed scheme, the total computation of FCS-MPC can be reduced to polynomial time from exponential time. The proposed approaches will not deteriorate the control performance. The control performance is validated by simulation results and the effectiveness is further demonstrated by implementing the algorithm on a low-cost DSP (TMS320F28335) in real time.

Closed-loop Formulation for Nonlinear Dynamic Real-time Optimization

Dynamic real-time optimization (DRTO) is a higher level online strategy that exploits plant economic potential by making appropriate adjustments to the lower level controller set-point trajectories. In this work, we propose a closed-loop formulation for a nonlinear DRTO calculation in the form of a bilevel programming problem. A nonlinear differential algebraic equation (DAE) system that describes the process dynamic behavior is utilized with an embedded constrained predictive control (MPC) optimization subproblem to generate the approximate closed-loop response dynamics at the primary economic optimization layer. The bilevel DRTO problem is reformulated as a single-level mathematical program with complementarity constraints (MPCC) by replacing the MPC optimization subproblem by its Karush-Kuhn-Tucker (KKT) optimality conditions. We investigate the economics and control performance of the proposed strategy based on a polymer grade transition case study in the presence of plant-model mismatch and a disturbance, and a comparison is made with the application of a linear DRTO prediction model.

A Model-Predictive Urban Traffic Control Approach with a Modified Flow Model and Endpoint Penalties**This research has been supported by COST ARTS and by the NWO-NFSC project “Multi-level predictive traffic control for large-scale urban networks” (629.001.011), which is partly financed by the Netherlands Organization for Scientific Research (NWO).

Abstract: Nowadays, congestion caused by traffic in urban areas is considered as a major problem. In order to make the best use of the existing road capacity traffic-responsive control systems, including model-predictive controllers, are excellent choices. A mo del-predictive controller can minimize a cost function along a given time horizon. We propose a model-predictive control system that aims to reduce the congestion, and uses an internal flow model, which is our proposed modified version of the S-model. In the formulation of the objective function for the controller, we take into account the effect of those vehicles that remain in the network at the end of the prediction horizon until the network is completely evacuated. We formulate this effect as endpoint penalties for the MPC optimization problem. Finally, we will apply the designed controller to an urban traffic network and compare two scenarios, i.e., the fixed-time control case and the model-predictive control approach with the endpoint penalties proposed in this paper. The results prove the excellent performance of the model-predictive controller compared with the fixed-time controller.

Control of centrifugal compressors via model predictive control for enhanced oil recovery applications

This paper proposes a control system for integrated pressure and surge control of centrifugal compressors for enhanced oil recovery application. The proposed control system is based on linear model predictive control. A fully validated non-linear dynamic model was developed in order to simulate the operation of the compressor at full and partial load. The model of the compression system includes a main process line with the compressor and a recycle line with the antisurge recycle valve. Different disturbance and control tuning scenarios were tested and the response of the model predictive controller was analysed, evaluated and also compared with a traditional control system. Temperature effects have been taken into account in the model of the process and in the constraint formulation of the MPC optimization problem. The results show that the proposed control technique is able to meet the process demand while preventing surge and also minimizing the amount of gas recycle.

A novel adaptive fuzzy predictive control for hybrid systems with mixed inputs

This paper proposes a new adaptive nonlinear model predictive control (NMPC) methodology for a class of hybrid systems with mixed inputs. For this purpose, an online fuzzy identification approach is presented to recursively estimate an evolving Takagi–Sugeno (eTS) model for the hybrid systems based on a potential clustering scheme. A receding horizon adaptive NMPC is then devised on the basis of the online identified eTS fuzzy model. The nonlinear MPC optimization problem is solved by a genetic algorithm (GA). Diverse sets of test scenarios have been conducted to comparatively demonstrate the robust performance of the proposed adaptive NMPC methodology on the challenging start-up operation of a hybrid continuous stirred tank reactor (CSTR) benchmark problem.

A Hybrid MPC Optimization approach for HVAC Direct Load Control

Direct load control posits the existence of a dynamic relationship between electric utilities and customers, enabling the utility to manage customer consumption as it deems appropriate. Thus, supply can be disconnected where necessary provided such action complies with customer-imposed requirements. Proper execution of a fully automated management plan will require a host of online tools including instrumentation, models, optimization algorithms and automation systems.This study develops a novel methodology that solves the online direct load control problem from an automation based formulation by means of hybrid model predictive control, using HVAC (Heating, Ventilating and Air Conditioning) systems as a particular case. The methodology models the thermal behavior of a standard zone in a building constrained by the customer's maximum temperature requirement.Our simulation results show that hybrid model predictive control is a viable alternative to solving the direct load control problem and can manage electricity demand while satisfying constraints set by consumers. It was also found that the controller operation is robust to simulated disturbances and uncertainties in its parameters.

A distributed MPC strategy based on Benders’ decomposition applied to multi-source multi-zone temperature regulation

Abstract This paper presents a distributed model predictive control (DMPC) algorithm based on Benders’ decomposition for temperature regulation in buildings using multiple heating sources. It is well known that the main objective of this control problem is to minimize the heating energy bills while maintaining a certain indoor thermal comfort. To reduce the heating costs, many buildings are equipped with different heating sources. An example is the use of a hot water based central heating system and local electric convectors as complementary heating sources. Using a linear system model of the controlled process, the MPC optimization problem can be solved by linear programming. In order to reduce the computational demand required to solve the minimization problem, the authors propose a DMPC algorithm based on the Benders’ decomposition. The effectiveness of the proposed approach compared to the currently used PI-based control is illustrated in a simulation study.