Reconfigurable predictive control for redundantly actuated systems with parameterised input constraints

A method is proposed for on-line reconfiguration of the terminal constraint used to provide theoretical nominal stability guarantees in linear model predictive control (MPC). By parameterising the terminal constraint, its complete reconstruction is avoided when input constraints are modified to accommodate faults. To enlarge the region of feasibility of the terminal control law for a certain class of input faults with redundantly actuated plants, the linear terminal controller is defined in terms of virtual commands. A suitable terminal cost weighting for the reconfigurable MPC is obtained by means of an upper bound on the cost for all feasible realisations of the virtual commands from the terminal controller. Conditions are proposed that guarantee feasibility recovery for a defined subset of faults. The proposed method is demonstrated by means of a numerical example.     

MPC for tracking piecewise constant references for constrained linear systems

In this paper, a novel model predictive control (MPC) for constrained (non-square) linear systems to track piecewise constant references is presented. This controller ensures constraint satisfaction and asymptotic evolution of the system to any target which is an admissible steady-state. Therefore, any sequence of piecewise admissible setpoints can be tracked without error. If the target steady state is not admissible, the controller steers the system to the closest admissible steady state.These objectives are achieved by: (i) adding an artificial steady state and input as decision variables, (ii) using a modified cost function to penalize the distance from the artificial to the target steady state (iii) considering an extended terminal constraint based on the notion of invariant set for tracking. The control law is derived from the solution of a single quadratic programming problem which is feasible for any target. Furthermore, the proposed controller provides a larger domain of attraction (for a given control horizon) than the standard MPC and can be explicitly computed by means of multiparametric programming tools. On the other hand, the extra degrees of freedom added to the MPC may cause a loss of optimality that can be arbitrarily reduced by an appropriate weighting of the offset cost term.     

六自由度机械臂约束预测控制系统的设计

本文提出了一种基于约束预测控制的机械臂实时运动控制方法.该控制方法分为两层,分别设计了约束预测控制器和跟踪控制器.其中,约束预测控制器在考虑系统物理约束的条件下,在线为跟踪控制器生成参考轨迹;跟踪控制器采用最优反馈控制律,使机械臂沿参考轨迹运动.为了简化控制器的设计和在线求解,本文采用输入输出线性化的方式简化机械臂动力学模型.同时,为了克服扰动,在约束预测控制器中引入前馈策略,提出了带前馈一反馈控制结构的预测控制设计.因此,本文设计的控制器可以使机械臂在满足物理约束的条件下快速稳定地跟踪到目标位置.通过在PUMA560机理模型上进行仿真实验,验证了预测控制算法的可行性和有效性.     

Control of the Tennessee Eastman process using input-output models

This paper presents a case-study where model predictive control is applied to control a nonlinear, open-loop unstable process called the Tennessee Eastman Challenge Process. Both the base case and transitions between different operating points are considered. The control scheme is based on an input-output model identified from plant data. The Model Predictive Controller (MPC) controller acts as a supervisory controller that dictates the setpoints for a lower level PID loop structure. Simulations are presented to illustrate its effectiveness or disturbance rejection and setpoint tracking.     

Dual closed‐loop tracking control for wheeled mobile robots via active disturbance rejection control and model predictive control

A dual closed‐loop tracking control is proposed for a wheeled mobile robot based on active disturbance rejection control (ADRC) and model predictive control (MPC). In the inner loop system, the ADRC scheme with an extended state observer (ESO) is proposed to estimate and compensate external disturbances. In the outer loop system, the MPC strategy is developed to generate a desired velocity for the inner loop dynamic system subject to a diamond‐shaped input constraint. Both effectiveness and stability analysis are given for the ESO and the dual closed‐loop system, respectively. Simulation results demonstrate the performances of the proposed control scheme.     

Optimal MPC for tracking of constrained linear systems

Model predictive control (MPC) is one of the few techniques which is able to handle constraints on both state and input of the plant. The admissible evolution and asymptotic convergence of the closed-loop system is ensured by means of suitable choice of the terminal cost and terminal constraint. However, most of the existing results on MPC are designed for a regulation problem. If the desired steady-state changes, the MPC controller must be redesigned to guarantee the feasibility of the optimisation problem, the admissible evolution as well as the asymptotic stability. Recently, a novel MPC has been proposed to ensure the feasibility of the optimisation problem, constraints satisfaction and asymptotic evolution of the system to any admissible target steady-state. A drawback of this controller is the loss of a desirable property of the MPC controllers: the local optimality property. In this article, a novel formulation of the MPC for tracking is proposed aimed to recover the optimality property maintaining all the properties of the original formulation.     

终端滑模约束的时滞系统模型预测控制

终端约束区域和终端代价项在模型预测控制中起着关键的作用,针对输入受限的时滞系统,提出了终端滑模约束的模型预测控制．将满足输入约束的滑模面作为终端约束区域,使得终端约束区域扩大,有效缩短预测时域,减少计算量,有利于在线应用．最后通过仿真验证了所提方法的有效性．     

An improved robust model predictive control for linear parameter‐varying input‐output models

This paper describes a new robust model predictive control (MPC) scheme to control the discrete‐time linear parameter‐varying input‐output models subject to input and output constraints. Closed‐loop asymptotic stability is guaranteed by including a quadratic terminal cost and an ellipsoidal terminal set, which are solved offline, for the underlying online MPC optimization problem. The main attractive feature of the proposed scheme in comparison with previously published results is that all offline computations are now based on the convex optimization problem, which significantly reduces conservatism and computational complexity. Moreover, the proposed scheme can handle a wider class of linear parameter‐varying input‐output models than those considered by previous schemes without increasing the complexity. For an illustration, the predictive control of a continuously stirred tank reactor is provided with the proposed method.     

基于等价输入干扰滑模观测器的磁悬浮球系统模型预测控制

本文针对系统不确定性和外部干扰引起的磁悬浮球系统控制性能下降的问题,提出了一种基于等价输入干扰滑模观测器的模型预测控制(MPC+EIDSMO)方法.首先将原系统转化为EID系统,采用等价输入干扰滑模观测器对EID系统状态变量及等价输入干扰进行估计;然后基于状态估计值设计模型预测控制器,并将等价输入干扰估计值以前馈的方式...     

Design of robust model predictive control with input constraints

This article addresses the problem of designing a robust output feedback model predictive control (MPC) with input constraints, which ensures a parameter-dependent quadratic stability and guaranteed cost for the case of linear polytopic systems. A new heuristic method is introduced to guarantee input constraints for the MPC. To reject disturbances and maintain the process at the optimal operating conditions or setpoints, the integrator is added to the controller design procedure. Finally, some numerical examples are given to illustrate the effectiveness of the proposed method.     

Constrained nonlinear MPC for accelerated tracking piece-wise references and its applications to thermal systems

In this paper, we propose a model predictive control (MPC) strategy for accelerated offset-free tracking piece-wise constant reference signals of nonlinear systems subject to state and control constraints. Some special contractive constraints on tracking errors and terminal constraints are embedded into the tracking nonlinear MPC formulation. Then, recursive feasibility and closed-loop convergence of the tracking MPC are guaranteed in the presence of piece-wise references and constraints by deriving some sufficient conditions. Moreover, the local optimality of the tracking MPC is achieved for unreachable output reference signals. By comparing to traditional tracking MPC, the simulation experiment of a thermal system is used to demonstrate the acceleration ability and the effectiveness of the tracking MPC scheme proposed here.     

状态空间模型的双层结构预测控制算法

双层结构预测控制是指先进行设定值优化、再进行设定值跟踪的预测控制.在已有的双层结构动态矩阵控制的基础上,本文给出基于状态空间模型的双层结构预测控制算法.该算法基于干扰模型和新定义的开环预测值,给出了新的开环预测模块.该开环预测模块采用Kalman滤波方法得到操作变量、被控变量的开环动、稳态预测值.基于这些开环预测值,稳态目标计算模块的基本原理同双层结构动态矩阵控制,但是具体细节上遵循状态空间方法.动态控制模块基于稳态目标计算提供的操作变量、被控变量的稳态目标(设定值),采用二次规划算法计算控制作用.仿真算例证实了该算法的有效性.     

Input-output linearizing control of constrained nonlinear processes

An input-output linearization strategy for constrained nonlinear processes is proposed. The system may have constraints on both the manipulated input and the controlled output. The nonlinear control system is comprised of: (i) an input-output linearizing controller that compensates for processes nonlinearities; (ii) a constraint mapping algorithm that transforms the original input constraints into constraints on the manipulated input of the feedback linearized system; (iii) a linear model predictive controller that regulates the resulting constrained linear system; and (iv) a disturbance model that ensures offset-free setpoint tracking. As a result of these features, the approach combines the computational simplicity of input output linearization and the constraint handling capability of model predictive control. Simulation results for a continuous stirred tank reactor demonstrate the superior performance of the proposed strategy as compared to conventional input-output linearizing control and model predictive control techniques.     

On the stability of constrained MPC without terminal constraint

The usual way to guarantee stability of model predictive control (MPC) strategies is based on a terminal cost function and a terminal constraint region. This note analyzes the stability of MPC when the terminal constraint is removed. This is particularly interesting when the system is unconstrained on the state. In this case, the computational burden of the optimization problem does not have to be increased by introducing terminal state constraints due to stabilizing reasons. A region in which the terminal constraint can be removed from the optimization problem is characterized depending on some of the design parameters of MPC. This region is a domain of attraction of the MPC without terminal constraint. Based on this result, it is proved that weighting the terminal cost, this domain of attraction of the MPC controller without terminal constraint is enlarged reaching (practically) the same domain of attraction of the MPC with terminal constraint; moreover, a practical procedure to calculate the stabilizing weighting factor for a given initial state is shown. Finally, these results are extended to the case of suboptimal solutions and an asymptotically stabilizing suboptimal controller without terminal constraint is presented.     

On real-time robust model predictive control

High-speed applications impose a hard real-time constraint on the solution of a model predictive control (MPC) problem, which generally prevents the computation of the optimal control input. As a result, in most MPC implementations guarantees on feasibility and stability are sacrificed in order to achieve a real-time setting. In this paper we develop a real-time MPC approach for linear systems that provides these guarantees for arbitrary time constraints, allowing one to trade off computation time vs. performance. Stability is guaranteed by means of a constraint, enforcing that the resulting suboptimal MPC cost is a Lyapunov function. The key is then to guarantee feasibility in real-time, which is achieved by the proposed algorithm through a warm-starting technique in combination with robust MPC design. We address both regulation and tracking of piecewise constant references. As a main contribution of this paper, a new warm-start procedure together with a Lyapunov function for real-time tracking is presented. In addition to providing strong theoretical guarantees, the proposed method can be implemented at high sampling rates. Simulation examples demonstrate the effectiveness of the real-time scheme and show that computation times in the millisecond range can be achieved.     

Model predictive control using reduced order models: Guaranteed stability for constrained linear systems

The problem of controlling a high-dimensional linear system subject to hard input and state constraints using model predictive control is considered. Applying model predictive control to high-dimensional systems typically leads to a prohibitive computational complexity. Therefore, reduced order models are employed in many applications. This introduces an approximation error which may deteriorate the closed loop behavior and may even lead to instability. We propose a novel model predictive control scheme using a reduced order model for prediction in combination with an error bounding system. We employ the explicit time and input dependent bound on the model order reduction error to achieve design conditions for constraint fulfillment, recursive feasibility and asymptotic stability for the closed loop of the model predictive controller when applied to the high-dimensional system. Moreover, for a special choice of design parameters, we establish local optimality of the proposed model predictive control scheme. The proposed MPC approach is assessed via examples demonstrating that a good trade-off between computational efficiency and conservatism can be achieved while guaranteeing constraint satisfaction and asymptotic stability.     

Use of model predictive controller in dual-loop control of three-phase PWM AC/DC converter

In the classical dual-loop voltage control scheme for an AC/DC converter, this paper proposes a simple stabilizing inner-loop model predictive controller (MPC) to regulate the output current and q-frame current to their references. The proposed MPC minimizes a cost function of the tracking error without any use of numerical methods using the specific property of the input matrix of the converter. It is shown that this MPC globally stabilizes the converter in the presence of input constraints. As the same manner of the classical dual-loop control scheme, PI controllers are adopted in the outerloop to regulate the output voltage while maintaining the maximum power factor. The simulation results show that the proposed inner-loop MPC considerably enhances the closed-loop performance despite the load changes.     

时变输出约束非线性系统的量化反馈 自适应终端滑模控制

针对一类复杂非线性系统,提出一种新型自适应快速非奇异终端滑模控制(IAFNTSMC)方法,用以解决其在输出时变约束及量化输入情形下的轨迹跟踪问题;利用鲁棒自适应方法处理扰动不确定性,并结合反演策略和终端滑模策略设计控制器;构造一种新型的时变约束障碍Lyapunov函数,用于实现对系统的输出误差进行随时间变化的幅值约束;为提高闭环系统的误差收敛速度,提出一种新型的滑模面构造方案.所提控制方法能够保证闭环系统的输出跟踪误差快速收敛到约束边界内,并确保闭环系统所有信号有界.数值仿真验证了所提方法的有效性.     

Novel MPC‐Based Fault Tolerant Tracking Control Against Sensor Faults

The problem of active fault‐tolerant tracking control with control input and system output constraints is studied for a class of discrete‐time systems subject to sensor faults. A time‐varying fault‐tolerant observer is first developed to estimate the real system state from the faulty sensor output and control input signals. Then by using the estimated state at each time step, a model predictive control (MPC)‐based fault‐tolerant tracking control scheme is presented to guarantee the desired tracking performance and the given input and output constraints on the faulty system. In comparison with many existing fault‐tolerant MPC methods, its main contribution is that the proposed state estimator is designed by the simple and online numerical computation to tolerate the possible sensor faults, so that the regular MPC algorithm without fault information can be adopted for the online calculation of fault‐tolerant control signal. The potential recursive infeasibility and computational complexity due to the faults are avoided in the scheme. Additionally, the closed‐loop stability of the post‐fault system is discussed. Simulative results of an electric throttle control system verify the effectiveness of the proposed method.     

Sensor‐fault tolerance using robust MPC with set‐based state estimation and active fault isolation

In this paper, a sensor fault‐tolerant control scheme using robust model predictive control (MPC) and set‐theoretic fault detection and isolation (FDI) is proposed. The robust MPC controller is used to control the plant in the presence of process disturbances and measurement noises while implementing a mechanism to tolerate faults. In the proposed scheme, fault detection (FD) is passive based on interval observers, while fault isolation (FI) is active by means of MPC and set manipulations. The basic idea is that for a healthy or faulty mode, one can construct the corresponding output set. The size and location of the output set can be manipulated by adjusting the size and center of the set of plant inputs. Furthermore, the inputs can be adjusted on‐line by changing the input‐constraint set of the MPC controller. In this way, one can design an input set able to separate all output sets corresponding to all considered healthy and faulty modes from each other. Consequently, all the considered healthy and faulty modes can be isolated after detecting a mode changing while preserving feasibility of MPC controller. As a case study, an electric circuit is used to illustrate the effectiveness of the proposed scheme. Copyright © 2016 John Wiley & Sons, Ltd.