Analytical performance prediction for robust constrained model predictive control

This paper presents a new analysis tool for predicting the closed-loop performance of a robust constrained model predictive control (MPC) scheme. Currently, performance is typically evaluated by numerical simulation, leading to an extensive computation when investigating the effect of controller parameters, such as the horizon length, the cost weightings and the constraint settings. The analytic method, in this paper, avoids this computational burden, thus enabling a rapid study of the trades between the design parameters and the performance. Previous work developed an MPC formulation employing constraint tightening to achieve robust feasibility and constraint satisfaction despite the action of an unknown but bounded disturbance. This paper shows that the expected performance of that controller can be predicted using a combination of the gains of two linear systems, the optimal control for the unconstrained system, and a candidate policy used in performing the constraint tightening. The method also accounts for the possible mismatch between the predicted level of disturbance and the actual level encountered. The analytic results are compared with simulation results for several examples and are shown to provide accurate predictions of performance and its variation with the system parameters.     

Online linearization-based neural predictive control of air–fuel ratio in SI engines with PID feedback correction scheme

Model predictive control (MPC) frequently uses online identification to overcome model mismatch. However, repeated online identification does not suit the real-time controller, due to its heavy computational burden. This work presents a computationally efficient constrained MPC scheme using nonlinear prediction and online linearization based on neural models for controlling air–fuel ratio of spark ignition engine to its stoichiometric value. The neural model for AFR identification has been trained offline. The model mismatch is taken care of by incorporating a PID feedback correction scheme. Quadratic programming using active set method has been applied for nonlinear optimization. The control scheme has been tested on mean value engine model simulations. It has been shown that neural predictive control with online linearization using PID feedback correction gives satisfactory performance and also adapts to the change in engine systems very quickly.     

Adaptive receding horizon predictive control for constrained discrete-time linear systems with parameter uncertainties

This paper proposes a discrete-time model predictive control (MPC) scheme combined with an adaptive mechanism. To this end, first, an adaptive parameter estimation algorithm suitable for MPC is proposed, which uses the available input and output signals to estimate the unknown system parameters. It enables the prediction of a monotonically decreasing worst-case estimation error bound over the prediction horizon of MPC. These distinctive features allow for future model improvement to be explicitly considered in MPC. Thus, a less conservative adaptive-type MPC controller can be developed based on the proposed estimation method. Second, we show how the discrete-time adaptive-type state-feedback MPC controller is constructed by combining the on-line parameter estimation scheme with a modified robust MPC method based on the comparison model. The developed MPC controller guarantees feasibility and stability of the closed-loop system theoretically in the presence of input and state constraints. A numerical example is given to demonstrate its effectiveness.     

基于改进卡尔曼滤波器的扰动抑制无模型自适应控制方案

针对无模型自适应控制方法在测量扰动作用下控制效果不佳的问题, 本文提出了一种新的扰动抑制无模 型自适应控制方案. 首先基于受控系统的动态线性化数据模型及测量扰动的统计特性, 在最小方差估计准则下推导 了基于系统输入输出数据的改进卡尔曼滤波器. 然后基于此滤波器给出了一种新的扰动抑制无模型自适应控制方 案. 该方案仅需用到受控系统的输入输出数据, 即可实现在强测量扰动作用下系统的无模型自适应控制. 仿真结果 显示, 相比现有的扰动抑制无模型自适应控制方案, 该方案在系统跟踪常值参考信号、时变参考信号时均能有效地 抑制测量扰动, 适用性更好的同时可以获得更小的跟踪误差及更大的数据信噪比.     

Reconstruction of cylinder pressure for SI engine using recurrent neural network

Model predictive control (MPC) frequently uses online identification to overcome model mismatch. However, repeated online identification does not suit the real-time controller, due to its heavy computational burden. This work presents a computationally efficient constrained MPC scheme using nonlinear prediction and online linearization based on neural models for controlling air–fuel ratio of spark ignition engine to its stoichiometric value. The neural model for AFR identification has been trained offline. The model mismatch is taken care of by incorporating a PID feedback correction scheme. Quadratic programming using active set method has been applied for nonlinear optimization. The control scheme has been tested on mean value engine model simulations. It has been shown that neural predictive control with online linearization using PID feedback correction gives satisfactory performance and also adapts to the change in engine systems very quickly.     

基于特征线法的双曲型分布参数模型预测控制及其应用

本文针对双曲型分布参数系统提出基于特征线法的模型预测控制算法. 通过特征线变换将描述分布参数模型的偏微分方程转化为常微分方程; 进而求解得到分布参数系统状态变量的解析式; 离散化后作为预测模型用于模型预测控制. 以循环流化床烟气脱硫系统中SO2浓度控制为例, 进行仿真研究, 结果表明基于特征线法的模型预测控制算法可以实现对双曲型分布参数系统的有效控制, 并且该算法的控制效果优于目前工程应用的前馈反馈 控制策略.     

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.     

Detection of model-plant mismatch in closed-loop control system

The performance of model-based control systems depends a lot on the process model quality, hence the process model-plant mismatch is an important factor degrading the control performance. In this paper, a new methodology based on a process model evaluation index is proposed for detecting process model mismatch in closed-loop control systems. The proposed index is the ratio between the variance of the disturbance innovation and that of the model quality variable. The disturbance innovations are estimated from the routine operation data by an orthogonal projection method. The model quality variable can be obtained using the closed-loop data and the disturbance model estimated by adaptive Least absolute shrinkage and selection operator (Lasso) method. When the order of the disturbance model is less than 2 or the process time delay is large enough, no external perturbations are required. Besides, the proposed index is independent of the controller tuning and insensitive to the changes in disturbance model, which indicates that the proposed method can isolate the process model-plant mismatch from other factors affecting the overall control performance. Three systems with proportional integral (PI) controller, linear quadratic (LQ) controller and unconstrained model predictive control (MPC) respectively are presented as examples to verify the effectiveness of the proposed technique. Besides, Tennessee Eastman process shows the proposed method is able to detect process model mismatch of nonlinear systems.     

Model analysis and performance analysis of two industrial MPCs

This paper presents two case studies on the performance evaluation and model validation of two industrial multivariate model predictive control (MPC) based controllers: (1) a 7-output, 3-input MPC with three measured disturbance variables for controlling a part of kerosene hydrotreating unit (KHU) and (2) a 8-output, 4-input MPC with five measured disturbances for controlling a part of naphtha hydrotreating unit (NHU). The first case study focuses on potential limits to control performance due to constraints and limits set at the time of controller commissioning. The root causes of sub-optimal performance of KHU are successfully isolated. Data from the NHU unit with MPC ‘on’ and with MPC ‘off’ are analyzed to obtain and compare several different measures of multivariate controller performance. Model quality assessment for the two MPCs are performed. A new model index is proposed to have a measure of simulation ability and prediction ability of a model. Closed-loop identification of KHU and closed-loop identification of NHU are conducted using the asymptotic method (ASYM) proposed by Zhu (1998).     

Model Predictive Control oriented experiment design for system identification: A graph theoretical approach

We present a new approach to Model Predictive Control (MPC) oriented experiment design for the identification of systems operating in closed-loop. The method considers the design of an experiment by minimizing the experimental cost, subject to probabilistic bounds on the input and output signals due to physical limitations of actuators, and quality constraints on the identified model. The excitation is done by intentionally adding a disturbance to the loop. We then design the external excitation to achieve the minimum experimental effort while we are also taking care of the tracking performance of MPC. The stability of the closed-loop system is guaranteed by employing robust MPC during the experiment. The problem is then defined as an optimization problem. However, the aforementioned constraints result in a non-convex optimization which is relaxed by using results from graph theory. The proposed technique is evaluated through a numerical example showing that it is an attractive alternative for closed-loop experiment design.     

Fault diagnosis and accommodation of nonlinear systems based on multiple-model adaptive unscented Kalman filter and switched MPC and H-infinity loop-shaping controller

In this paper, a new active fault tolerant control (AFTC) methodology is proposed based on a state estimation scheme for fault detection and identification (FDI) to deal with the potential problems due to possible fault scenarios. A bank of adaptive unscented Kalman filters (AUKFs) is used as a core of FDI module. The AUKF approach alleviates the inflexibility of the conventional UKF due to constant covariance set up, leading to probable divergence. A fuzzy-based decision making (FDM) algorithm is introduced to diagnose sensor and/or actuator faults. The proposed FDI approach is utilized to recursively correct the measurement vector and the model used for both state estimation and output prediction in a model predictive control (MPC) formulation. Robustness of the proposed FTC system, H_∞ optimal robust controller and MPC are combined via a fuzzy switch that is used for switching between MPC and robust controller such that FTC system is able to maintain the offset free behavior in the face of abrupt changes in model parameters and unmeasured disturbances. This methodology is applied on benchmark three-tank system; the proposed FTC approach facilitates recovery of the closed loop performance after the faults have been isolated leading to an offset free behavior in the presence of sensor/actuator faults that can be either abrupt or drift change in biases. Analysis of the simulation results reveals that the proposed approach provides an effective method for treating faults (biases/drifts in sensors/actuators, changes in model parameters and unmeasured disturbances) under the unified framework of robust fault tolerant control.     

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.     

A disturbance observer enhanced composite cascade control with experimental studies

The presence of strong disturbances usually causes great performance degradation of industrial process control systems. A disturbance observer (DOB) enhanced composite cascade control consisting of model predictive control (MPC), proportional-integral-derivative (PID) control, and DOB is proposed in this paper. DOB is employed here to estimate the severe disturbances and the estimated values are applied for feed-forward compensation, forming a composite control together with MPC. To evaluate the efficiency and validity of the proposed control structure, the simulation as well as experimental studies have been carried out for a level tank process which represents a typical first-order plus dead-time (FODT) industry process. Both the simulation and experimental results show that the proposed composite control method significantly improves the disturbance attenuation property of the MPC scheme in controlling such a typical industrial process.     

Adaptive air-fuel ratio control with MLP network

This paper presents an application of adaptive neural network model-based predictive control (MPC) to the air-fuel ratio of an engine simulation. A multi-layer perceptron (MLP) neural network is trained using two on-line training algorithms: a back propagation algorithm and a recursive least squares (RLS) algorithm. It is used to model parameter uncertainties in the nonlinear dynamics of internal combustion (IC) engines. Based on the adaptive model, an MPC strategy for controlling air-fuel ratio is realized, and its control performance compared with that of a traditional PI controller. A reduced Hessian method, a newly developed sequential quadratic programming (SQP) method for solving nonlinear programming (NLP) problems, is implemented to speed up nonlinear optimization in the MPC.     

Robust disturbance modeling for model predictive control with application to multivariable ill-conditioned processes

In this paper the disturbance model, used by MPC algorithms to achieve offset-free control, is optimally designed to enhance the robustness of single-model predictive controllers. The proposed methodology requires the off-line solution of a min-max optimization problem in which the disturbance model is chosen to guarantee the best closed-loop performance in the worst case of plant in a given uncertainty region. Application to a well-known ill-conditioned distillation column is presented to show that, for ill-conditioned processes, the use of a disturbance model that adds the correction term to the process inputs guarantees a robust performance, while the disturbance model that adds the correction term to the process outputs (used by industrial MPC algorithms) does not.     

Robust tracking enhancement of robot systems including motordynamics: a fuzzy-based dynamic game approach

A robust tracking control design of robot systems including motor dynamics with parameter perturbation and external disturbance is proposed in this study via adaptive fuzzy cancellation technique. A minimax controller equipped with a fuzzy-based scheme is used to enhance the tracking performance in spite of system uncertainties and external disturbance. The design procedure is divided into three steps. At first, a linear nominal robotic control design is obtained via model reference tracking with desired eigenvalue assignment. Next, a fuzzy logic system is constructed and then tuned to eliminate the nonlinear uncertainties as possibly as it can to enhance the tracking robustness. Finally, a minimax control scheme is specified to optimally attenuate the worst-case effect of both the residue due to fuzzy cancellation and external disturbance to achieve a minimax tracking performance. In addition, an adaptive fuzzy-based dynamic game theory is introduced to solve the minimax tracking problem. The proposed method is appropriate for the robust tracking design of robotic systems with large parameter perturbation and external disturbance. A simulation example of a two-link robotic manipulator driven by DC motors is also given to demonstrate the effectiveness of proposed design method's tracking performance     

Disturbance observer based multi-variable control of ball mill grinding circuits

Ball mill grinding circuits are essentially multi-variable systems characterized with couplings, time-varying parameters and time delays. The control schemes in previous literatures, including detuned multi-loop PID control, model predictive control (MPC), robust control, adaptive control, and so on, demonstrate limited abilities in control ball mill grinding process in the presence of strong disturbances. The reason is that they do not handle the disturbances directly by controller design. To this end, a disturbance observer based multi-variable control (DOMC) scheme is developed to control a two-input-two-output ball mill grinding circuit. The systems considered here are with lumped disturbances which include external disturbances, such as the variations of ore hardness and feed particle size, and internal disturbances, such as model mismatches and coupling effects. The proposed control scheme consists of two compound controllers, one for the loop of product particle size and the other for the loop of circulating load. Each controller includes a PI feedback part and a feed-forward compensation part for the disturbances by using a disturbance observer (DOB). A rigorous analysis is also given to show the reason why the DOB can effectively suppress the disturbances. Performance of the proposed scheme is compared with those of the MPC and multi-loop PI schemes in the cases of model mismatches and strong external disturbances, respectively. The simulation results demonstrate that the proposed method has a better disturbance rejection property than those of the MPC and PI methods in controlling ball mill grinding circuits.     

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...     

Multivariable process identification for mpc: the asymptotic method and its applications

In this work we will introduce the asymptotic method (ASYM) of identification and provide two case studies. The ASYM was developed for multivariable process identification for model based control. The method calculates time domain parametric models using frequency domain criterion. Fundamental problems, such as test signal design for control, model order/structure selection, parameter estimation and model error quantification, are solved in a systematic manner. The method can supply not only input/output model and unmeasured disturbance model which are asymptotic maximum likelihood estimates, but also the upper bound matrix for the model errors that can be used for model validation and robustness analysis. To demonstrate the use of the method for model predictive control (MPC), the identification of a Shell benchmark process (a simulated distillation column) and an industrial application to a crude unit atmospheric tower will be presented.     

基于惯量辨识的测试转台自适应内模控制

为了降低系统模型参数变化对测试转台控制系统的影响,提出了基于惯量辨识技术的自适应内模控制方案.首先建立了某型号测试转台数学模型,设计了测试转台内模控制器,在此基础上采用基于扰动转矩观测器的惯量辨识算法来辨识测试转台转动惯量的变化情况,然后通过模糊控制器根据转动惯量的变化自动调整内模控制器的参数,从而确保了控制器的控制性能.仿真和实验结果表明,该控制方案对惯量的变化有着很强的自适应性,提高了测试转台控制系统的抗干扰性能和系统的鲁棒性,取得了较好的控制效果.