A hybrid Gaussian process approach to robust economic model predictive control

This paper proposes a hybrid Gaussian process (GP) approach to robust economic model predictive control under unknown future disturbances in order to reduce the conservatism of the controller. The proposed hybrid GP is a combination of two well-known methods, namely, kernel composition and nonlinear auto-regressive. A switching mechanism is employed to select one of these methods for disturbance prediction after analyzing the prediction outcomes. The hybrid GP is intended to detect not only patterns but also unexpected behaviors in the unknown disturbances by using past disturbance measurements. A novel forgetting factor concept is also utilized in the hybrid GP, giving less weight to older measurements, in order to increase prediction accuracy based on recent disturbances values. The detected disturbance information is used to reduce prediction uncertainty in economic model predictive controllers systematically. The simulation results show that the proposed method can improve the overall performance of an economic model predictive controller compared to other GP-based methods in cases when disturbances have discernible patterns.     

鲁棒自适应前馈控制器及其在间歇式余热锅炉给水系统中的应用

本文提出了基于降阶模型的自适应前馈控制器.当被控对象是开环不稳定或是非最小相 位系统,当存在未建模动态时,当受到有界干扰和可测干扰作用时该控制器不仅可以使自适 应控制系统稳定运行,而且实现对可测干扰的补偿.本文将该控制器应用于本溪第二炼钢厂 间歇式余热锅炉给水系统获得满意效果.     

Nonlinear system identification for predictive control using continuous time recurrent neural networks and automatic differentiation

In this paper, a continuous time recurrent neural network (CTRNN) is developed to be used in nonlinear model predictive control (NMPC) context. The neural network represented in a general nonlinear state-space form is used to predict the future dynamic behavior of the nonlinear process in real time. An efficient training algorithm for the proposed network is developed using automatic differentiation (AD) techniques. By automatically generating Taylor coefficients, the algorithm not only solves the differentiation equations of the network but also produces the sensitivity for the training problem. The same approach is also used to solve the online optimization problem in the predictive controller. The proposed neural network and the nonlinear predictive controller were tested on an evaporation case study. A good model fitting for the nonlinear plant is obtained using the new method. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. The CTRNN trained is used as an internal model in a predictive controller and results in good performance under different operating conditions.     

Tracking control of small-scale helicopters using explicit nonlinear MPC augmented with disturbance observers

Small-scale helicopters are very attractive for a wide range of civilian and military applications due to their unique features. However, the autonomous flight for small helicopters is quite challenging because they are naturally unstable, have strong nonlinearities and couplings, and are very susceptible to wind and small structural variations.A nonlinear optimal control scheme is proposed to address these issues. It consists of a nonlinear model predictive controller (MPC) and a nonlinear disturbance observer. First, an analytical solution of the MPC is developed based on the nominal model under the assumption that all disturbances are measurable. Then, a nonlinear disturbance observer is designed to estimate the influence of the external force/torque introduced by wind turbulences, unmodelled dynamics and variations of the helicopter dynamics. The global asymptotic stability of the composite controller has been established through stability analysis. Flight tests including hovering under wind gust and performing very challenging pirouette have been carried out to demonstrate the performance of the proposed control scheme.     

一种新的多模自适应前馈控制器

本文针对高频焊管焊接过程的控制,提出了一种适用于具有多个确定性扰动对象的多模自适应前馈控制器,它的特点是综合了从参考模型取状态的MRAC、多输入前馈控制和开关-比例-保持模式控制各自的优点。该控制器不仅可以消除可测干扰的影响,具有较好的控制性能,而且也适用于非最小相位系统。文中针对焊接过程的数学模型,给出了仿真实例研究。     

具有降阶模型的多变量鲁棒自适应前馈控制器

本文提出了一种多变量鲁棒自适应前馈控制器。该控制器采用低阶模型来控制参数未知的高阶多变量系统时,在可测干扰和有界不可测干扰作用下能保证自适应系统稳定运行。当可测干扰与系统输出之间存在未建模动态时,它可以对可测干扰实行有效的动静态补偿。当只有有界干扰作用时,它能使有界干扰对系统产生的影响最小。本文还给出了采用所提出的控制器控制某钢厂间歇式余热锅炉的仿真结果。     

REAL‐TIME IMPLEMENTATION OF A DECENTRALIZED CONTROL FOR AN OPEN IRRIGATION CANAL PROTOTYPE

This paper presents a real‐time implementation of a decentralized LQG controller to regulate the downstream levels at the end of the pools in a four‐pool open irrigation canal prototype with an upstream control concept. The objective of the controller is to keep the downstream level at a constant target value in despite of flow disturbances. Controller synthesis uses a “black box” input‐output identified linear model. A previous interaction analysis, via Relative Gain Array “RGA”, carried on the process model was made to verify the feasibility to design a decentralized control. The real‐time close‐loop results show satisfactory performance and they are compared with those obtained with a centralized LQG controller.     

Adaptive UKF-based model predictive control of a Fresnel collector field

One of the ways to improve the efficiency of solar energy plants is by using advanced control and optimization algorithms. In particular, model predictive control strategies have been applied successfully in their control.The control objective of this kind of plant is to regulate the solar field outlet temperature around a desired set-point. Due to the highly nonlinear dynamics of these plants, a simple linear controller with fixed parameters is not able to cope with the changing dynamics and the multiple disturbance sources affecting the field.In this paper, an adaptative model predictive control strategy is designed for a Fresnel collector field belonging to the solar cooling plant installed at the Escuela Superior de Ingenieros in Sevilla. The controller changes the linear model used to predict the future evolution of the system with respect to the operating point.Since only the inlet and outlet temperatures of the heat transfer fluid are measurable, the intermediate temperatures have to be estimated. An unscented Kalman filter is used as a state estimator. It estimates metal-fluid temperature profiles and effective solar radiation.Simulation results are provided comparing the proposed strategy with a PID + feedforward series controller showing better performance. The controller is also compared to a gain scheduling generalized predictive controller (GS-GPC) which has previously been tested at the actual plant with a very good performance. The proposed strategy outperforms these two strategies.Furthermore, two real tests are presented. These tests show that the proposed controller achieves adequate set-point tracking in spite of strong disturbances.     

Latent variable iterative learning model predictive control for multivariable control of batch processes

A latent variable iterative learning model predictive control (LV-ILMPC) method is presented for trajectory tracking in batch processes. Different from the iterative learning model predictive control (ILMPC) model built from the original variable space, LV-ILMPC develops a latent variable model based on dynamic partial least squares (DyPLS) to capture the dominant features of each batch. In each latent variable space, we use a state–space model to describe the dynamic characteristics of the internal model, and an LV-ILMPC controller is designed. Each LV-ILMPC controller tracks the set points of the current batch projection in the corresponding latent variable space, and the optimal control law is determined and the persistent process disturbances is rejected along both time and batch horizons. The proposed LV-ILMPC formulation is based on general LV-MPC and incorporates an iterative learning function into LV-MPC. In addition, the real physical input that drives the process can be reconstructed from the latent variable space. Therefore, this algorithm is particularly suitable for multiple-input, multiple-output (MIMO) systems with strong coupling and serious collinearity. Three studies are used to illustrate the effectiveness of the proposed LV-ILMPC .     

Disturbance modeling for offset-free linear model predictive control

An offset-free controller is one that drives controlled outputs to their desired targets at steady state. In the linear model predictive control (MPC) framework, offset-free control is usually achieved by adding step disturbances to the process model. The most widely-used industrial MPC implementations assume a constant output disturbance that can lead to sluggish rejection of disturbances that enter the process elsewhere. This paper presents a general disturbance model that accommodates unmeasured disturbances entering through the process input, state, or output. Conditions that guarantee detectability of the augmented system model are provided, and a steady-state target calculation is constructed to remove the effects of estimated disturbances. Conditions for which offset-free control is possible are stated for the combined estimator, steady-state target calculation, and dynamic controller. Simulation examples are provided to illustrate trade-offs in disturbance model design.     

Control of human arm movement in machine-human cooperative welding process

This paper studies accurate control of human arm movement in machine-human cooperative control of GTAW process. An innovative teleoperated virtualized welding platform is utilized to conduct dynamic experiments to correlate the human welder arm movement with the visual signal input. An adaptive ANFIS model is proposed to model the intrinsic nonlinear and time-varying characteristic of the human welder response. A model based predictive control algorithm is then proposed and an analytical solution is derived. Human control experimental results verify that the proposed controller is able to track varying set-points and is robust under measurement and input disturbances.     

Optimal disturbance rejection control approach based on a compound neural network prediction method

A new optimal disturbance rejection control method is proposed for the system with disturbances via a compound neural network prediction approach in this paper. The disturbances caused by external disturbances and model mismatches can be estimated by a disturbance observer, and the estimation of disturbances is introduced into the neural network predictive model to make the predictive output more accurate. Then based on the new compound neural network predictive model, a controller, which ensures both optimal performance by the receding horizon optimization and strong disturbance rejection ability, is obtained. The proposed scheme is applied to control the temperature of a simplified jacketed stirred tank heater (JSTH). Simulation results demonstrate the effectiveness of the proposed control method.     

工业锅炉燃烧过程的建模及控制

在锅炉燃烧过程的控制中 ,系统常常会受到不可测干扰的影响 ,造成能源浪费和环境污染。其主要问题是燃烧过程的输出量难以测量。对于这一类的过程控制 ,由于扰动及输出量不能测量 ,就不得不采用控制辅助输出量的方法间接控制过程的主要输出量。文章通过对工业锅炉燃烧过程的机理分析与数学建模 ,实现了由可测输出量估计这些干扰对过程的影响 ,并采用推理控制削弱了这种干扰的影响。仿真实验证明了建模分析和推理控制方法是可行的。     

基于不确定逼近的机械手自适应鲁棒预测控制

针对具有参数不确定性和未知外部干扰的机械手轨迹跟踪问题提出了一种多输入多输出自适应鲁棒预测控制方法. 首先根据机械手模型设计非线性鲁棒预测控制律, 并在控制律中引入监督控制项; 然后利用函数逼近的方法逼近控制律中因模型不确定性以及外部干扰引起的未知项. 理论证明了所设计的控制律能够使机械手无静差跟踪期望的关节角轨迹. 仿真验证了本文设计方法的有效性.     

Switching model predictive attitude control for a quadrotor helicopter subject to atmospheric disturbances

In this article a switching model predictive attitude controller for an unmanned quadrotor helicopter subject to atmospheric disturbances is presented. The proposed control scheme is computed based on a piecewise affine (PWA) model of the quadrotor's attitude dynamics, where the effects of the atmospheric turbulence are taken into consideration as additive disturbances. The switchings among the PWA models are ruled by the rate of the rotation angles and for each PWA system a corresponding model predictive controller is computed. The suggested algorithm is verified in experimental studies in the execution of sudden maneuvers subject to forcible wind disturbances. The quadrotor rejects the induced wind disturbances while performing accurate attitude tracking.     

Observer-based predictive controller design with network-enhanced time-delay compensation

State feedback control is very attractive due to the precise computation of the gain matrix, but the implementation of a state feedback controller is possible only when all state variables are directly measurable. This condition is almost impossible to accomplish due to the excess number of required sensors or unavailability of states for measurement in most of the practical situations. Hence, the need for an estimator or observer is obvious to estimate all the state variables by observing the input and the output of the controlled system. As such, the goal of this paper is to provide a control design methodology based on a Luenberger observer design that can assure the closed-loop performances of a vehicle drivetrain with backlash, while compensating the network-enhanced time-varying delays. This goal is achieved in a sequential manner: firstly, a piecewise linear model of two inertias drivetrain, which takes into consideration the backlash nonlinearity and the network-enhanced time-varying delay effects is derived; then, a Luenberger observer which estimates the state variables is synthesized and the robust full state-feedback predictive controller based on flexible control Lyapunov functions is designed to explicitly take into account the bounds of the disturbances caused by time-varying delays and to guarantee also the input-to-state stability of the system in a non-conservative way. The full state-feedback predictive control strategy based on the Luenberger observer design was experimentally tested on a vehicle drivetrain emulator controlled through controller area network, with the aim of minimizing the backlash effects while compensating the network-enhanced delays.     

Projection based MIMO control performance monitoring: II––measured disturbances and setpoint changes

In this paper the performance monitoring method based on subspace projections from Part I [J. Proc. Cont. 13 (2003) 739] is extended to include measured disturbances and setpoint changes. It was shown in [J. Proc. Cont. 13 (2003) 739] that the minimum variance output space is an optimal subspace of the general closed-loop output space and that orthogonal projections of filtered output data onto past closed-loop output data can be used to assess the performance of feedback controllers. This paper demonstrates that the same framework is directly applicable to systems with measured disturbances by augmenting the data matrix with those measured disturbances. Furthermore, it provides a means of separating suboptimal control performance between that arising from unmeasured disturbances and that due to measured disturbances. The effect of setpoint changes on control performance can be calculated as special feedforward variables. The controller is generally time-varying to include the case of model predictive control. A simulation example and an industrial boiler process are used to demonstrate the effectiveness of the proposed method.     

A multivariate statistical controller for on-line quality improvement

Producing good quality products is an important process control objective. However, achieving this objective can be very difficult in a continuous process, especially when quality measurements are not available on-line or they have long time delays. In this paper, a control approach using multivariate statistical models is presented to achieve this objective. The goal of the control approach is to decrease variations in product quality without real time quality measurements. A PCA model which incorporates time lagged variables is used, and the control objective is expressed in the score space of this PCA model. A controller is designed in the model predictive control (MPC) framework, and it is used to control the equivalent score space representation of the process. The score predictive model for the MPC algorithm is built using partial least squares (PLS). The proposed controller can be developed from and implemented on top of existing PID control systems, and it is demonstrated in two case studies, which involve a binary distillation column and the Tennessee Eastman process.     

Handling uncertainty in economic nonlinear model predictive control: A comparative case study

In the last years, the use of an economic cost function for model predictive control (MPC) has been widely discussed in the literature. The main motivation for this choice is that often the real goal of control is to maximize the profit or the efficiency of a certain system, rather than tracking a predefined set-point as done in the typical MPC approaches, which can be even counter-productive. Since the economic optimal operation of a system resulting from the application of an economic model predictive control approach drives the system to the constraints, the explicit consideration of the uncertainties becomes crucial in order to avoid constraint violations. Although robust MPC has been studied during the past years, little attention has yet been devoted to this topic in the context of economic nonlinear model predictive control, especially when analyzing the performance of the different MPC approaches. In this work, we present the use of multi-stage scenario-based nonlinear model predictive control as a promising strategy to deal with uncertainties in the context of economic NMPC. We make a comparison based on simulations of the advantages of the proposed approach with an open-loop NMPC controller in which no feedback is introduced in the prediction and with an NMPC controller which optimizes over affine control policies. The approach is efficiently implemented using CasADi, which makes it possible to achieve real-time computations for an industrial batch polymerization reactor model provided by BASF SE. Finally, a novel algorithm inspired by tube-based MPC is proposed in order to achieve a trade-off between the variability of the controlled system and the economic performance under uncertainty. Simulations results show that a closed-loop approach for robust NMPC increases the performance and that enforcing low variability under uncertainty of the controlled system might result in a big performance loss.     

Predictive functional control based on fuzzy T-S model for HVAC systems temperature control

In heating, ventilating and air-conditioning (HVAC) systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno (T-S) fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc.