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 output feedback model predictive control using off-line linear matrix inequalities

A fundamental question about model predictive control (MPC) is its robustness to model uncertainty. In this paper, we present a robust constrained output feedback MPC algorithm that can stabilize plants with both polytopic uncertainty and norm-bound uncertainty. The design procedure involves off-line design of a robust constrained state feedback MPC law and a state estimator using linear matrix inequalities (LMIs). Since we employ an off-line approach for the controller design which gives a sequence of explicit control laws, we are able to analyze the robust stabilizability of the combined control laws and estimator, and by adjusting the design parameters, guarantee robust stability of the closed-loop system in the presence of constraints. The algorithm is illustrated with two examples.     

Robust visual tracking control system of a mobile robot based on a dual-Jacobian visual interaction model

This paper presents a novel design of a robust visual tracking control system, which consists of a visual tracking controller and a visual state estimator. This system facilitates human–robot interaction of a unicycle-modeled mobile robot equipped with a tilt camera. Based on a novel dual-Jacobian visual interaction model, a robust visual tracking controller is proposed to track a dynamic moving target. The proposed controller not only possesses some degree of robustness against the system model uncertainties, but also tracks the target without its 3D velocity information. The visual state estimator aims to estimate the optimal system state and target image velocity, which is used by the visual tracking controller. To achieve this, a self-tuning Kalman filter is proposed to estimate interesting parameters and to overcome the temporary occlusion problem. Furthermore, because the proposed method is fully working in the image space, the computational complexity and the sensor/camera modeling errors can be reduced. Experimental results validate the effectiveness of the proposed method, in terms of tracking performance, system convergence, and robustness.     

一类随机摄动系统的鲁棒控制与仿真

在内模控制(IMC)结构下对一类随机摄动系统的鲁棒控制及其仿真研究作了探讨.首先针对一类随机模型误差的描述定义了一个实际敏感度和标称敏感度之间的加权敏感度误差,然后应用谱分解的方法调整标称控制器来最小化加权敏感度误差在整个频段上的方差,为一类随机摄动系统提供了一种鲁棒控制器设计方法,可使系统期望的标称性能对模型误差具有良好的鲁棒性.最后根据随机摄动系统的特点进行仿真研究,进一步说明了所得控制方法的有效性.     

A method of MPC model error detection

This work introduces a method of multivariable model error detection in model prediction control (MPC). The idea is to use non-disturbing small sinusoidal test signals to obtain accurate estimates of process frequency responses at several frequency points. Then, the differences between estimated frequency responses and the frequency responses of current MPC model are used to form the model error index matrix which is used to access the model error of the MPC controller. An upper error bound is developed for quantifying the error of frequency response estimation. The method works in closed-loop operation with the MPC controller online. Simulation studies are used to demonstrate the use of the method.     

一类不确定系统的最优鲁棒控制

运用最优方法探讨了一类模型不确定系统的鲁棒控制问题。定义了一个实际敏感度和标称敏感度之间的加权敏感度误差,并通过调整标称控制器最小化加权敏感度误差在整个频段上的方差,从而为一类不确定系统提供了一种最优的鲁棒控制器设计方法,可使系统性能对模型误差具有良好的鲁棒性。针对控制工程领域典型的一阶时滞系统进行仿真研究,其结果说明了该方法的有效性。     

基于NSGA-Ⅱ的自动调参控制器设计

针对传统全包线控制器设计方法——增益调度法耗时、低效、可移植性差等缺点,提出了基于改进的多目标遗传算法(NS-GA-Ⅱ)的自调参控制器设计方法,以提高控制器设计的效率和控制器的鲁棒性;方法中,以无人机系统输出与参考模型输出的误差为目标函数,频域指标为约束,预先设定调参规律,利用NSGA-Ⅱ算法对自动调参系数进行求解,同时实现了固定设计点控制器参数的优化和全状态控制器参数的拟合;运行一次优化程序就得到了全状态控制器;仿真结果表明:在没有人工调参和增益调度插值的情况下,基于NSGA-Ⅱ算法设计的控制器,控制性能良好,证明了设计方法的有效性。     

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.     

High gain observer based extended generic model control with application to a reactive distillation column

This article aims at synthesizing an estimator based hybrid control scheme that consists of a high gain nonlinear observer and the extended generic model controller (EGMC) that is developed by the application of differential geometry theory. The model-based EGMC control system demands the knowledge of some physical state variables of the process and therefore, the development of a suitable algorithm to perform the state estimation has captured the attention. Here, we design a high gain observer so that it estimates a limited number of states which are solely required for the controller simulation. As a consequence, there exists a significant structural discrepancy. Despite this large mismatch, the state observer performs satisfactorily in converging the estimation error for the case of an example ethylene glycol reactive distillation system. With the same reduced-order predictor model, a comparison is also made between the high gain observer and the extended Kalman filter (EKF). Finally, the high gain observer based EGMC control structure shows promising performance in regulating the ethylene glycol column.     

Tuning SISO offset-free Model Predictive Control based on ARX models

In this paper, we present a tuning methodology for a simple offset-free SISO Model Predictive Controller (MPC) based on autoregressive models with exogenous inputs (ARX models). ARX models simplify system identification as they can be identified from data using convex optimization. Furthermore, the proposed controller is simple to tune as it has only one free tuning parameter. These two features are advantageous in predictive process control as they simplify industrial commissioning of MPC. Disturbance rejection and offset-free control is important in industrial process control. To achieve offset-free control in face of unknown disturbances or model-plant mismatch, integrators must be introduced in either the estimator or the regulator. Traditionally, offset-free control is achieved using Brownian disturbance models in the estimator. In this paper we achieve offset-free control by extending the noise model with a filter containing an integrator. This filter is a first order ARMA model. By simulation and analysis, we argue that it is independent of the parameterization of the underlying linear plant; while the tuning of traditional disturbance models is system dependent. Using this insight, we present MPC for SISO systems based on ARX models combined with the first order filter. We derive expressions for the closed-loop variance of the unconstrained MPC based on a state space representation in innovation form and use these expressions to develop a tuning procedure for the regulator. We establish formal equivalence between GPC and state space based off-set free MPC. By simulation we demonstrate this procedure for a third order system. The offset-free ARX MPC demonstrates satisfactory set point tracking and rejection of an unmeasured step disturbance for a simulated furnace with a long time delay.     

MPC-based compensation control system for the yaw stability of distributed drive electric vehicle

Conventional yaw stability strategy of distributed drive electric vehicle (DDEV) is usually realised by torque distribution strategy. However, the instantaneous variations of four independent tyres slip ratio and the effect of disturbance have not been considered sufficiently. Therefore, it is difficult to realise the robustness of yaw stability for DDEV under various operating conditions. To solve this problem, a novel model predictive controller-based compensation control system (MPC-CCS) is proposed in this paper. The proposed MPC-CCS consists of two parts, an MPC based-feedback controller and a Kalman filter based-feedforward controller. In the feedback controller, a dual torque distribution scheme is adopted to obtain optimal torque values derived from the real-time signals of four independent tyres slip ratio, an MPC is designed to realise optimal torque values for vehicle yaw motion. In the feedforward controller, a Kalman filter is employed to attenuate the effect of the disturbance on yaw performance. In this way, the robustness of yaw stability for DDEV can be guaranteed by the proposed MPC-CCS. The proposed MPC-CCS is evaluated on eight degrees of freedom simulation platform and simulation results of different conditions show the effectiveness of the MPC-CCS.     

Performance assessment and robustness analysis using an ARMarkov approach

Application of the ARMarkov model-based formulation offers significant advantages for assessment/monitoring and robustness analysis of process systems. The ARMarkov method does not require a priori specification of the system time delay/interactor matrix, needs only an approximate estimate of model order and can be done using open or closed-loop process data. By appropriate use of standard, linear model estimation techniques, it directly produces statistically consistent estimates of the first few, user-specified number of Markov parameters even in the presence of colored noise. It is shown in this paper that the Markov parameters and the ARMarkov model can be used to calculate the interactor matrix and several process performance metrics including sensitivity/complementary-sensitivity functions and time-domain criteria such as speed of response, minimum variance values etc. In addition it is shown that model-based predictive control (MPC) systems formulated using ARMarkov models have a special state space structure that leads to less conservative robustness bounds for specific types of uncertainties (such as gain mismatch, uncertainty in the fast or slow dynamics, etc.) than applying the Small Gain Theorem directly to the conventional state space model structure.     

Improving transient performance of adaptive control architectures using frequency-limited system error dynamics

Although adaptive control theory offers mathematical tools to achieve system performance without excessive reliance on dynamical system models, its applications to safety-critical systems can be limited due to poor transient performance and robustness. In this paper, we develop an adaptive control architecture to achieve stabilisation and command following of uncertain dynamical systems with improved transient performance. Our framework consists of a new reference system and an adaptive controller. The proposed reference system captures a desired closed-loop dynamical system behaviour modified by a mismatch term representing the high-frequency content between the uncertain dynamical system and this reference system, i.e., the system error. In particular, this mismatch term allows the frequency content of the system error dynamics to be limited, which is used to drive the adaptive controller. It is shown that this key feature of our framework yields fast adaptation without incurring high-frequency oscillations in the transient performance. We further show the effects of design parameters on the system performance, analyse closeness of the uncertain dynamical system to the unmodified (ideal) reference system, discuss robustness of the proposed approach with respect to time-varying uncertainties and disturbances, and make connections to gradient minimisation and classical control theory. A numerical example is provided to demonstrate the efficacy of the proposed architecture.     

A method of robust multi-rate state estimation

The inadequacy of the standard notions of detectability and observability to ascertain robust state estimation is shown. The notion of robust state estimation is defined, and for a class of processes the conditions under which the robust state estimation is possible, are given. A method of robust, nonlinear, multi-rate, state estimator design is presented. It can be used to improve robustness in an existing estimator or design a new robust estimator. Estimator tuning guidelines that ensure the asymptotic stability of the estimator error dynamics are given. To ensure that estimation error does not exceed a desired limit, the sampling period of infrequent measurements should be less than an upper bound that depends on factors such as the size of the process dominant time constant, the magnitude of measurement noise, and the level of process–model mismatch. An expression that can be used to calculate the upper bound on the sampling period of infrequent measurements, is presented. The upper bound is the latest time at which the next infrequent measurements should arrive to ensure that estimation error does not exceed a desired limit. The expression also allows one to calculate the highest quality of estimation achievable in a given process. A binary distillation flash tank and a free-radical polymerization reactor are considered to show the application and performance of the estimator.     

Model Predictive Control Tuning by Controller Matching

The effectiveness of model predictive control (MPC) in dealing with input and state constraints during transient operations is well known. However, in contrast with several linear control techniques, closed-loop frequency-domain properties such as sensitivities and robustness to small perturbations are usually not taken into account in the MPC design. This technical note considers the problem of tuning an MPC controller that behaves as a given linear controller when the constraints are not active (e.g., for perturbations around the equilibrium that remain within the given input and state bounds), therefore inheriting the small-signal properties of the linear control design, and that still optimally deals with constraints during transients. We provide two methods for selecting the MPC weight matrices so that the resulting MPC controller behaves as the given linear controller, therefore solving the posed inverse problem of controller matching, and is globally asymptotically stable.      

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.     

Model predictive position control of permanent magnet synchronous motor servo system with sliding mode observer

In order to improve the control accuracy and robustness of permanent magnet synchronous motor (PMSM) servo system, a new non-cascade predictive control strategy is proposed to replace the traditional three-closed-loop servo control in this paper. The design process is as follows. First, the state variables and a discrete-time state space model of motor are defined; meanwhile, the lumped term of disturbance is included in the motor model. Second, the optimal cost function is chosen to design the model predictive controller (MPC). Then, according to the uncertain parameters and external disturbance, the sliding mode observer (SMO) is introduced to estimate and compensate the disturbance. Finally, the comparative experimental result proves that the proposed predictive control method not only has less regulation parameters but also has high position tracking accuracy and strong anti-interference ability even under different conditions.     

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.     

Robust tracking, error feedback, and two-degree-of-freedomcontrollers

The purpose of this paper is to establish first, that in the absence of error feedback, asymptotic tracking is a property that is fragile with respect to the controller parameters. This implies that arbitrary small perturbation of the parameters of such a controller will cause asymptotic tracking to fail. Second, we propose a general 2-DOF controller architecture. We prove that in this structure, asymptotic tracking is, in general, fragile with respect to the controller parameters F_r, F_y and C, while it is robust with respect to the plant parameters as well as the components H and L of the 2-DOF controller. Moreover, the only way to realize a 2-DOF controller in a nonfragile way is to generate the error signal exactly, which amounts to setting F_r=F_y=1. The results reconcile the requirements of the internal model principle, namely the necessity of error feedback, with the additional design freedom potentially offered by 2-DOF controllers. It specifies the controller architecture necessary for robustness and identifies the blocks whose parameters are available for tuning in the design process