Robust model predictive control for constrained continuous-time nonlinear systems

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.     

Robust tracking control for an air-breathing hypersonic vehicle with input constraints

The focus of this paper is on the design and simulation of robust tracking control for an air-breathing hypersonic vehicle (AHV), which is affected by high nonlinearity, uncertain parameters and input constraints. The linearisation method is employed for the longitudinal AHV model about a specific trim condition, and then considering the additive uncertainties of three parameters, the linearised model is just in the form of affine parameter dependence. From this point, the linear parameter-varying method is applied to design the desired controller. The poles for the closed-loop system of the linearised model are placed into a desired vertical strip, and the quadratic stability of the closed-loop system is guaranteed. Input constraints of the AHV are addressed by additional linear matrix inequalities. Finally, the designed controller is evaluated on the nonlinear AHV model and simulation results demonstrate excellent tracking performance with good robustness.     

An integrated robust iterative learning control strategy for batch processes based on 2D system

This paper studies the problem of integrated control in the 2-dimensional (2D) system with parameter uncertainties for batch processes. An integrated iterative learning control (ILC) strategy based on quadratic performance for batch processes is proposed. It realizes comprehensive control by combining robust ILC in batch-axis with model predictive control (MPC) in time-axis. The design of quadratic-criterion-based ILC for the system can be converted into a min-max problem. Then a model predictive controller with time-varying prediction horizon is designed based on a quadratic cost function. For an uncertain model, a novel integrated robust ILC scheme based on a nominal model is further proposed. As a result, the control law of the 2D system can be regulated during one batch, which leads to good tracking performance and strong robustness against the disturbance and the uncertainties. Moreover, the analyses of the convergence and tracking performance are given. The proposed methods are applied to batch reactor, and results demonstrate that the system has good robustness and convergence. This paper provides a new way for batch processes control.     

基于非线性干扰观测器的不确定非线性系统鲁棒轨迹线性化控制

针对一类不确定非线性系统，基于轨迹线性化控制方法(TLC)及非线性干扰观测器技术(NDO)研究了一种新的非线性鲁棒控制策略．TLC是一种有效的非线性跟踪和解耦控制方法，但当系统中存在内部未建模动态和外界干扰时，当前TLC控制器性能将显著下降．本文利用NDO对系统中的不确定项进行估计，其输出与TLC控制律结合来对消不确定性的影响．最后通过一个数值仿真实例验证了本文提出的方法的有效性,仿真结果表明该鲁棒轨迹线性化控制方法具有很好的干扰衰减能力和鲁棒性能．     

Distributed model predictive control of constrained weakly coupled nonlinear systems

This paper proposes a distributed model predictive control (MPC) strategy for a large-scale system that consists of several dynamically coupled nonlinear systems with decoupled control constraints and disturbances. In the proposed strategy, all subsystems compute their control signals by solving local optimizations constrained by their nominal decoupled dynamics. The dynamic couplings and the disturbances are accommodated through new robustness constraints in the local optimizations. The paper derives relationships among, and designs procedures for, the parameters involved in the proposed distributed MPC strategy based on the analysis of the recursive feasibility and the robust stability of the overall system. The paper shows that, for a given bound on the disturbances, the recursive feasibility is guaranteed if the sampling interval is properly chosen. Moreover, it establishes sufficient conditions for the overall system state to converge to a robust positively invariant set. The paper illustrates the effectiveness of the proposed distributed MPC strategy by applying it to three coupled cart-(nonlinear) spring–damper subsystems.     

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     

含有不灵敏区有界不确定非线性系统的鲁棒跟踪控制

针对具有控制输入不灵敏区及有界不确定性的非线性系统,研究其鲁棒跟踪问题.利用变结构控制方法和自适应参数估计方法,在同时存在的参数、结构及干扰的不确定性和未知控制输入不灵敏区的情形下,提出了鲁棒控制律设计方法,并提出克服控制信号抖动的改进算法.所提出的控制律可以保证闭环系统的一致终结有界,并且算法比较简单,便于实现.用数字仿真方法验证了所得控制律设计方法的有效性.     

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

A new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.     

Sliding mode predictive tracking control for uncertain Steer-by-Wire system

The Steer-by-Wire (SbW) system is probably the most significant innovation among drive-by-Wire technologies in the automotive industry. Without the mechanical link, the most challenging issue is to control the wheels to closely follow the driver’s command. To improve the robustness of the model predictive control (MPC) in the presence of modeling uncertainties and disturbances in the steering control processes, a sliding mode predictive tracking control (SMPC) strategy for a SbW system with uncertain dynamics is proposed. The simulation and experimental results demonstrate that the performance of the proposed SMPC tracking controller is superior to both SMC and MPC methods for the steering angle tracking task.     

高超声速飞行器非线性鲁棒控制律设计

高超声速飞行器具有模型非线性程度高、耦合程度强、参数不确定性大、抗干扰能力弱等特点,其自主控制具有较大的挑战.论文提出了一种基于鲁棒补偿技术和反馈线性化方法的非线性鲁棒控制方法.文中首先采用反馈线性化的方法对纵向模型进行输入输出线性化,实现速度和高度通道的解耦和非线性模型的线性化.针对得到的线性模型,设计包括标称控制器和鲁棒补偿器的线性控制器.基于极点配置原理,设计标称控制器使标称线性系统具有期望的输入输出特性,利用鲁棒补偿器来抑制参数不确定性和外界扰动对于闭环控制系统的影响.基于小增益定理,证明了闭环控制系统的鲁棒稳定性和鲁棒跟踪性能.相比于非线性回路成形控制方法,仿真结果表明了所设计非线性鲁棒控制算法的有效性和优越性.     

Continuous Robust Control for Series ElasticActuator With Unknown Payload Parametersand External Disturbances

In this paper, the torque tracking control problem for a class of series elastic actuators (SEAs) in the presence of unknown payload parameters and external disturbances is investigated. The uncertainties/disturbances rejection problem for SEAs is addressed from the view of a continuous nonlinear robust control development. Specifically, based on the analysis of a nonlinear SEA, the generic dynamics of SEA systems is described and a novel nonlinear control framework for SEAs is constructed. Then a RISE (robust integral of the sign of the error)-based second-order filter is introduced to synthesize the control law. Moreover, the control performance is theoretically ensured by Lyapunov analysis. Finally, some experimental results are included to demonstrate the superior performance of the proposed control method, in terms of transient response and robustness.      

Robust discrete-time set-based adaptive predictive control for nonlinear systems

The problem of robust adaptive predictive control for a class of discrete-time nonlinear systems is considered. First, a parameter estimation technique, based on an uncertainty set estimation, is formulated. This technique is able to provide robust performance for nonlinear systems subject to exogenous variables. Second, an adaptive MPC is developed to use the uncertainty estimation in a framework of min–max robust control. A Lipschitz-based approach, which provides a conservative approximation for the min–max problem, is used to solve the control problem, retaining the computational complexity of nominal MPC formulations and the robustness of the min–max approach. Finally, the set-based estimation algorithm and the robust predictive controller are successfully applied in two case studies. The first one is the control of anonisothermal CSTR governed by the van de Vusse reaction. Concentration and temperature regulation is considered with the simultaneous estimation of the frequency (or pre-exponential) factors of the Arrhenius equation. In the second example, a biomedical model for chemotherapy control is simulated using control actions provided by the proposed algorithm. The methods for estimation and control were tested using different disturbances scenarios.     

Time-varying control via nominal trajectory linearization for an air-breathing hypersonic vehicle

A time-varying control law via nominal trajectory linearization for an air-breathing hypersonic vehicle (ABHV) model is applied. Feasible guidance command signal serials are generated by nonlinear dynamic inverse (NDI) method considering interactions between aerodynamic effects and propulsion systems. Multiple-time-scale continuous time-varying control, which meets the requirement with accurate, robust, and decoupled tracking of both the commanded trajectory and angular rate profiles in the presence of modeling uncertainties and external disturbances are applied. The simulations for an ABHV model with modeling uncertainties, wind gust, and measuring noises are presented to demonstrate the capacity and reliability of this proposed method.     

小型无人直升机姿态非线性鲁棒控制设计

本文针对小型无人直升机的姿态控制问题,通过系统参数辨识,获得了较为准确的无人直升机姿态动力学模型.并根据无人直升机的动态特性,设计了基于神经网络前馈与滑模控制的非线性鲁棒姿态控制律,该控制律对直升机模型的先验知识要求较低.利用基于Lyapunov的分析方法证明,设计的控制律能够实现对无人直升机姿态角的半全局指数收敛镇定控制,并能确保闭环系统的稳定性.基于姿态飞行控制实验平台的实时飞行控制实验结果表明,提出的控制设计取得了很好的姿态控制效果,并对系统不确定性和外界风扰动具有较好的鲁棒性.     

Discrete terminal sliding mode repetitive control for a linear actuator with nonlinear friction and uncertainties

A robust discrete terminal sliding mode repetitive controller is proposed for a class of nonlinear positioning systems with parameter uncertainties and nonlinear friction. The terminal sliding mode control (TSMC) part is designed to improve the transient characteristics of the system, as well as the robustness against parameter uncertainties, nonperiodic nonlinearities, and disturbances. The repetitive control (RC) part is then integrated to eliminate the effects of the periodic uncertainties present in the system. Moreover, a pure phase lead compensator is incorporated into the RC to improve the tracking at high frequencies. A robust stability analysis and an analysis of the finite time convergence properties of the proposed controller are also provided in this paper. Simulation testing and an experimental validation using a linear actuator system with nonlinear friction and parameter uncertainties are conducted to verify the effectiveness of the proposed controller.     

倾转式三旋翼无人飞行器抗扰非线性控制设计

针对倾转式三旋翼无人飞行器姿态和高度系统存在未知扰动和模型参数不确定性的问题,提出一种连续的非线性自适应鲁棒控制方法.该方法基于浸入-不变集原理估计模型未知参数,采用一种连续的鲁棒控制算法抑制未知扰动和补偿估计偏差.利用Lyapunov函数从理论上证明此方法能保证闭环系统的稳定性,并能实现飞行器姿态与高度控制误差的渐近收敛.最后通过实时实验结果验证所提出控制算法的有效性和鲁棒性.     

H∞ tracking-based sliding mode control foruncertain nonlinear systems via an adaptive fuzzy-neural approach

A novel adaptive fuzzy-neural sliding-mode controller with H(infinity) tracking performance for uncertain nonlinear systems is proposed to attenuate the effects caused by unmodeled dynamics, disturbances and approximate errors. Because of the advantages of fuzzy-neural systems, which can uniformly approximate nonlinear continuous functions to arbitrary accuracy, adaptive fuzzy-neural control theory is then employed to derive the update laws for approximating the uncertain nonlinear functions of the dynamical system. Furthermore, the H(infinity) tracking design technique and the sliding-mode control method are incorporated into the adaptive fuzzy-neural control scheme so that the derived controller is robust with respect to unmodeled dynamics, disturbances and approximate errors. Compared with conventional methods, the proposed approach not only assures closed-loop stability, but also guarantees an H(infinity) tracking performance for the overall system based on a much relaxed assumption without prior knowledge on the upper bound of the lumped uncertainties. Simulation results have demonstrated that the effect of the lumped uncertainties on tracking error is efficiently attenuated, and chattering of the control input is significantly reduced by using the proposed approach.     

一类干扰有界约束非线性系统的鲁棒模型预测控制

针对一类干扰有界约束非线性系统设计了基于控制不变集切换策略的鲁棒模型预测控制算法.针对非线性系统线性化之后的结果,给出了平衡点的非线性标称系统控制不变集的计算方法.然后在考虑线性化误差和加性有界干扰影响的基础上,构造了平衡点附近最小鲁棒正不变集.结合不变集切换策略和Tube不变集控制方法,提出了干扰有界约束非线性系统的不变集切换策略.最后将该算法应用到一类典型的非线性化工过程连续搅拌反应釜(CSTR)中,仿真结果验证了算法的有效性.     

Dynamical adaptive integral backstepping variable structure controller design for uncertain systems and experimental application

In this study, a dynamical adaptive integral backstepping variable structure control (DAIBVSC) system based on the Lyapunov stability theorem is proposed for the trajectory tracking control of a nonlinear uncertain mechatronic system with disturbances. In this control scheme, no prior knowledge is required on the uncertain parameters and disturbances because it is estimated by two types of dynamical adaptive laws. These adaptive laws are integrated into the dynamical adaptive integral backstepping control and variable structure control (VSC) parts of the DAIBVSC. The dynamical adaptive law in the dynamical adaptive integral backstepping control part updates parametric uncertainties, while the other in the VSC part adapts upper bounds of non‐parametric uncertainties and disturbances. In order to achieve a more robust output tracking and better parameter adaptation, the control system is extended by one integrator and sliding surface is augmented by an integral action. Experimental evaluation of the DAIBVSC is conducted with respect to performance and robustness to parametric uncertainties. Experimental results of the DAIBVSC are compared with those of a traditional VSC. The proposed DAIBVSC exhibits satisfactory output tracking performance, good estimation of the uncertain parameters and can reject disturbances with a chattering free control law. Copyright © 2017 John Wiley & Sons, Ltd.     

Adaptive Sliding Mode Control for Re-entry Attitude of Near Space Hypersonic Vehicle Based on Backstepping Design

Combining sliding mode control method with radial basis function neural network (RBFNN), this paper proposes a robust adaptive control scheme based on backstepping design for re-entry attitude tracking control of near space hypersonic vehicle (NSHV) in the presence of parameter variations and external disturbances. In the attitude angle loop, a robust adaptive virtual control law is designed by using the adaptive method to estimate the unknown upper bound of the compound uncertainties. In the angular velocity loop, an adaptive sliding mode control law is designed to suppress the effect of parameter variations and external disturbances. The main benefit of the sliding mode control is robustness to parameter variations and external disturbances. To further improve the control performance, RBFNNs are introduced to approximate the compound uncertainties in the attitude angle loop and angular velocity loop, respectively. Based on Lyapunov stability theory, the tracking errors are shown to be asymptotically stable. Simulation results show that the proposed control system attains a satisfied control performance and is robust against parameter variations and external disturbances.