Reliable decentralized integral-action controller design

Reliable stabilizing controller design with integral-action is considered for linear time-invariant, multi-input-multi-output decentralized systems with stable plants. Design methods are proposed to achieve reliable closed-loop stability with integral-action in each output channel for asymptotic tracking of step-input references applied at each input. The design approaches guarantee stability and integral-action in the active channels when all controllers are operational and when any of the controllers is set equal to zero due to failure     

Simultaneous stabilization of MIMO systems with integral action controllers

Simultaneous stabilization with asymptotic tracking of step-input references is explored for linear, time-invariant, multi-input multi-output stable plants. Necessary conditions are presented for existence of simultaneous integral-action controllers and existence of simultaneous PID-controllers. A systematic simultaneous PID-controller synthesis method is proposed under a sufficient condition.     

Low order integral-action controller synthesis

A simple controller synthesis method is developed for certain classes of linear, time-invariant, multi-input multi-output plants. The number of poles in each entry of these controllers depends on the number of right-half plane plant zeros, and is independent of the number of poles of the plant to be stabilized. Furthermore, these controllers have integral-action so that they achieve asymptotic tracking of step input references with zero steady-state error. The designed controller’s poles and zeros are all in the stable region with the exception of one pole at the origin for the integral-action design requirement. The freedom available in the design parameters may be used for additional performance objectives, although the only goal here is stabilization and tracking of constant references.     

State observer-based robust control scheme for electrically driven robot manipulators

By using a state observer, a new robust trajectory tracking control scheme is developed in this paper for electrically driven robot manipulators. The role of the observer is to estimate joint angular velocities. The proposed controller does not employ adaptation, but assures robust stability of tracking error between joint angles and desired trajectories. At sacrificing asymptotical stability of the tracking errors, the configuration of the proposed controller becomes very simple, compared with regressor-based adaptive controllers. It is shown in the closed-loop system using the proposed controller that the Euclidian norm of tracking errors arrives at any small closed region with any convergent rate by setting only one design parameter. Especially for the desired trajectories converging to constant ultimate values, it is assured that tracking errors converge to zero.     

静电刚度式谐振微加速度计闭环驱动控制

分析了谐振微加速度计闭环驱动控制的要求,并根据要求建立了幅度和频率自适应控制的双闭环驱动分析模型．鉴于系统的高阶非线性,采用近似平均法分析了系统的稳态平衡点和稳定条件．对基于锁相技术的频率跟踪环,得到了环路频率稳定跟踪的积分控制器临界条件．对基于自动增益的幅度控制环,分析表明在没有PI控制器时不能实现恒幅振动,在引入PI控制器后,振动幅度与品质因数和频率无关;同时,较小的直流参考电压能实现同样大的振幅．仿真结果有效的验证了上述结论,理论分析和仿真有助于驱动电路的设计和调试．     

Global optimal fuzzy tracker design based on local concept approach

In this paper, we propose a global optimal fuzzy tracking controller, implemented by fuzzily blending the individual local fuzzy tracking laws, for continuous and discrete-time fuzzy systems with the aim of solving, respectively, the continuous and discrete-time quadratic tracking problems with moving or model-following targets under finite or infinite horizon (time). The differential or recursive Riccati equations, and more, the differential or difference equations in tracing the variation of the target, are derived. Moreover, in the case of time-invariant fuzzy tracking systems, we show that the optimal tracking controller can be obtained by just solving algebraic Riccati equations and algebraic matrix equations. Grounding on this, several fascinating characteristics of the resultant closed-loop continuous or discrete time-invariant fuzzy tracking systems can be elicited easily. The stability of both closed-loop fuzzy tracking systems can be ensured by the designed optimal fuzzy tracking controllers. The optimal closed-loop fuzzy tracking systems cannot only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Moreover, the resulting closed-loop fuzzy tracking systems possess infinite gain margin; that is, their stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the performance of the proposed optimal fuzzy tracker design schemes and to demonstrate the proved stability properties     

Adaptive integral backstepping sliding mode control for opto-electronic tracking system based on modified LuGre friction model

In order to improve the control accuracy and stability of opto-electronic tracking system fixed on reef or airport under friction and external disturbance conditions, adaptive integral backstepping sliding mode control approach with friction compensation is developed to achieve accurate and stable tracking for fast moving target. The nonlinear observer and slide mode controller based on modified LuGre model with friction compensation can effectively reduce the influence of nonlinear friction and disturbance of this servo system. The stability of the closed-loop system is guaranteed by Lyapunov theory. The steady-state error of the system is eliminated by integral action. The adaptive integral backstepping sliding mode controller and its performance are validated by a nonlinear modified LuGre dynamic model of the opto-electronic tracking system in simulation and practical experiments. The experiment results demonstrate that the proposed controller can effectively realise the accuracy and stability control of opto-electronic tracking system.     

一类非线性系统的积分变结构模糊自适应跟踪控制

针对一类具有未知常数控制增益的不确定非线性系统,基于变结构控制原理,并利用具有非线性可调参数的模糊系统逼近等价控制,提出一种具有监督控制器的积分变结构模糊自适应跟踪控制策略.该策略通过监督控制器保证闭环系统所有信号有界.进一步,通过引入最优逼近误差的自适应补偿项来消除建模误差的影响.理论分析证明了跟踪误差能够收敛到零.仿真结果表明了该方法的有效性.     

Multipurpose controllers for multivariable systems

The primary purpose of this paper is to outline a new procedure for designing controllers which simultaneously achieve a variety of desired design goals in deterministic, unity feedback, linear multivariable systems. More specifically, we will present a new algorithm for the systematic design of a "three-part" multivariable controller which simultaneously ensures: 1) a noninteractive or decoupled closed-loop design, 2) complete and arbitrary closed-loop pole placement, which implies desired (single-loop) transient performance as well as closed-loop stability, 3) zero steady-state errors between the plant outputs and any nondecreasing deterministic inputs, 4) complete steady-state output rejection of nondecreasing deterministic disturbances, and 5) robustness with respect to stability, disturbance rejection, and zero error tracking for rather substantial plant parameter variations. Our development will employ the more "modern" (Laplace-transformed) differential operator approach for controller synthesis, which involves transfer matrix factorizations and the manipulation of polynomial matrices in the Laplace operators.     

干扰下的无人直升机自适应反步法鲁棒跟踪控制

针对无人直升机干扰下的鲁棒轨迹跟踪问题,设计了一种自适应反步控制方法.鉴于作用在直升机上的干扰是产生跟踪误差的主要原因,该方法的主要思想是寻求一种方法来补偿这种干扰.首先,将未建模动态如外部阵风干扰、配平误差、机身、垂尾、平尾以及其他可忽略的动态产生的力和力矩看成一种组合干扰,从而建立了一个方便反步法控制器设计的简化模型.当设计好反步法控制器后,设计了一个非线性自适应律来估计这种组合干扰,并通过将干扰估计值整合到反步控制器中,使得闭环跟踪系统的鲁棒稳定性得到了保证,即基于李雅普诺夫稳定性理论证明了所设的控制器对于干扰主动阻隔,特别是低频干扰的主动阻隔是有效的.最后,两个仿真研究验证了该方法是优于常规反步法和积分反步法的.     

Passivity-based tracking control of an omnidirectional mobile robot using only one geometrical parameter

This paper presents an output feedback tracking control scheme for a three-wheeled omnidirectional mobile robot, based on passivity property and a modified generalized proportional integral (GPI) observer. The proposed control approach is attractive from an implementation point of view, since only one robot geometrical parameter (i.e., contact radius) is required. Firstly, a nominal dynamic model is given and the passivity property is analyzed. Then the controller is designed based on passivity property and a modified GPI observer. The controller design objective is to preserve the passivity property of the robot system in the closed-loop system, which is conceptually different from the traditional model-based control methodology. Particularly, the designed control system takes full advantage of the robot natural damping. Therefore, only considerably small or non differential feedback is needed. In addition, theoretical analysis is given to show the closed-loop stability behavior. Finally, experiments are conducted to validate the effectiveness of the proposed control system design in both tracking and robustness performance.     

Intelligent Control of Discrete Linear Systems Based on a Supervised Adaptive Multiestimation Scheme

A pole-placement based adaptive controller synthesised from a multiestimation scheme is designed for linear plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterisation of the adaptive controller in real time. The basic usefulness of the proposed scheme is to improve the transient response so that the closed-loop stability is guaranteed. The switching process is subject to a minimum dwelling or residence time within which the supervisor is not allowed to switch between the multiple estimation schemes. The high level supervision is based on the multiestimation identification scheme. The residence time condition guarantees the closed-loop stability. The above higher level switching structure is on-line supervised by a closed-loop tracking error based algorithm. This second supervision on-line tunes the free design parameters which appear as time varying weights in the loss function of the above switching structure. Thus, the closed-loop behaviour, compared to the constant parameter case one, is improved when the design parameter is not tightly initialised. Both supervisors are hierarchically organised in the sense that they act on the system at different rates. Furthermore, a projection algorithm has been considered in the estimation scheme in order to include a possible a priori knowledge of the estimates parameter vector value in the estimation algorithm.     

带有常数干扰的正则线性系统的镇定

本文考虑带有常数干扰的抽象正则线性系统的状态反馈镇定问题.本文控制设计采用线性系统的动态补偿方法,将传统的PID控制推广到无穷维正则线性系统.通过引入积分作用,控制器可以有效地补偿常数干扰.论文给出了具体的状态反馈法则,并证明了对应闭环系统的指数稳定性.理论结果被应用于带有常数干扰的不稳定热方程,给出了控制器及其闭环系统的指数稳定性,数值仿真验证了本文理论结果的有效性.     

多输入输出反馈系统虚轴的零点对跟踪问题的约束

反馈系统的设计会受到闭环系统特性的制约. 本文给出了反馈控制系统接近虚轴或虚轴上的稳定零点对跟踪误差的时间域积分约束. 这一时间域积分约束是任何一个线性时不变系统为保证其闭环系统的稳定性, 其跟踪误差必须满足的. 接近虚轴或虚轴上的稳定零的存在表明跟踪误差与调节时间之间存在某种折中. 对固定的调节时间, 本文给出了在虚轴上存在零点情形下, 其跟踪误差的无穷范数下界的一个有效估计. 此估计表明, 零点的绝对值越小, 其无穷范数的下界越大. 这些约束由一个例子加以解释.     

Analysis of distributed power control under constant and time-varying delays

This work studies the distributed power control algorithm proposed in 1993 by Foschini-Miljanic, standardised for universal mobile telecommunication systems. Continuous and discrete time versions of this algorithm are analysed. First, the stability of the distributed power allocation schemes was studied, where sufficient conditions to guarantee stability and convergence to a desired quality of service were provided. In this study, the channel gains are assumed to be slowly time-varying or piece-wise constant. For closed-loop control, a proportional controller is then employed under integral action in order to achieve good tracking despite time-varying and unknown channel gains. Next, the effects of constant and time-varying time delays in the closed-loop structure are studied. Explicit stability regions for the control gains in the Foschini-Miljanic scheme are derived for both the continuous and discrete-time versions of the algorithm, under constant and time-varying delays. For time-varying scenario, the resulting stability regions do not impose limitations on the rate change of the time-varying profiles. A comprehensive evaluation using simulations is performed to validate the analytical derivations described in the paper.     

Reliable stabilization with integral action in decentralized control systems

Reliable stabilization with integral action is studied in a linear, time-invariant, multi-input, multi-output, two-channel decentralized control system, where the plant is stable. The objective is to achieve closed-loop stability when both controllers act together and when each controller acts alone. Necessary and sufficient conditions are obtained for existence of block-diagonal decentralized controllers that ensure reliable stabilization, and integral action and all such decentralized controllers are parametrized. Explicit controller design approaches are discussed for the case of square channels.     

基于自组织小波小脑模型关节控制器的不确定非线性系统鲁棒自适应终端滑模控制

针对一类不确定非线性系统的跟踪控制问题,在考虑建模误差、参数不确定和外部干扰情况下,以良好的跟踪性能及强鲁棒性为目标,提出基于自组织小脑模型(self-organizing wavelet cerebellar model articulation controller,SOWCMAC)的鲁棒自适应积分末端(terminal)滑模控制策略.首先,将小脑模型、自组织神经网络和小波函数各自优势相结合,给出一种SOWCMAC,以保证干扰估计方法具有快速学习能力和更好的泛化能力.其次,设计两种改进的terminal滑模面构造方法,并分别给出各自的收敛时间.然后,基于SOWCMAC和改进的积分terminal滑模面,给出不确定非线性系统鲁棒自适应非奇异terminal控制器的设计过程,其中通过构造自适应鲁棒项抑制干扰估计误差对系统跟踪性能的影响,并利用Lyapunov理论证明闭环系统的稳定性.最后,将该方法应用于近空间飞行器姿态的控制仿真实验,结果表明所提出方法有效性.     

Robustly Stable Adaptive Control of a Tandem of Master–Slave Robotic Manipulators With Force Reflection by Using a Multiestimation Scheme

The problem of controlling a tandem of robotic manipulators composing a teleoperation system with force reflection is addressed in this paper. The final objective of this paper is twofold: 1) to design a robust control law capable of ensuring closed-loop stability for robots with uncertainties and 2) to use the so-obtained control law to improve the tracking of each robot to its corresponding reference model in comparison with previously existing controllers when the slave is interacting with the obstacle. In this way, a multiestimation-based adaptive controller is proposed. Thus, the master robot is able to follow more accurately the constrained motion defined by the slave when interacting with an obstacle than when a single-estimation-based controller is used, improving the transparency property of the teleoperation scheme. The closed-loop stability is guaranteed if a minimum residence time, which might be updated online when unknown, between different controller parameterizations is respected. Furthermore, the analysis of the teleoperation and stability capabilities of the overall scheme is carried out. Finally, some simulation examples showing the working of the multiestimation scheme complete this paper.     

Robustly stable adaptive control of a tandem of master-slave robotic manipulators with force reflection by using a multiestimation scheme.

The problem of controlling a tandem of robotic manipulators composing a teleoperation system with force reflection is addressed in this paper. The final objective of this paper is twofold: 1) to design a robust control law capable of ensuring closed-loop stability for robots with uncertainties and 2) to use the so-obtained control law to improve the tracking of each robot to its corresponding reference model in comparison with previously existing controllers when the slave is interacting with the obstacle. In this way, a multiestimation-based adaptive controller is proposed. Thus, the master robot is able to follow more accurately the constrained motion defined by the slave when interacting with an obstacle than when a single-estimation-based controller is used, improving the transparency property of the teleoperation scheme. The closed-loop stability is guaranteed if a minimum residence time, which might be updated online when unknown, between different controller parameterizations is respected. Furthermore, the analysis of the teleoperation and stability capabilities of the overall scheme is carried out. Finally, some simulation examples showing the working of the multiestimation scheme complete this paper.     

Force Reflecting Bilateral Control of Master–Slave Systems in Teleoperation

In this paper, a simple structure design with arbitrary motion/force scaling to control teleoperation systems, with model mismatches is presented. The goal of this paper is to achieve transparency in presence of uncertainties. The master–slave systems are approximated by linear dynamic models with perturbed parameters, which is called the model mismatch. Moreover, the time delay in communication channel with uncertainties is considered. The stability analysis will be considered for two cases: (1) stability under time delay uncertainties and (2) stability under model mismatches. For the first case, two local controllers are designed. The first controller is responsible for tracking the master commands, while the second controller is in charge of force tracking as well as guaranteeing stability of the overall closed-loop system. In the second case, an additional term will be added to the control law to provide robustness to the closed-loop system. Moreover, in this case, the local slave controller guarantees the position tracking and the local master controller guarantees stability of the inner closed-loop system. The advantages of the proposed method are two folds: (1) robust stability of the system against model mismatches is guaranteed and (2) structured system uncertainties are well compensated by applying independent controllers to the master and the slave sites. Simulation results show good performance of the proposed method in motion tracking as well force tracking in presence of model mismatches and time delay uncertainties.