Stability analysis and robust composite controller synthesis for flexible joint robots

In this paper the control of flexible joint manipulators is studied in detail. The model of N-axis flexible joint manipulators is derived and reformulated in the form of singular perturbation theory and an integral manifold is used to separate fast dynamics from slow dynamics. A composite control algorithm is proposed for the flexible joint robots, which consists of two main parts. Fast control, u _f, guarantees that the fast dynamics remains asymptotically stable and the corresponding integral manifold remains invariant. Slow control, u _s, consists of a robust PID designed based on the rigid model and a corrective term designed based on the reduced flexible model. The stability of the fast dynamics and robust stability of the PID scheme are analyzed separately, and finally, the closed-loop system is proved to be uniformly ultimately bounded (UUB) stable by Lyapunov stability analysis. Finally, the effectiveness of the proposed control law is verified through simulations. The simulation results of single- and two-link flexible joint manipulators are compared with the literature. It is shown that the proposed control law ensures robust stability and performance despite the modeling uncertainties.     

阳极焙烧温度的建模与多变量解耦控制

阳极焙烧温度系统是一个含有耦合、大时滞、非线性的多变量控制系统。为实现对阳极焙烧温度的精确控制,依据现场采集的大量温度数据,辨识出阳极焙烧炉温度的二阶惯性滞后控制模型。以此模型为初始预测模型,提出阳极焙烧温度的多变量预测函数解耦控制方法,对焙烧温度进行多变量预测函数解耦控制。仿真和应用结果表明,这种控制方法的控制精度和鲁棒性优于原有的PID方法,具有很好的控制效果。     

基于X-Y定位平台的力/位置混合控制

在确定了X-Y定位平台系统数学模型的基础上,提出了一种力/位置混合控制方法。在位置控制部分,采用了基于重复控制补偿的PID控制方法。用重复控制作为误差补偿与传统简单的PID控制器相结合作为位置控制部分所采用的控制算法。在力控制回路中采用一种自适应模糊控制方法。通过引入一个切换函数来确定控制律形式,根据所设计的模糊规则对变量进行模糊化,通过解模糊得到控制律结果,自适应律是通过调制饱和度得到的。仿真结果表明,该控制方法能使系统的自适应能力和鲁棒性均有显著改善。     

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.     

滑模变结构控制在双闭环调速系统中的应用

为提高双闭环调速系统的快速跟踪性能,提出了一种新的滑模变结构速度控制策略。为了有限抑制系统在滑模切换面上的抖振,提高系统鲁棒性,在建立无刷直流电动机模型的基础上,提出了一种新型指数趋近率的变结构控制策略,使切换函数快速进入滑模面,有效地减小了系统的抖动。仿真实验结果表明采用的改进指数趋近率的滑模变结构控制相比传统的PID控制,系统在快速性、稳定性、准确性得到显著提高,系统对参数扰动具有较强的鲁棒性。     

改进的倾转旋翼机平稳过渡控制系统设计

针对倾转旋翼机在过渡模式下的过渡过程极其不稳定，控制系统设计难度大的问题，研究了倾转旋翼机平稳过渡控制方案。设计了平稳过渡控制系统结构，提出了改进的基于杂交粒子群的神经网络PID控制律设计，给出了该控制算法的具体流程。以XV-15为例进行仿真验证，结果表明提出的方法比BP神经网络PID方法得到的曲线变化更加平稳，没有出现幅值较大的震荡，达到了预期控制效果。     

Statistic PID tracking control for non-Gaussian stochastic systems based on T-S fuzzy model

A new robust proportional-integral-derivative （PID） tracking control framework is considered for stochastic systems with non-Gaussian variable based on B-spline neural network approximation and T-S fuzzy model identification. The tracked object is the statistical information of a given target probability density function （PDF）, rather than a deterministic signal. Following B-spline approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. Different from the previous related works, the time delay T-S fuzzy models with the exogenous disturbances are applied to identify the nonlinear weighting dynamics. Meanwhile, the generalized PID controller structure and the improved convex linear matrix inequalities （LMI） algorithms are proposed to fulfil the tracking problem. Furthermore, in order to enhance the robust performance, the peak-to-peak measure index is applied to optimize the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.     

Maximum sensitivity based fractional IMC–PID controller design for non-integer order system with time delay

A simple approach with a small number of tuning parameters is a key goal in fractional order controller design. Recently there have been a number of limited attempts to bring about improvements in these areas. In this paper, a new design method for a fractional order PID controller based on internal model control (IMC) is proposed to handle non-integer order systems with time delay. In order to reduce the number of tuning parameters and mitigate the impact of time delay, the fractional order internal model control scheme is used. Considering the robustness of the control system with respect to process variations and model uncertainty, maximum sensitivity is applied to the tuning of the parameters. The resulting controller has the structure of a fractional order PID which is cascaded with a filter. This is named a fractional IMC–PID controller. Numerical results are given to show the efficiency of the proposed controller.     

带有大型挠性网状天线航天器的鲁棒H∞控制方法

针对带有大型挠性网状天线航天器存在的挠性结构不确定性问题,提出了基于比例微分(PD)结构滤波器的鲁棒H∞双层反馈控制方法,第1层采用经典的PD+结构滤波器,确保刚体部分双积分环节稳定,第2层在提取第1层标称模型后,给出通用加权函数,通过构造增广模型得到鲁棒H∞控制器.该控制器结构简单,适合工程应用.通过仿真表明,本方法相对于传统PID+结构滤波器方法能够快速稳定三轴姿态;当结构参数变化较大且三轴姿态偏置为动态时变时,有可能导致传统方法失稳,而本方法具有较强的鲁棒适应性,仍能完成航天器天线的指向任务.     

基于AFSMC算法的四旋翼飞行器控制策略研究

针对四旋翼飞行器在飞行过程中,控制系统存在非线性、强耦合、不确定性和鲁棒性差的问题,建立了关于四旋翼飞行器的动力学数学模型,将自适应控制、模糊控制和滑模控制相结合,提出基于自适应模糊滑模控制(AFSMC)的快速平稳控制策略。采用模糊系统推理方法实现理想控制律的逼近。在满足李雅普诺夫稳定性条件的前提下进行控制器的设计和稳定性分析,并结合四旋翼的数学模型和给定参数进行了MATLAB仿真。仿真结果表明,AFSMC控制器相比常规PID控制器具有良好的动态性能和抗干扰能力。     

Model and robust gain‐scheduled PID control of a bio‐inspired morphing UAV based on LPV method

In this paper, a linear parameter‐varying (LPV)‐based model and robust gain‐scheduled structural proportion integral and derivative (PID) control design solution are proposed and applied on a bio‐inspired morphing wing unmanned aerial vehicle (UAV) for the morphing process. In the LPV model method, the authors propose an improved modeling method for LPV systems. The method combines partial linearization and function substitution. Using the proposed method, we can choose the varying parameters simply, thus creating a model that is more flexible and applicable. Then, a robust gain‐scheduled structural PID control design method is given by introducing a structural matrix to design a structural PID controller, which is more consistent with the structure of the PID controller used in practice and has a simpler structure than representative ones in the existing literature. The simulation results show that the developed LPV morphing UAV model is able to catch the response of the original nonlinear model with a smaller error than the existing Jacobian linearization method and the designed controller can maintain stable flights in practice with satisfactory robustness and performance.     

具有H_∞跟踪性能的机器人自适应PID控制

针对非线性不确定机器人系统的轨迹跟踪控制问题,提出一种鲁棒自适应PID控制算法.该控制器由主控制器和监督控制器组成.主控制器以常规PID控制为基础,基于滑模控制思想设计PID参数的自适应律,根据误差实时修正PID参数.基于Lyapunov函数设计的监督控制器补偿自适应PID控制器与理想控制器之间的差异,使系统具有设定的H_∞的跟踪性能.最后,两关节机器人的仿真实验结果表明了算法的有效性.

Abstract：

A robust adaptive PID control algorithm is proposed for trajectory tracking of robot manipulators with nonlinear uncertainties.The controller is composed of a main controller and a supervisory controller.The main controller is designed based on the traditional PID controller.The parameters of the PID controller are updated online according to the system running errors with the adaptation law based on the sliding mode control.The supervisory controller is proposed to compensate the error between the adaptive PID controller and the ideal controller in the sense of the Lyapunov function with the specified H_∞ tracking performance.Finally, the simulation results based on a two-joint robot manipulator show the effectiveness of the presented controller.     

四旋翼无人机轨迹稳定跟踪控制

针对四旋翼无人机轨迹稳定跟踪控制问题,为抑制外界扰动和参数不确定性的影响,设计一种双环鲁棒控制系统.首先,基于动态面内模法设计输出调节器进行位置控制,可解决系统的渐近跟踪及干扰抑制问题;其次,利用高阶滑模设计姿态控制器,可实现全局有限时间收敛,消除系统抖振和相对阶的限制;再次,为进一步提高控制精度,采用一种鲁棒精确微分器对姿态角指令信号进行精确求导;最后,对系统稳定性进行严格的数学证明,并与PID控制和传统滑模控制进行仿真对比,结果验证了所提出控制策略的优越性和鲁棒性.     

Robust model predictive control with guaranteed setpoint tracking

In this paper a novel robust model predictive control (RMPC) algorithm is proposed, which is guaranteed to stabilize any linear time-varying system in a given convex uncertainty region while respecting state and input constraints. Moreover, unlike most existing RMPC algorithms, the proposed algorithm is guaranteed to remove steady-state offset in the controlled variables for setpoints (possibly) different from the origin when the system is unknown linear time-invariant. The controller uses a dual-mode paradigm (linear control law plus free control moves to reach an appropriate invariant region), and the key step is the design of a robust linear state feedback controller with integral action and the construction of an appropriate polyhedral invariant region in which this controller is guaranteed to satisfy the process constraints. The proposed algorithm is efficient since the on-line implementation only requires one to solve a convex quadratic program with a number of decision variables that scale linearly with the control horizon. The main features of the new control algorithm are illustrated through an example of the temperature control of an open-loop unstable continuous stirred tank reactor.     

蒸发过程的非线性控制仿真研究

为了研究蒸发过程的非线性控制,对六效逆流蒸发系统的稳态工作点附近建立了动态模型,并将模型转化为仿射非线性系统的形式。接下来应用MIMO的GLC结构对这个非线性系统进行了输入输出线性化,对线性化后的系统应用PI控制律进行控制,并与常规的多回路PID控制做了对比。仿真结果表明,应用输入输出线性化控制策略消除了回路之间的耦合,能够更好地跟踪系统的设定值,并达到了节能降耗的目的。     

IMC–PID Design: Analytical Optimization for Performance/Robustness Tradeoff Tuning for Servo/Regulation Mode

This paper addresses the analytical design of a one‐degree‐of‐freedom (1‐DoF) robust proportional–integral–derivative (PID) controller for the servo/regulation mode in line with the enhanced internal model control (IMC) principle based on a first order plus dead time (FOPDT) model. The proposed enhanced IMC–PID can provide acceptable performance both for set‐point tracking and for load disturbance rejection. The design procedure is formulated as a constrained optimization problem, in which the robustness of the system is adequately considered. Therefore, the resulting PID controller gives optimal performance with an exact selected robustness degree. Illustrative examples are given to show the effectiveness and merits of the analytical tuning rules for a wide range of plants.     

基于遗传算法的生物芯片反应仪温控箱PID控制系统

为了改进原有的常规PID控制器,从传热学原理出发,针对生物芯片反应仪温控箱的数字式温度控制系统,建立了该温控箱的传递函数模型,并通过大量实验确定了模型的系数;由此提出了一种较实用的遗传算法PID方案;仿真结果表明,改进的温控器较原控制器,有更小的振荡幅度和更短的调整时间;将所得结果应用到生物芯片反应仪温控箱表明,改进的PID控制器提高了系统动态性能,增强了系统稳定性和快速性;此算法以实际工程为基础,因此具有一定的理论价值和较大的实际意义.     

一种基于H∞与PID混合控制的速度控制器设计

以PID为核心的速度控制系统易受到参数摄动以及外部扰动的影响,鲁棒性较差。针对这点不足,以某型飞机的数学模型为基础,提出了基于H∞与PID混合控制的速度控制器设计方法,以鲁棒控制姿态,实现内回路的设计,以PID控制速度,实现外回路的设计。在参数摄动情况下,将混合控制器与单纯PID控制器的控制效果进行对比评估,仿真结果表明所设计控制器性能满足要求,且比单纯的PID控制器具有更好的鲁棒性。     

Self-tuning and stable adaptive control of a batch polymerization reactor

Two adaptive control techniques are evaluated by application to a realistic mathematical model of a suspension polyvinyl chloride (PVC) reactor. Both techniques, the self-tuning regulator and a globally stable adaptive control algorithm, prove to be very robust and give excellent control of the temperature or the rate of conversion in the PVC reactor by manipulating the heat removal rate from the reactor jacket. Satisfactory regulation and setpoint changes in the temperature and the conversion rate are obtained in each case even in the presence of measurement noise and highly nonlinear reactor dynamics. The performance of the two adaptive techniques is compared with the performance of a classical, PID controller. The adaptive controllers are shown to always outperform the PID controller.