A compact design scheme of adaptive output-feedback control for uncertain nonlinear systems

Multiple uncertainties/noises, frequently exist in a plant, usually require multiple compensation techniques, which renders feedback controllers highly dynamic and nonlinear. This motivates us to search for a compact design scheme of compensation to reduce the complexity of controllers. In this paper, global output-feedback stabilisation is investigated for a class of uncertain nonlinear systems with unknown unmeasured states-dependent growth and input matching uncertainty. To solve the problem, a compact scheme is proposed to design a global adaptive output-feedback controller, which combines the technique of dynamic gain and extended state observer together. Particularly, only one dynamic gain, rather than two dynamic gains, is introduced to deal with the unknown polynomial-of-output growth rate, which makes our controller to have lower dynamics than those in the related works. Moreover, the input matching uncertainty is asymptotically estimated by the extended state observer, and thus its effect is well counteracted. It is shown that, under the designed controller, the system states globally converge to zero. A simulation example on non-zero set-point regulation demonstrates the effectiveness of the proposed approach.     

Optimal decentralized control of large scale systems

This paper presents a new optimized decentralized controller design method for solving the tracking and disturbance rejection problems for large-scale linear time-invariant systems, using only low-order decentralized controllers. To illustrate the type of results which can be obtained using the new optimized decentralized control design method, the control of a large flexible space structure is studied and compared with the standard centralized LQR-observer controller. The order of the resultant decentralized controller is much smaller than that of the standard centralized LQR-observer controller. The proposed controller also has certain fail-safe properties and, in addition, it can be five orders of magnitude more robust than the standard LQR-observer controller based on their real stability radii. The new decentralized controller design method is applied to a large flexible space structure system with 5 inputs and 5 outputs and of order 24.     

On the design of approximate non‐linear parametric controllers

This paper focuses on the design of non‐linear parametric controllers, around a nominal input/output trajectory of a discrete‐time non‐linear system. The main result provided herein is a relationship between the tracking performance of the closed‐loop control system in the neighbourhood of a nominal trajectory, and some local features (the first‐order linear approximations about the nominal trajectory) of the non‐linear mappings which characterize the plant and the feedback controller. Such a result can be used to predict the dynamic behaviour of the control system, and to reduce the computational complexity of the optimization task associated with the tuning of the parametric feedback controller. Copyright © 2000 John Wiley & Sons, Ltd.     

Digital parameter-adaptive control of an air-conditioning plant

Two parameter-adaptive (self-tuning) control algorithms for multivariable systems are described. The algorithms are designed on the basis of linear input-output system models by the combination of recursive parameter estimation and control algorithms: a parameter-adaptive deadbeat controller and a parameter-adaptive optimal state controller. These controllers are applied to a two-input two-output air-conditioning pilot plant, which consists of an air heater and an air humidifier and whose output variables are the temperature and the relative humidity of the air measured at the air outlet. The air-conditioning plant is a nonlinear system and its linearized static and dynamic behaviour is strongly dependent on the operating point characterized mainly by the output variables and by the air flow rate through the plant. The results of the real-time control experiments indicate that it is possible to use the self-tuning features of the parameter-adaptive controllers to stabilize the controlled system after a short adaption phase and to achieve at least a satisfactory control performance for time varying air flow rates and for time varying setpoints of the output variables.     

Decentralized and adaptive control of multiple nonholonomic robots for sensing coverage

This work deals with decentralized control of multiple nonholonomic mobile sensors for optimal coverage of a given area for sensing purposes. We assume a density function over the region to be covered, which can be viewed as a probability density of the phenomena to be sensed. The density function is unknown but assumed to be linearly parameterized with unknown parameter weights. We consider a second‐order dynamic model for the mobile agents and derive decentralized adaptive control laws to achieve optimal coverage of the region. We then consider the case where the dynamic model of the agents are not fully known, and then develop parameter adaptation laws to achieve the optimal coverage objective. We test the derived algorithms using simulations and compare our proposed controllers with kinematics‐based controllers. We find that the feedback control design based on the dynamic model performs significantly better than controllers solely relying on kinematic models. Furthermore, for the unknown dynamics case, our controller outperforms the nonadaptive controller with poor initial parameter estimates.     

Statistically optimized FOPID for output force control of SEAs

Fractional order PID (FOPID) controllers have recently found an increasing application in different fields of control. Comparing to traditional PID algorithms, FOPID controllers provide more flexibility and better performances. The simple and non-model-based structure of FOPID controllers has boosted their usage in real-world applications. However, due to having two more control parameters than regular PID controllers and the non-linear structure of FOPID controllers, the tuning procedure of these controllers is still a challenge. The authors of the present paper have recently proposed a Taguchi-based gain tuning algorithm for tuning of control parameters of FOPID controller. The present paper is an experimental evaluation of the proposed method. A custom made SEA, FUM-LSEA, is used as the test bed in this study. Deriving a dynamic model of the FUM-LSEA, feed-forward terms are added to the controller to compensate for disturbances from motions of the output block. Optimal gains and orders of the controller are obtained through a set of experiments suggested by the Taguchi method. The Taguchi optimized controller is also compared to a Ziegler–Nichols tuned controller. The experimental results indicate 45% improvements in force tracking error.     

On the Lyapunov-based adaptive control redesign for a class of nonlinear sampled-data systems

Stabilization of the exact discrete-time models of a class of nonlinear sampled-data systems, with an unknown parameter, is addressed. Given a Lyapunov-based continuous-time adaptive controller that ensures some stability properties for the closed-loop system, a sufficient condition for the design of high order discrete-time controllers is given. The stability analysis is carried out considering the truncated Fliess series of the Lyapunov difference equation. Due to the appearance of power terms of the unknown parameter, the problem is reparameterized in a convex-like form and an estimation law for the new unknown parameter is derived with no need of overparametrization or projection techniques. Then, assuming appropriate conditions hold, high order controllers can be designed. The boundedness of the extended state vector is ensured under some conditions, for a sufficiently small sampling period. It is shown how increasing the controller order can improve system performance.     

不确定遥操作系统带干扰观测器的自适应控制

遥操作系统受到不同类型的不确定性因素影响, 这些不确定性会降低系统的透明性, 甚至会使得系统不稳定. 本文提出了一种带干扰观测器的自适应控制器(adaptive controller with disturbance observer, ACWDO) 用来处理遥操作系统中同时受到的外部干扰和内部动力学参数不确定性. 首先建立了受外部干扰的遥操作系统的非线性动力学模型; 然后分别对主机器人和从机器人设计非线性干扰观测器用来对外部干扰进行估计和补偿; 之后在干扰观测器基础之上分别对主机器人和从机器人设计自适应控制器用来处理内部不确定的动力学参数; 最后再将所设计的ACWDO融入到四通道遥操作系统结构中. 理论分析和仿真结果表明, 所设计的控制器可以取得良好的位置跟踪和力跟踪效果, 确保了遥操作系统的透明性.     

Adaptive output feedback control of uncertain nonlinear systems based on dynamic surface control technique

An adaptive output feedback control approach is studied for a class of uncertain nonlinear systems in the parametric output feedback form. Unlike the previous works on the adaptive output feedback control, the problem of ‘explosion of complexity’ of the controller in the conventional backstepping design is overcome in this paper by introducing the dynamic surface control (DSC) technique. In the previous schemes for the DSC technique, the time derivative for the virtual controllers is assumed to be bounded. In this paper, this assumption is removed. It can be proven that the resulting closed‐loop system is stable in the sense that all the signals are semi‐global uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set. A simulation example is given to verify the effectiveness of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

随机激励下单杆柔性关节机械臂的建模与控制

机械系统如移动机器人、机械臂等在运动过程中通常会受到随机干扰.针对随机激励下单连杆柔性机械臂的数学建模和控制问题,目前还没有相关的研究.本文引入随机干扰,建立了一个具有未知参数的随机动力学模型.然后通过坐标变换,将该模型化成一个4阶系统.在此基础上,结合自适应理论,动态面方法和Lyapunov方法,设计了一种新的控制器.这种控制器有效地避免了传统方法中的过参数估计和复杂性爆炸的问题,同时可以保证跟踪误差在均方意义下任意小,且闭环系统的所有信号依概率有界.最后通过一个仿真例子验证了本文理论的有效性.     

一类离散时间切换线性系统的无差拍控制

研究一类带多控制器和多传感器离散时间线性系统的无差拍控制.对能控系统,通过适当的状态坐标变换获得系统矩阵的块三角结构,再设计状态反馈和周期切换策略使得状态反馈矩阵在有限周期内为零,从而保证闭环系统的无差拍稳定.进一步,对能观系统,设计具有有限时间精确估计的动态输出反馈,通过适当的周期切换策略实现闭环系统的无差拍稳定.最后,给出一个例子以验证所提设计方法的有效性.     

近空间飞行器多模型软切换保性能非脆弱控制

针对可变机翼后掠角近空间飞行器存在严重非线性、强耦合等特性, 在考虑控制器存在摄动的情况下, 设计了可以平滑切换的多模型软切换保性能非脆弱控制方案. 首先利用可测前提变量将系统的工作空间划分为多个子空间, 然后在每一个子空间中根据给定的性能指标设计局部模糊鲁棒保性能非脆弱控制器. 由于采用了广义系统的设计方法, 有效地减少了求解的计算量和复杂度. 系统的全局控制器由各局部控制器进行模糊加权得到, 从而实现了软切换. 对变机翼后掠角近空间飞行器的仿真实验表明了所提方法是有效的.     

Partially decentralized control of large-scale variable-refrigerant-flow systems in buildings

We consider the problem of designing a scalable control architecture for large-scale variable-refrigerant-flow (VRF) systems. Using a gray-box modeling approach, and by exploiting the one-way coupling between the fluid dynamics and thermal dynamics, we derive individual linearized models for each class of dynamics. This sufficiently reduces the complexity of the problem so that a scalable analysis is possible. Based on the natural dynamics and coupling of the VRF system, which become apparent through the structure of the derived models, a partially decentralized control architecture is proposed. Communication is limited to one-way sensor information flow from the individual decentralized controllers to a global controller, leading to a simple yet highly effective control architecture which easily scales for systems with a large number of evaporators. The ability of the proposed control architecture and design to provide both high performance and reduced energy consumption is demonstrated through a simulated case study.     

Decentralized control of symmetric systems

This paper is concerned with the stabilizability problem of symmetric systems by means of decentralized controllers. It is shown that the set of decentralized fixed modes of a symmetric system is equal to the set of uncontrollable and unobservable modes of the system and implies that the stabilizability of a state-space symmetric system by means of a decentralized controller is equivalent to the stabilizability for the system by means of a centralized controller.     

Adaptive dynamic surface control for disturbance attenuation of nonlinear systems

This paper proposes an adaptive dynamic surface control (DSC) approach for disturbance attenuation of uncertain nonlinear systems in the parametric strict-feedback form. In the proposed control system, a smooth projection algorithm is employed to train uncertain parameters. The proposed DSC system can overcome the complexity of an actual controller caused by the recursive differentiation of virtual controllers and parameter adaptation laws in the backstepping design procedure. From Lyapunov stability analysis, it is shown that the proposed controller has H_∞ tracking performance to attenuate external disturbances     

Multi-rate digital redesign of cascaded and dynamic output feedback systems

In this paper, a new indirect digital redesign method is presented for multi-rate sampled-data control systems with cascaded and dynamic output feedback controllers. These analogue controllers are often pre-designed based on desirable frequency specifications, such as bandwidth, natural angular frequency, etc. To take advantage of the digital controller over the analogue controller, digital implementation of these analogue controllers are often desirable. As only measured input-output signals are available, an ideal state reconstructing algorithm is utilised to obtain the multi-rate discrete-time states of the original continuous-time system. Based on the Chebyshev quadrature method, the gains of the multi-rate cascaded and the output feedback digital controllers are determined from their continuous-time counterparts according to the different sampling rates employed in the different parts of the closed-loop system. As a result, the respective analogue controllers with the high-frequency and low-frequency characteristics can be implemented using the respective fast-rate sampling and slow-rate sampling digital controllers. Unlike the classical direct bilinear transform method, which is an open-loop direct digital redesign method, the proposed digital controllers take into account the state-matching of the original continuous-time closed-loop system and the digitally redesigned sampled-data closed-loop system. To further improve the state-matching performance, an improved digital redesign approach is also developed to construct the multi-rate cascaded and dynamic output feedback digital controllers. Illustrative examples are given to demonstrate the effectiveness of the developed methods.     

A novel approach to output feedback control of fuzzy stochastic systems

This paper investigates the problem of Hankel-norm output feedback controller design for a class of T–S fuzzy stochastic systems. The full-order output feedback controller design technique with the Hankel-norm performance is proposed by the fuzzy-basis-dependent Lyapunov function approach and the conversion on the Hankel-norm controller parameters. Sufficient conditions are established to design the controllers such that the resulting closed-loop system is stochastically stable and satisfies a prescribed performance. The desired output feedback controller can be obtained by solving a convex optimization problem, which can be efficiently solved by standard numerical algorithms. Finally, a Henon map system is used to illustrate the effectiveness of the proposed techniques.     

Relatively optimal control and its linear implementation

Motivated by the fact that determining a feedback solution for the optimal control problem under constraints is a hard task we introduce the concept of relative optimality, roughly optimality for a specific (nominal) plant initial condition. We consider a generic discrete-time finite-horizon constrained optimal control problem for linear systems, and we seek for a state feedback (possibly dynamic) controller. As a fundamental requirement, we do not admit preactions or controller-state initialization based on the plant initial state and we assume our controller to be time-invariant. In particular, we do not consider controllers simply achieved by the feedforward and tracking of the optimal trajectory. A relatively optimal control is a stabilizing controller such that, if initialized at its zero state, produces the optimal (constrained) trajectory for the nominal initial condition of the plant. We show that one of such controllers is linear, dead-beat, and its order is equal to the length of the horizon minus the plant order, thus, of complexity which is known a priori. Some additional features such as the assignment of the compensator poles to achieve strong stabilization are proposed. We show that, by means of the proposed approach, we can face several problems such as optimal point-to-point operations, optimal impulse response and optimal tracking.     

A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

The problems of stability analysis and controllers design for discrete-time linear systems subject to state saturation nonlinearities are investigated in this paper. Both full state saturation and partial state saturation are considered. It is well known to all that the controller design problem under state saturation is very difficult and complex to deal with. In order to overcome the difficulty, a new and tractable system is constructed, and it can be proved that the constructed system is with the same domain of attraction as the original system. With the aid of this property, to estimate the domain of attraction of the original system, an LMI-based method is presented for estimating the domain of attraction of the origin for the new constructed system under state saturation. Further, two optimization algorithms are developed for constructing dynamic output-feedback controllers and state feedback controllers, respectively, which guarantee that the domain of attraction of the origin for the closed-loop system is as ’large’ as possible. An example is provided to demonstrate the effectiveness of the new method.