Robust control of constrained systems via convex optimization

A successful controller design paradigm must take into account both model uncertainty and design specifications. Model uncertainty can be successfully addressed using ??^∞ robust control theory. However, this framework cannot directly accommodate the realistic case where in addition to robustness considerations the system is subject to both time- and frequency-domain specifications, such as bounds on the control action. In this paper we propose a design procedure, based upon the use of convex optimization, that takes explicitly into account both time- and frequency-domain specifications. The main result of the paper is a new framework to address problems having both control and output constraints and model uncertainty. Additionally, the paper serves as a brief tutorial on the issues involved in addressing design problems with multiple design specifications via convex optimization.     

Implementation of feedback linearization GPC control for a solar furnace

In this paper the temperature control of a solar furnace is addressed. In particular, we propose the use of a feedback linearization generalized predictive control strategy where both the reference tracking task and the rejection of disturbances (represented by the variation of the input energy provided by the Sun, mainly because of the solar daily cycle and passing clouds) are considered. This allows the physical and security constraints to be explicitly taken into account in the design. Simulation and experimental results show the effectiveness of the methodology and that this kind of plants can be considered as a cheap or alternative option for the material treatment and testing in the industrial context.     

Model Predictive Control for Constrained Image‐Based Visual Servoing in Uncalibrated Environments

This paper presents a novel approach for image‐based visual servoing (IBVS) of a robotic system by considering the constraints in the case when the camera intrinsic and extrinsic parameters are uncalibrated and the position parameters of the features in 3‐D space are unknown. Based on the model predictive control method, the robotic system's input and output constraints, such as visibility constraints and actuators limitations, can be explicitly taken into account. Most of the constrained IBVS controllers use the traditional image Jacobian matrix, the proposed IBVS scheme is developed by using the depth‐independent interaction matrix. The unknown parameters can appear linearly in the prediction model and they can be estimated by the identification algorithm effectively. In addition, the model predictive control determines the optimal control input and updates the estimated parameters together with the prediction model. The proposed approach can simultaneously handle system constraints, unknown camera parameters and depth parameters. Both the visual positioning and tracking tasks can be achieved desired performances. Simulation results based on a 2‐DOF planar robot manipulator for both the eye‐in‐hand and eye‐to‐hand camera configurations are used to demonstrate the effectiveness of the proposed method.     

Constrained model predictive force control of an electrohydraulic actuator

An analytical MPC controller was designed for force control of a single-rod electrohydraulic actuator. The controller based on a difference equation uses short control horizon. The constraints on both input and output variables are taken into consideration by the controller. The mechanism of output constraints satisfaction uses output prediction and makes possible to constrain the output values many sampling instants ahead. Thus, it extends capabilities of the analytical MPC controllers to the field reserved so far for much more computationally expensive numerical MPC algorithms. Results of real life experiments illustrate efficiency of the proposed controller. The results also show that the MPC controller has better tracking performance than conventional P and PI controllers. The MPC controller with the constraint handling mechanisms, though relatively simple, offers very good performance. As the design process is detailed, it is possible to relatively easy adapt the proposed approach to other control plants.     

输入变量关联约束对约束优化控制的影响特性分析

过程工业控制中除了存在常见的输入变量和输出变量幅值高低限约束, 由于工艺或者控制的需要也可能具有关于输入变量线性函数的关联约束. 不同约束条件之间的矛盾可能会造成约束条件无法全部满足, 失去了实施预测控制的基础. 从凸体顶点角度, 将具有输入关联约束的约束优化控制的可行性判定转化为凸多面集是否非空的问题. 为保证具有输入关联约束预测控制的有效实施, 本文将输入关联约束纳入到预测控制控制律的求解当中. 基于Newton控制框架, 考虑具有输入关联约束条件下, 得到基于区间控制思想的预测控制律的解析表达式, 从而分析输入关联约束条件对控制的影响. 通过典型系统模型的控制仿真实验, 验证以上方法的有效性.     

Constrained multi-variable generalized predictive control using a dual neural network

Multi-variable generalized predictive control algorithm has obtained great success in process industries. However, it suffers from a high computational cost because the multi-stage optimization approach in the algorithm is time-consuming when constraints of the control system are considered. In this paper, a dual neural network is employed to deal with the multi-stage optimization problem, and bounded constraints on the input and output signals of the control system are taken into account. The dual neural network has many favorable features such as simple structure, rapid execution, and easy implementation. Therefore, the computation efficiency, in comparison with the consecutive executions of numerical algorithms on digital computers, is increased dramatically. In addition, the dual network model can yield the exact optimum values of future control signals while many other neural networks only obtain the approximate optimal solutions. Hence the multi-variable generalized predictive control algorithm based on the dual neural network is suitable for industrial applications with the real-time computation requirement. Simulation examples are given to demonstrate the efficiency of the proposed approach.     

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.     

矿井通风的H_∞优化控制

提出了基于H∞优化控制理论的矿井通风控制问题。首先建立了将主风流作为当前状态、主扇风机输出功率作为控制输入,并考虑实际井下环境干扰和瓦斯检测滞后的动态模型,然后对该模型进行了考虑控制成本的、以瓦斯检测输出作为反馈的H∞控制设计。仿真结果表明,矿井通风的H∞优化控制是一种既体现了技术优势,又兼顾了经济效益的整体优化策略。     

Adaptive receding horizon control for constrained MIMO systems

An adaptive control algorithm for open-loop stable, constrained, linear, multiple input multiple output systems is presented. The proposed approach can deal with both input and output constraints, as well as measurement noise and output disturbances. The adaptive controller consists of an iterative set membership identification algorithm, that provides a set of candidate plant models at each time step, and a model predictive controller, that enforces input and output constraints for all the plants inside the model set. The algorithm relies only on the solution of standard convex optimization problems that are guaranteed to be recursively feasible. The experimental results obtained by applying the proposed controller to a quad-tank testbed are presented.     

保持生理特征的人脸编辑

提出了一种保持生理特征的交互式人脸编辑方法。采用控制点分层策略，即以用户直接操作的控制点对（称为主控制点对）为输入层，其他控制点对（称为次控制点对）为输出层，建立人工神经网络；然后采用误差反向传播法（Error Back Propagation）学习，从而建立主、次控制点之间的约束关系；最后通过输出层将编辑信息在模型中进行插值。该编辑结果可以应用到具有相同拓扑的任意人脸模型上。实验结果表明，采用分层控制的方法不仅保持了编辑操作的方便性、精确性，同时还保持了人脸生理特征的真实性。     

基于区间控制的约束预测控制及约束影响

在实际被控过程中往往存在着很多约束条件,这使得预测控制的在线优化问题表现为非线性,难以获得控制律的具体表达式,为约束预测控制的分析造成困难基于Newton控制框架,针对线性系统离散状态空间的动态模型,考虑具有输入、输出区间约束条件下,基于区间控制思想的预测控制律的解析表达式,分别得到无约束和有约束情况下状态反馈控制律的...     

An improved state-space model structure and a corresponding predictive functional control design with improved control performance

Conventional state-space model predictive control requires a state estimator/observer to access the state information for feedback controller design. Its drawbacks are the numerical convergence stability of the observer and closed-loop control performance deterioration with activated plant input/output constraints. The recent direct use of measured input and output variables to formulate a non-minimal state-space (NMSS) model overcomes these problems, but the subsequent controller is too sensitive to model mismatch. In this article, an improved structure of NMSS model that incorporates the output-tracking error is first formulated and then a subsequent predictive functional control design is proposed. The proposed controller is tested on both model match and model mismatch cases for comparison with previous controllers. Results show that control performance is improved. In addition, a linear programming method for constraints dealing and a closed form of transfer function representation of the control system are provided for further insight into the proposed method.     

Learning control of process systems with hard input constraints

In this paper, a novel and simple learning control strategy based on using a bounded nonlinear controller for process systems with hard input constraints is proposed. To enable the bounded nonlinear controller to learn to control a changing plant by merely observing the process output errors, a simple learning algorithm for parameter updating is derived based on the Lyapunov stability theorem. The learning scheme is easy to implement, and does not require any a priori process knowledge except the system output response direction. For demonstrating the effectiveness and applicability of the learning control strategy, the control of a once-through boiler, as well as an open-loop unstable continuously stirred tank reactor (CSTR), were investigated. Furthermore, extensive comparisons of the proposed scheme with the conventional PI controller and with some existing model-free intelligent controllers were also performed. Due to significant features of simple structure, efficient algorithm and good performance, the proposed learning control strategy appears to be a promising and practical approach to the intelligent control of process systems subject to hard input constraints.     

基于增量加权的预测函数控制

介绍了预测函数控制方法的主要思想和特点。针对通常的预测函数控制在优化求解的目标函数中仅含有输出误差的平方和序列,没有考虑控制增量的变化,通过在性能指标中对控制增量适当加权,提出了一种双值预测函数控制算法,提高了系统的稳定性,克服了系统的稳态偏差。在工业过程模型中,用Matlab软件进行了仿真研究,取得了良好的控制效果,表明该算法跟踪快、控制精度高、稳定性强,是一种比较有效的控制方法。     

一种新型的输入受约束的自适应控制

在系统输入受约束时,采用一般的广义预测控制有可能会造成算法的不可行,从而使系统的控制质量变坏,甚至造成系统的不稳定。针对输入受约束系统,采用简化的三角化脉冲响应模型,提出一种输入受约束的自适应模型算法控制。该算法只需在线辨识一个参数。不必求逆矩阵,极大地减少了计算量。而且,在输入和输入增量约束条件下,通过调整参考输出,使得约束条件的个数简化为一个,并可保证闭环系统的渐近稳定和全局收敛性。仿真结果进一步证实了该算法的有效性。     

Robust nonlinear MPC based on Volterra series and polynomial chaos expansions

A robust nonlinear model predictive controller (NMPC) based on a Volterra series is proposed. Polynomial chaos expansions (PCE) are used to represent the uncertainty in the Volterra series coefficients and this uncertainty is then propagated onto the output predictions. The key advantage of the PCE is that it provides an analytical expression to compute the L²-norm of the output prediction error resulting in computational savings, compared to previously proposed techniques, which are essential for real time implementation. Terminal and input constraints based on Structured Singular Value based-norms are used to ensure convergence to a set-point and compliance with constraints in manipulated variables. The algorithm is applied to a multivariable pH neutralization system. A comparative study shows superior closed loop performance and computational efficiency of the proposed technique as compared to previously proposed algorithms.     

Adaptive control of a quadrotor aerial vehicle with input constraints and uncertain parameters

In this paper, we address the problem of adaptive bounded control for the trajectory tracking of a Quadrotor Aerial Vehicle (QAV) while the input saturations and uncertain parameters with the known bounds are simultaneously taken into account. First, to deal with the underactuated property of the QAV model, we decouple and construct the QAV model as a cascaded structure which consists of two fully actuated subsystems. Second, to handle the input constraints and uncertain parameters, we use a combination of the smooth saturation function and smooth projection operator in the control design. Third, to ensure the stability of the overall system of the QAV, we develop the technique for the cascaded system in the presence of both the input constraints and uncertain parameters. Finally, the region of stability of the closed-loop system is constructed explicitly, and our design ensures the asymptotic convergence of the tracking errors to the origin. The simulation results are provided to illustrate the effectiveness of the proposed method.     

基于Ziegler-Nichols频率响应方法的自适应PID控制

提出一种基于Ziegler-Nichols频率响应方法的自适应PID控制器,它通过控制回路正常运行中的过程对象输入输出数据在线辨识出过程对象重要的临界频率响应特性,然后基于Zieger-Nichols整定规则或改进的方法在线更新PID控制器参数.PID控制器的自适应过程不需要系统的任何先验知识,也不需要建立任何对象模型,可以保证控制回路始终运行在最佳状态.仿真实验表明了自适应PID控制的有效性和可行性.     

Neural observer-based adaptive compensation control for nonlinear time-varying delays systems with input constraints

This paper describes a neural network state observer-based adaptive saturation compensation control for a class of time-varying delayed nonlinear systems with input constraints. An advantage of the presented study lies in that the state estimation problem for a class of uncertain systems with time-varying state delays and input saturation nonlinearities is handled by using the NNs learning process strategy, novel type Lyapunov-Krasovskii functional and the adaptive memoryless neural network observer. Furthermore, by utilizing the property of the function tan h²(?/?)/?, NNs compensation technique and backstepping method, an adaptive output feedback controller is constructed which not only efficiently avoids the problem of controller singularity and input saturation, but also can achieve the output tracking. And the proposed approach is obtained free of any restrictive assumptions on the delayed states and Lispchitz condition for the unknown nonlinear functions. The semiglobal uniform ultimate boundedness of all signals of the closed-loop systems and the convergence of tracking error to a small neighborhood are all rigorously proven based on the NN-basis function property, Lyapunov method and sliding model theory. Finally, two examples are simulated to confirm the effectiveness and applicability of the proposed approach.     

Design of a Robust Optimal Decentralized PI Controller Based on Nonlinear Constraint Optimization For Level Regulation: An Experimental Study

This paper presents the development of a new robust optimal decentralized PI controller based on nonlinear optimization for liquid level control in a coupled tank system. The proposed controller maximizes the closed-loop bandwidth for specified gain and phase margins, with constraints on the overshoot ratio to achieve both closed-loop performance and robustness. In the proposed work, a frequency response fitting model reduction technique is initially employed to obtain a first order plus dead time (FOPDT) model of each higher order subsystem. Furthermore, based on the reduced order model, a proposed controller is designed. The stability and performance of the proposed controller are verified by considering multiplicative input and output uncertainties. The performance of the proposed optimal robust decentralized control scheme has been compared with that of a decentralized PI controller. The proposed controller is implemented in real-time on a coupled tank system. From the obtained results, it is shown that the proposed optimal decentralized PI controller exhibits superior control performance to maintain the desired level, for both the nominal as well as the perturbed case as compared to a decentralized PI controller.