Passivity‐based control for stabilization,regulation and tracking purposes of a class of nonlinear systems

In this paper, a new passivity‐based control (PBC) scheme based on state feedback is proposed in order to solve tracking, regulation and stabilization problems for a class of multi‐input multi‐output (MIMO) nonlinear systems expressed in the normal form, with time‐invariant parameters and locally bounded reference weakly minimum phase. For the proposed control scheme two new different state feedbacks, one non‐adaptive for the case when the system parameters are assumed to be known and the other adaptive for the case of unknown parameters, are developed. For the adaptive case it is assumed that the unknown parameters appear linearly in the equations. Analysis of the transient behaviour of the proposed control schemes is presented through the simulation of two examples. Copyright © 2006 John Wiley & Sons, Ltd.     

Passivity‐based sliding mode control for nonlinear systems

Passivity with sliding mode control for a class of nonlinear systems with and without unknown parameters is considered in this paper. In fact, a method for deriving a nonlinear system with external disturbances to a passive system is considered. Then a passive sliding mode control is designed corresponding to a given storage function. The passivity property guarantees the system stability while sliding mode control techniques assures the robustness of the proposed controller. When the system includes unknown parameters, an appropriate updated law is obtained so that the new transformed system is passive. The passivation property of linear systems with sliding mode is also analysed. The linear and nonlinear theories are applied to a simple pendulum model and the gravity‐flow/pipeline system, respectively. Copyright © 2008 John Wiley & Sons, Ltd.     

Parameter‐dependent Riccati equation–based output feedback adaptive control

A parameter‐dependent Riccati equation approach is proposed to design and analyze the stability properties of an output feedback adaptive control law design. The adaptive controller is intended to augment an existing fixed‐gain observer‐based output feedback control law. Although the formulation is in the setting of model reference adaptive control, the realization of the adaptive controller does not require implementing the reference model. In this regard, the increased complexity of implementing the adaptive controller, above that of a fixed‐gain control law, is less than that of other methods. The error signals are shown to be uniformly ultimately bounded, and an estimate for the ultimate bound is provided. The issue of sensor noise is addressed by introducing an error filter. The control design process and the theoretical results are illustrated using a model for wing rock dynamics.     

基于模糊自适应不确定性机械臂的轨迹跟踪控制

针对一类不确定性机械臂的轨迹跟踪问题,提出了一种计算力矩加模糊补偿器的控制方案,计算力矩用来控制系统的标称部分,模糊补偿器用来控制系统的不确定部分,模糊补偿器的参数基于Lynapunov稳定性理论自适应调节,整个控制器保证了闭环系统的渐近稳定。在二自由度机械臂上的仿真验证了本文算法的有效性。     

Passification‐based adaptive control of linear systems: Robustness issues

Passivity is a widely used concept in control theory having led to many significant results. This paper concentrates on one characteristic of passivity, namely passification‐based adaptive control. This concept applies to multi‐input multi‐output systems for which exists a combination of outputs that renders the open‐loop system hyper‐minimum phase. Under such assumptions, the system may be passified by both high‐gain static output feedback and by a particular adaptive control algorithm. This last control law is modified here to guarantee its coefficients to be bounded. The contribution of this paper is to investigate its robustness with respect to parametric uncertainty. Time response characteristics are illustrated on examples including realistic situations with noisy output and saturated input. Theoretical results are formulated as linear matrix inequalities and can hence be readily solved with semi‐definite programming solvers. Copyright © 2007 John Wiley & Sons, Ltd.     

A passivity‐based simple adaptive synergetic control for a class of nonlinear systems

For a class of nonlinear systems with the representation {A(x), B(x), C} and where the system parameters and dynamics are unknown, a simple adaptive synergetic controller ensuring the asymptotic convergence of the system to a desired manifold is proposed based on the technique of simple adaptive control (SAC). It is well known that the design of the synergetic control (SC) law requires a thorough knowledge of the system parameters and dynamics. Such problem obstructs the synthesis of the SC law and the designer is prompted to pass through the estimation methods, which, in turn, poses a problem of increasing the computation time of the control algorithm. To cope with this problem, a solution is proposed by modifying the original SC law to develop an SAC‐like adaptive SC law without the need of prior knowledge of the system. The stability of the proposed adaptive controller is formally proven via the Lyapunov approach. Experimental application to a quadrotor system is given to validate the theoretical results.     

Passivity‐based adaptive output tracking control for switched nonlinear systems with uncertain parameters

This paper addresses the issue of the adaptive output tracking control for switched nonlinear systems with uncertain parameters. The solvability of the tracking control problem for each subsystem is not necessary to hold. Individual update laws corresponding to different unknown parameters are adopted to reduce the conservativeness produced from the adoption of a common undated law. By means of the dual design of the adaptive controllers and a state‐dependent switching law using multiple storage functions technique, several conditions are obtained under which the adaptive output tracking control problem for switched nonlinear systems is solvable. Finally, an example shows the effectiveness of the proposed method.     

Passivity‐based parameterized adaptive disturbance attenuation controller design for switched polynomial nonlinear systems

This paper is concerned with the adaptive disturbance attenuation control problem for a class of switched polynomial nonlinear systems. At first, a parameterized controller is designed to transform the switched polynomial nonlinear systems into switched Hamiltonian systems with polynomial structure. Then, combining with the solve‐parameter algorithm described in this paper, a mixed adaptive passivity and H₂/H_∞ control method is devoted. Comparing with the existing results, the obtained adaptive disturbance attenuation controller has better performance. Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.     

一种考虑加热器效率的自适应PID温控方法

某化学分析仪器需对处理过程进行温度控制,控制涉及多个部位,各部位加热器效率并不相同,并且每个控制点在不同的处理流程中存在不同的目标温度.为解决上述问题,采用PID控制和模糊控制相结合的自适应温控方法,根据被控系统的实际响应,运用模糊推理,考虑各加热器的效率,目标温度与环境温度差等因素,实现温控过程中PID参数的自适应调...     

Stability analysis of a combined direct variable structure adaptive control – the discrete‐time case

This paper presents the proofs of robust stability of a discrete‐time robust model reference controller combined with variable structure in an adaptive framework. All the proofs of robust stability are derived for the discrete‐time case and are similar to those already existing for the conventional non‐combined case. The controller is applied to a SISO LTI plant with unmodeled dynamics of multiplicative and additive types. It is shown that the combined controller can arbitrarily improve the convergence of the error while maintaining the robustness if compared with the non–combined case. Simulation results illustrate the performance of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

Multiple characteristic model‐based golden‐section adaptive control: Stability and optimization

The characteristic model‐based golden‐section adaptive control (CM‐GSAC) law has been developed for over 20 years in China with a broad range of applications in various fields. However, quite a few theoretical problems remain open despite its satisfying performance in practice. This paper revisits the stability of the CM‐GSAC from its very beginning and explores the underlying implications of the so‐called golden‐section parameter l₂≈0.618. The closed‐loop system, which consists of the CM and the GSAC, is a discrete time‐varying system, and its stability is discussed from three perspectives. First, attentions have been paid to select the optimal controller coefficients such that the closed‐loop system exhibits the best transient performance in the worst case. Second, efforts are made to improve the robustness in the presence of parameter estimation errors, which provide another choice when designing the adaptive controller. Finally, by measuring the slowly time‐varying nature in an explicit inequality form, a bridge is built between the instantaneous stability and the time‐varying stability. In order to relax the constraints on the parameter bounds of the CM, the GSAC is further extended to multiple CMs, which shows more satisfying tracking performance than that of the traditional multiple model adaptive control method. Copyright © 2014 John Wiley & Sons, Ltd.     

Neural network‐based adaptive control of piezoelectric actuators with unknown hysteresis

This paper proposes a neural network (NN)‐based adaptive control of piezoelectric actuators with unknown hysteresis. Based on the classical Duhem model described by a differential equation, the explicit solution to the equation is explored and a new hysteresis model is constructed as a linear model in series with a piecewise continuous nonlinear function. An NN‐based dynamic pre‐inversion compensator is designed to cancel out the effect of the hysteresis. With the incorporation of the pre‐inversion compensator, an adaptive control scheme is proposed to have the position of the piezoelectric actuator track the desired trajectory. This paper has three distinct features. First, it applies the NN to online approximate complicated piecewise continuous unknown nonlinear functions in the explicit solution to Duhem model. Second, an observer is designed to estimate the output of hysteresis of piezoelectric actuator based on the system input and output. Third, the stability of the controlled piezoelectric actuator with the observer is guaranteed. Simulation results for a practical system validate the effectiveness of the proposed method in this paper. Copyright © 2008 John Wiley & Sons, Ltd.     

Dynamic modeling and adaptive robust boundary control of a flexible robotic arm with 2‐dimensional rigid body rotation

This paper investigates the control of a single‐link flexible robot manipulator with a tip payload appointed to rotate about 2 perpendicular axes in space. The control objective is to regulate the rigid body rotation of the manipulator with guaranteeing the stability of its vibration in the presence of exogenous disturbances. To achieve this, a Lyapunov‐based control design procedure is used and accomplished in some steps. First, the partial differential equation (PDE) dynamic model governing the rigid‐flexible hybrid motion of the arm is derived by applying Hamilton's principle. Next, based on the developed PDE model, an adaptive robust boundary control is established using the Lyapunov redesign approach. To this end, an adaptation mechanism is proposed so that the robust boundary control gains are dynamically updated online and there is no need for prior knowledge of disturbance upper bounds. The actuators and sensors are fully implemented at the arm boundary without using distributed actuators or sensors. Furthermore, in order to avoid control errors resulting from the spillover, control design is directly based on infinite‐dimensional PDE model without resorting to model truncation. Simulation results illustrate the efficacy of the considered method.     

Realization of precise force control using both 2‐DOF control and learning control

Recently, two degrees‐of‐freedom (2DOF) control has been widely recognized to be efficient. The major merit of 2DOF control is independence between tracking performance and the feedback performance. However, there is a limitation on tracking performance in the 2DOF control system. In this paper, we propose a new control system that consists of a conventional 2DOF controller and a learning controller. The role of the learning controller is to realize high tracking performance, which cannot be realized alone by the 2DOF controller. The learning controller can be designed by using only information specifying a 2DOF controller, and it does not need information about the controlled plant. We show some experimental results to verify the effectiveness of the proposed system. © 1999 Scripta Technica, Electr Eng Jpn, 128(4): 102–110, 1999     

Neural network‐based adaptive attitude tracking control for flexible spacecraft with unknown high‐frequency gain

Adaptive control design using neural networks (a) is investigated for attitude tracking and vibration stabilization of a flexible spacecraft, which is operated at highly nonlinear dynamic regimes. The spacecraft considered consists of a rigid body and two flexible appendages, and it is assumed that the system parameters are unknown and the truncated model of the spacecraft has finite but arbitrary dimension as well, for the purpose of design. Based on this nonlinear model, the derivation of an adaptive control law using neural networks (NNs) is treated, when the dynamics of unstructured and state‐dependent nonlinear function are completely unknown. A radial basis function network that is used here for synthesizing the controller and adaptive mechanisms is derived for adjusting the parameters of the network and estimating the unknown parameters. In this derivation, the Nussbaum gain technique is also employed to relax the sign assumption for the high‐frequency gain for the neural adaptive control. Moreover, systematic design procedure is developed for the synthesis of adaptive NN tracking control with L₂ ‐gain performance. The resulting closed‐loop system is proven to be globally stable by Lyapunov's theory and the effect of the external disturbances and elastic vibrations on the tracking error can be attenuated to the prescribed level by appropriately choosing the design parameters. Numerical simulations are performed to show that attitude tracking control and vibration suppression are accomplished in spite of the presence of disturbance torque/parameter uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.     

Observer‐based adaptive neural control of uncertain MIMO nonlinear systems with unknown control direction

This paper investigates adaptive neural network output feedback control for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems with an unknown sign of control gain matrix. Because the system states are not required to be available for measurement, an observer is designed to estimate the system states. In order to deal with the unknown sign of control gain matrix, the Nussbaum‐type function is utilized. By using neural network, we approximated the unknown nonlinear functions and perfectly avoided the controller singularity problem. The stability of the closed‐loop system is analyzed by using Lyapunov method. Theoretical results are illustrated through a simulation example. Copyright © 2012 John Wiley & Sons, Ltd.     

Dual high‐gain‐based adaptive output‐feedback control for a class of nonlinear systems

We propose an adaptive output‐feedback controller for a general class of nonlinear triangular (strict‐feedback‐like) systems. The design is based on our recent results on a new high‐gain control design approach utilizing a dual high‐gain observer and controller architecture with a dynamic scaling. The technique provides strong robustness properties and allows the system class to contain unknown functions dependent on all states and involving unknown parameters (with no magnitude bounds required). Unlike our earlier result on this problem where a time‐varying design of the high‐gain scaling parameter was utilized, the technique proposed here achieves an autonomous dynamic controller by introducing a novel design of the observer, the scaling parameter, and the adaptation parameter. This provides a time‐invariant dynamic output‐feedback globally asymptotically stabilizing solution for the benchmark open problem proposed in our earlier work with no magnitude bounds or sign information on the unknown parameter being necessary. Copyright © 2007 John Wiley & Sons, Ltd.     

基于预估模型切换的过热汽温无辨识自适应控制

针对电厂锅炉的过热汽温系统具有大惯性、大时滞和多模型等特性.研究一种基于预估模型切换的无辨识自适应预估控制方法.该方法需设计一个无辨识自适应预估控制器和基于主蒸汽流量变化率的切换律,给出若干个一阶预估模型.在系统运行过程中,这些预估模型在切换律控制下根据运行工况按优化切换时间自适应地切换,而其中的优化切换时间是用切换系统优化理论计算得到的.仿真试验结果表明,该方法适用于过热汽温系统,具有良好的控制品质、较强的抗扰和自适应能力,且对预估模型的精度要求不高,控制参数容易整定,易于工程实现.     

An adaptive iterative learning algorithm for boundary control of a flexible manipulator

In this study, we consider the boundary control problem of a flexible manipulator in the presence of system parametric uncertainty and external disturbances. The dynamic behavior of the flexible manipulator is represented by partial differential equations (PDEs). Based on the Lyapunov method, we propose an adaptive iterative learning control scheme for trajectory tracking and vibration suppressing of a flexible manipulator. The proposed control scheme is designed using both a proportional‐derivative feedback structure and an iterative term. The learning convergence of iterative learning control is achieved through rigorous analysis without any simplification or discretization of the PDE dynamics. Finally, the results are illustrated using numerical simulations for control performance verification. Copyright © 2016 John Wiley & Sons, Ltd.     

Sampled‐data adaptive control of a class of nonlinear systems

The paper considers the discrete‐time implementation of a class of backstepping adaptive controllers for uncertain nonlinear systems in the parametric strict‐feedback form. The stability of the resultant sampled‐data system cannot be guaranteed when the direct discretization of the continuous‐time backstepping controller is applied to the same system via a sampling and hold device. Therefore, the paper has presented a sampled‐data control scheme which involves first modifying the existing continuous‐time controller and then discretizing it using the forward Euler method. It has been shown that the proposed control guarantees in a semi‐global sense the boundedness of all the variables of the overall sampled‐data system under some conditions. Particularly, the state of the nonlinear system to be controlled can converge to any arbitrarily small neighbourhood of the origin. Copyright © 2011 John Wiley & Sons, Ltd.