Robust hybrid predictive control of nonlinear systems

In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability region within which any available MPC formulation can be implemented. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event that the predictive controller fails to yield a control move (due, e.g., to computational difficulties in the optimization or infeasibility) or leads to instability (due, e.g., to inappropriate penalties and/or horizon length in the objective function). The implementation and efficacy of the robust hybrid predictive control structure are demonstrated through simulations using a chemical process example.     

Design of networked control systems with bounded arbitrary time delays

This paper is mainly concerned with the model predictive control (MPC) of networked control systems (NCSs) with uncertain time delay and data packets disorder. The network-induced time delay is described as bounded and arbitrary process. For the usual state feedback controller, by considering all the possibilities of delays, an augmented state space model of the closed-loop system, which characterizes all the delay cases, is obtained. The stability conditions are given according to the Lyapunov method based on this augmented model. The stability property is inherited in MPC which explicitly considers the physical constraints. A numerical example is given to demonstrate the effectiveness of the proposed MPC.     

Sensor validation and process fault diagnosis for FCC units under MPC feedback

Model predictive control (MPC) has been widely applied in industry, especially in the refining industry. As all feedback controllers require correct sensor measurements, unreliable sensors can cause the MPC controller to move the process in an erroneous manner. Data validation of sensor measurements is a prerequisite in applying advanced control, particularly multivariable control which depends on many sensors. However, little research work is available on how feedback controllers like MPC complicate the task of sensor validation and process fault diagnosis. In theory, a controller can transfer the effect of a sensor fault in a controlled variable to the manipulated variables. In this paper, principal component analysis (PCA) is applied to detect, identify and reconstruct faulty sensors in a simulated FCC unit. A base PCA model is generated by perturbing the process throughout the operating region. Performance of MPC with and without data validation is compared. The same base PCA model is applied to detect and identify dynamic process faults. We demonstrate that process faults can be detected and diagnosed at an early stage.     

基于累积平方误差–总平方波动指标的模型预测控制器性能评价及自愈

本文针对模型预测控制器实际投运中遇到性能下降问题,提出了一种基于累积平方误差(ISE)–总平方波动(TSV)指标的模型预测控制器性能评价及自愈方法.先基于累积平方误差(ISE)和总平方波动(TSV)指标对模型预测控制器进行实时性能评价,再根据无限时域模型预测控制器(MPC)的逆特性,基于ISE–TSV指标的分析,提出了...     

Robust MPC for Linear Systems with Structured Time‐Varying Uncertainties and Saturating Actuator

In this paper, a synthesis of model predictive control (MPC) algorithm is presented for uncertain systems subject to structured time‐varying uncertainties and actuator saturation. The system matrices are not exactly known, but are affine functions of a time varying parameter vector. To deal with the nonlinear actuator saturation, a saturated linear feedback control law is expressed into a convex hull of a group of auxiliary linear feedback laws. At each time instant, a state feedback law is designed to ensure the robust stability of the closed‐loop system. The robust MPC controller design problem is formulated into solving a minimization problem of a worst‐case performance index with respect to model uncertainties. The design of controller is then cast into solving a feasibility of linear matrix inequality (LMI) optimization problem. Then, the result is further extended to saturation dependent robust MPC approach by introducing additional variables. A saturation dependent quadratic function is used to reduce the conservatism of controller design. To show the effectiveness, the proposed robust MPC algorithms are applied to a continuous‐time stirred tank reactor (CSTR) process.     

Adaptive predictive path following control based on least squares support vector machines for underactuated autonomous vessels

Since vessel dynamics could vary during maneuvering because of load changes, speed changing, environmental disturbances, aging of mechanism, etc., the performance of model‐based path following control may be degraded if the controller uses the same motion model all the time. This article proposes an adaptive path following control method based on least squares support vector machines (LS‐SVM) to deal with parameter changes of the motion model. The path following controller consists of two components: the online identification of varying parameters and model predictive control (MPC) using the adaptively identified models. For the online parameter identification, an improved online LS‐SVM identification method is proposed based on weighted LS‐SVM. Specifically, the objective function of LS‐SVM is modified to decrease the errors of parameter estimation, an index is proposed to detect the possible model changes, which speeds up the rate of parameter convergence, and the sliding data window strategy is used to realize the online identification. MPC is combined with the line‐of‐sight guidance to track straight line reference paths. Finally, case studies are conducted to verify the effectiveness of the proposed path following adaptive controller. Typical parameter varying scenarios, such as rudder aging, current variations and changes of the maneuverability are considered. Simulation results show that the proposed method can handle the above situations effectively.     

Discrete model predictive controller design using Laguerre functions

In Model Predictive Controller (MPC) design, the traditional approach of expanding the future control signal uses the forward shift operator to obtain the linear-in-the-parameters relation for predicted output. As a consequence, in case of rapid sampling, complicated process dynamics and/or high demands on closed-loop performance, satisfactory approximation of the control signal requires a very large number of forward shift operators, and leads to poorly numerically conditioned solutions and heavy computational load when implemented on-line. In this paper, by using a performance specification on the exponential change rate of the control signal, a more appropriate expansion, related to Laguerre net-works, is introduced and analyzed. It is shown that the number of terms used in the optimization procedure can be reduced to a fraction of that required by the usual procedure. By relaxing the constraint on the exponential change rate of the control signal and allowing arbitrary complexity in describing the trajectory, the proposed approach becomes equivalent to the traditional approach in MPC design. Closed-loop stability of the proposed model predictive control system is analyzed by using terminal state variable constraints.     

An improved model predictive control approach based on extended non-minimal state space formulation

This paper presents a new design method of model predictive control (MPC) based on extended non-minimal state space models, in which the measured input and output variables, their past values together with the defined output errors are chosen as the state variables. It shows that this approach does not need the design of an observer to access the state information any more and by augmenting the process model and its objective function to include the changes of the system state variables, the control performances are superior to those of the controller that does not bear this feature. Furthermore, closed-loop transfer function representation of the model predictive control system facilitates the use of frequency response analysis methods for the nominal control performances of the system.     

一种基于衰减集结的鲁棒预测控制器

高效鲁棒预测控制 (ERPC) 是一种在线计算量较小, 且控制性能较好的鲁棒预测控制算法. 但采用单一椭圆不变集的设计方法存在保守性. 本文采用衰减集结策略, 通过离线设计在系统状态空间中投影彼此正交的两个椭圆不变集, 在线进行凸组合的方法设计 ERPC 控制器, 使系统初始可行域进一步扩大, 并在一定程度上改善了控制性能.     

Stochastic closed-loop model predictive control of continuous nonlinear chemical processes

A new predictive control framework for chemical processes is presented, that has a number of fundamental differences to classical MPC. Both future disturbances and future process measurements are explicitly introduced in the model prediction, while back-off prevents violation of the inequality constraints. A feedforward trajectory, used for constraint pushing, is optimized simultaneously with a linear time-varying feedback controller, used to minimize the back-off. No feedback is generated by the receding horizon implementation itself. Via several transformations, the resulting optimization problem is rendered convex. For nonlinear processes, this applies to the sub-problem in a sequential conic optimization approach. A two stage LQG approach reduces the complexity even further for large scale systems. The method is illustrated on a HDPE reactor example and compared to a LTV-MPC.     

Nonlinear model predictive control using parameter varying BP-ARX combination model

A novel back-propagation AutoRegressive with eXternal input (BP-ARX) combination model is constructed for model predictive control (MPC) of MIMO nonlinear systems, whose steady-state relation between inputs and outputs can be obtained. The BP neural network represents the steady-state relation, and the ARX model represents the linear dynamic relation between inputs and outputs of the nonlinear systems. The BP-ARX model is a global model and is identified offline, while the parameters of the ARX model are rescaled online according to BP neural network and operating data. Sequential quadratic programming is employed to solve the quadratic objective function online, and a shift coefficient is defined to constrain the effect time of the recursive least-squares algorithm. Thus, a parameter varying nonlinear MPC (PVNMPC) algorithm that responds quickly to large changes in system set-points and shows good dynamic performance when system outputs approach set-points is proposed. Simulation results in a multivariable stirred tank and a multivariable pH neutralisation process illustrate the applicability of the proposed method and comparisons of the control effect between PVNMPC and multivariable recursive generalised predictive controller are also performed.     

Integrated condition monitoring and control of fed-batch fermentation processes

This paper investigates the benefits that the partial least squares (PLS) modelling approach offers engineers involved in the operation of fed-batch fermentation processes. It is shown that models developed using PLS can be used to provide accurate inference of quality variables that are difficult to measure on-line, such as biomass concentration. It is further shown that this model can be used to provide fault detection and isolation capabilities and that it can be integrated within a standard model predictive control framework to regulate the growth of biomass within the fermenter. This model predictive controller is shown to provide its own monitoring capabilities that can be used to identify faults within the process and also within the controller itself. Finally it is demonstrated that the performance of the controller can be maintained in the presence of fault conditions within the process.     

Model predictive control for batch processes: Ensuring validity of predictions

The intuitive and simple ideas that support model predictive control (MPC) along with its capabilities have been the key to its success both in industry and academia. The contribution this paper makes is to further enhance the capabilities of MPC by easing its application to industrial batch processes. Specifically, this paper addresses the problem of ensuring the validity of predictions when applying MPC to such processes. Validity of predictions can be ensured by constraining the decision space of the MPC problem. The performance of the MPC control strategy relies on the ability of the model to predict the behaviour of the process. Using the model in the region in which it is valid improves the resulting performance. In the proposed approach four validity indicators on predictions are defined: two of them consider all the variables in the model, and the other two consider the degrees of freedom of the controller. The validity indicators are defined from the latent variable model of the process. Further to this, these are incorporated as constraints in the MPC optimization problem to bound the decision space and ensure the proper use of the model. Finally, the MPC cost function is modified to enable fine case-specific tuning if desired. Provided the indicators are quadratic, the controller yields a quadratic constrained quadratic programming problem for which efficient solvers are commercially available. A fed-batch fermentation example shows how MPC ensuring validity of predictions improves performance and eases tuning of the controller. The target in the example provided is end-point control accounting for variations in the initial measurable conditions of the batch.     

在线优化线性反馈增益的非线性鲁棒预测控制方法

以鲁棒控制不变集作为预测控制的终端约束集,设计了一种新的鲁棒预测控制算法.将预测控制在不同采样点的待优化控制律考虑为线性反馈控制律,并通过在线优化求解线性反馈增益.从理论上证明了若采用所设计的鲁棒预测控制器,则系统是输入状态稳定的.最后通过计算机仿真验证了所提出设计方法的可行性.     

Unscented model predictive control of chance constrained nonlinear systems

This paper introduces an unscented model predictive approach for the control of constrained nonlinear systems under uncertainty. The main contribution of this paper is related to incorporation of statistical linearization, rather than commonly used analytical linearization, of the process and measurement models to provide a closer approximation of belief space propagation. Specifically, the state transition is approximated using an unscented transform to obtain a Gaussian belief space. This approximation allows for realization of closed-form solutions, which are otherwise available to linear systems only. Subsequently, the proposed approach is used to develop a model predictive motion control scheme that yields optimal control policies in presence of nonholonomic constraints as well as state estimation and collision avoidance chance constraints. As an example, successful kinematic control of a two-wheeled mobile robot is demonstrated in unstructured environments. Finally, the superiority of the proposed unscented model predictive control (MPC) over the traditional linearization-based MPC is discussed.     

Non-fragile observer-based output feedback control for polytopic uncertain system under distributed model predictive control approach

In this paper, a non-fragile observer-based output feedback control problem for the polytopic uncertain system under distributed model predictive control (MPC) approach is discussed. By decomposing the global system into some subsystems, the computation complexity is reduced, so it follows that the online designing time can be saved.Moreover, an observer-based output feedback control algorithm is proposed in the framework of distributed MPC to deal with the difficulties in obtaining the states measurements. In this way, the presented observer-based output-feedback MPC strategy is more flexible and applicable in practice than the traditional state-feedback one. What is more, the non-fragility of the controller has been taken into consideration in favour of increasing the robustness of the polytopic uncertain system. After that, a sufficient stability criterion is presented by using Lyapunov-like functional approach, meanwhile, the corresponding control law and the upper bound of the quadratic cost function are derived by solving an optimisation subject to convex constraints. Finally, some simulation examples are employed to show the effectiveness of the method.     

一种基于状态估计的鲁棒型预测控制器

针对某些情况下只能得到系统的状态估计,当其作为预测控制的初始状态时传统方法无法保证其目标函数递减的问题,提出一种针对状态估计的预测控制器,由该控制器得到的反馈控制律可以使受控系统渐近稳定.进而,给出了相应的算法,并通过仿真实例验证了所得结论的正确性.     

三相脉宽调制整流器的约束预测控制

本文将基于并行神经网络优化的约束模型预测控制(MPC)应用于脉宽调制(PWM)整流器中,提高了电网的质量.在三相静止坐标系下,建立了三相PWM整流器的解耦数学模型,采用约束模型预测控制策略,突破了有限集和无约束条件下预测控制的局限性.为了提高单步优化的速度,采用神经网络优化算法求解模型预测控制的在线优化.在保证系统单位功率因数的前提下,当系统负载突然变化时,具有快速动态响应稳定输出直流电压的性能.采用FPGA控制器实现并行计算,减少了预测控制算法的计算时间.最后,通过仿真和实验结果得到,采用本文的控制策略,总谐波失真(THD)降低了2.5%,达到稳态的时间大约是PI控制算法的五分之一,为12 ms,验证了该方法的可行性和有效性.     

Model-based Predictive Control for Spatially-distributed Systems Using Dimensional Reduction Models

In this paper, a low-dimensional multiple-input and multiple-output (MIMO) model predictive control (MPC) configuration is presented for partial differential equation (PDE) unknown spatially-distributed systems (SDSs). First, the dimension reduction with principal component analysis (PCA) is used to transform the high-dimensional spatio-temporal data into a low-dimensional time domain. The MPC strategy is proposed based on the online correction low-dimensional models, where the state of the system at a previous time is used to correct the output of low-dimensional models. Sufficient conditions for closed-loop stability are presented and proven. Simulations demonstrate the accuracy and efficiency of the proposed methodologies.