Adaptive actuator failure compensation for multivariable feedback linearizable systems

A feedback linearization‐based adaptive control scheme is developed for multivariable nonlinear systems with redundant actuators subject to uncertain failures. Such an adaptive controller contains a direct adaptive actuator failure compensator to compensate the uncertain actuator failure, a nonlinear feedback to linearize the nonlinear dynamics, and a linear feedback to stabilize the linearized system. The key new design feature is the estimation of both the failure patterns and the failure values, for direct adaptive actuator failure compensation, newly developed for multivariable feedback linearizable nonlinear systems. With direct control signal adaptation, the adaptive failure compensation design ensures closed‐loop stability and asymptotic output tracking in the presence of actuator failure uncertainties. Simulation results from an application to attitude control of a near‐space vehicle dynamic model are presented to verify the desired system performance with adaptive actuator failure compensation. Copyright © 2015 John Wiley & Sons, Ltd.     

Global stability of trajectory tracking of robot underPD control

It is shown for the first time that, even if there exist nonlinear unknown dynamics, aPD feedback control without higher-order nonlinear compensation can guarantee global stability for the trajectory following problem of a robot manipulator. ThePD control under investigation is a position and velocity feedback control with a time-varying gain, and does not contain any higher-order nonlinearity. The proposed control is in general continuous and does not require any knowledge of robotic systems except size bounding function on nonlinear dynamics. Asymptotic stability of velocity tracking error and arbitrarily small position tracking error are guaranteed. Another novel and interesting result shown in this paper is that a measure on protection against saturation of actuators has been incorporated into consideration of control design and robustness analysis.This work is supported in part by U.S. National Science Foundation under grant MSS-9110034.     

Transient performance for discrete‐time singular systems with actuators saturation via composite nonlinear feedback control

This paper is concerned with the transient performance improvement in tracking control problems for linear multivariable discrete‐time singular systems subject to actuators saturation. A composite nonlinear feedback control strategy is considered, and the resulting controller consists of a linear feedback law and a nonlinear feedback law without any switching element. The nonlinear term leads to a varying damping ratio of the closed‐loop system and yields a small overshoot as the output approaches the target reference, whereas the linear component is designed to achieve a quick response of the closed‐loop system. Two composite nonlinear feedback control laws by both state feedback and measurement output feedback are addressed. An illustrative example is included to show the validity of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.     

Constructive Tool for Orbital Stabilization of Underactuated Nonlinear Systems: Virtual Constraints Approach

We present a constructive tool for generation and orbital stabilization of periodic solutions for underactuated nonlinear systems. Our method can be applied to any mechanical system with a number of independent actuators smaller than the number of degrees of freedom by one. The synthesized feedback control law is nonlinear and time-dependent. It is derived from a feedback structure that explicitly uses the general or full integral of the systems zero dynamics. The control law generates a periodic solution and makes it exponentially orbitally stable.     

Composite nonlinear control with state and measurement feedback for general multivariable systems with input saturation

In this paper, we present a design procedure of composite nonlinear feedback control for general multivariable systems with actuator saturation. We consider both the state feedback case and the measurement feedback case without imposing any restrictive assumption on the given systems. The composite nonlinear feedback control consists of a linear feedback law and a nonlinear feedback law without any switching element. The linear feedback part is designed to yield a closed-loop system with faster rise time, while at the same time not exceeding the actuator limits for the desired command input levels. The nonlinear feedback law is used to reduce overshoot and undershoot caused by the linear part. As such, a highly desired tracking performance with faster settling time and smaller overshoot can be obtained. The result is illustrated by a numerical example, which shows that the proposed design method yields a very satisfactory performance.     

Feedback stabilization of bifurcations in multivariable nonlinear systems—Part II: Hopf bifurcations

In this paper we derive necessary and sufficient conditions of stabilizability for multi‐input nonlinear systems possessing a Hopf bifurcation with the critical mode being linearly uncontrollable, under the non‐degeneracy assumption that stability can be determined by the third order term in the normal form of the dynamics on the centre manifold. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the Hopf bifurcation of the closed‐loop system is supercritical, which is equivalent to local asymptotic stability of the system at the bifurcation point. We prove that under the non‐degeneracy conditions, stabilizability is equivalent to the existence of solutions to a third order algebraic inequality of the feedback gains. Explicit conditions for the existence of solutions to the algebraic inequality are derived, and the stabilizing feedback laws are constructed. Part of the sufficient conditions are equivalent to the rank conditions of an augmented matrix which is a generalization of the Popov–Belevitch–Hautus (PBH) rank test of controllability for linear time invariant (LTI) systems. We also apply our theory to feedback control of rotating stall in axial compression systems using bleed valve as actuators. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust exponential stabilization for network-based switched control systems

It has become a common practice to employ networks in control systems for connecting controllers and sensors/actuators on controlled plants and processes. A network-based switched control system, as a special case of networked control systems, is studied. Such a system is represented with network-induced delays and packet dropout as a switched delay system. Sufficient conditions for robust exponential stability are derived for a class of switching signals with average dwell time. A stabilization design for continuous-time, linear switched plant with nonlinear perturbation under a given communication network via a hybrid state feedback controller is proposed. A hybrid controller design is network-dependent and given in terms of linear matrix inequalities.     

Robust State Feedback Control Through Actuators With Generalized Sector Nonlinearities And Saturation

In control systems, actuators often have nonlinear characteristics that can not be neglected. For linear systems driven by actuators satisfying the generalized sector condition, a robust state feedback controller synthesis method is proposed to achieve the ultimate boundedness control. The method is based on the linear matrix inequality approach and is easy to apply. As an important special case of the generalized sector condition, the saturation characteristic of actuators is discussed separately, and non‐conservative results are obtained.     

互联非线性系统反馈主导控制设计方法及汽门开度控制应用

分析了电力系统非线性的数学性质,指出电力系统非线性是一种有界非线性.在此基础上,将反馈主导方法(feedback domination method,FDM)引入多机电力系统非线性控制.该方法与反馈线性化方法不同;反馈线性化方法是通过反馈将原非线性系统转化为线性系统,反馈主导方法则是通过反馈将原非线性系统转换为特定形式的非线性系统,该特定形式的非线性系统的动态由反馈引入的非线性部分主导.以多机系统非线性汽门控制问题为例,设计了反馈主导非线性汽门控制器,该控制器仅包含本地量测量,易于实现.数值仿真表明,多机系统反馈主导非线性汽门控制器可显著提高电力系统暂态稳定性.     

CPG-based control of a turtle-like underwater vehicle

This paper presents biologically inspired control strategies for an autonomous underwater vehicle (AUV) propelled by flapping fins that resemble the paddle-like forelimbs of a sea turtle. Our proposed framework exploits limit cycle oscillators and diffusive couplings, thereby constructing coupled nonlinear oscillators, similar to the central pattern generators (CPGs) in animal spinal cords. This paper first presents rigorous stability analyses and experimental results of CPG-based control methods with and without actuator feedback to the CPG. In these methods, the CPG module generates synchronized oscillation patterns, which are sent to position-servoed flapping fin actuators as a reference input. In order to overcome the limitation of the open-loop CPG that the synchronization is occurring only between the reference signals, this paper introduces a new single-layered CPG method, where the CPG and the physical layers are combined as a single layer, to ensure the synchronization of the physical actuators in the presence of external disturbances. The key idea is to replace nonlinear oscillators in the conventional CPG models with physical actuators that oscillate due to nonlinear state feedback of the actuator states. Using contraction theory, a relatively new nonlinear stability tool, we show that coupled nonlinear oscillators globally synchronize to a specific pattern that can be stereotyped by an outer-loop controller. Results of experimentation with a turtle-like AUV show the feasibility of the proposed control laws.     

负载Cartesian柔性臂非线性反馈控制

本文考虑ｘ和ｙ方向水平运动的Ｃａｒｔｅｓｉａｎ机器人控制系统。对末端具有负载的单杆柔性机械臂，我们给出了一个连续的分布参数模型，并提出了一类传感器和控制器并置在根部的非线性反馈控制。运用抽象Ｈｉｌｂｅｒｔ空间非线性算子半群理论，获得整个闭环系统的强渐近稳定。     

Active vibration control for nonlinear vehicle suspension with actuator delay via I/O feedback linearization

The problem of nonlinear vibration control for active vehicle suspension systems with actuator delay is considered. Through feedback linearization, the open-loop nonlinearity is eliminated by the feedback nonlinear term. Based on the finite spectrum assignment, the quarter-car suspension system with actuator delay is converted into an equivalent delay-free one. The nonlinear control includes a linear feedback term, a feedforward compensator, and a control memory term, which can be derived from a Riccati equation and a Sylvester equation, so that the effects produced by the road disturbances and the actuator delay are compensated, respectively. A predictor is designed to implement the predictive state in the designed control. Moreover, a reduced-order observer is constructed to solve its physical unrealisability problem. The stability proofs for the zero dynamics and the closed-loop system are provided. Numerical simulations illustrate the effectiveness and the simplicity of the designed control.     

机器人系统全局渐近稳定非线性PD+轨迹跟踪控制

采用一类具有“小误差放大、大误差饱和”功能的非线性饱和函数来改进常用的线性比例微分加（ＰＤ＋）机器人系统动力学控制,以形成非线性ＰＤ＋（ＮＰＤ＋）控制,从而获得更快的响应速度和轨迹跟踪精度．应用Ｌｙａｐｕｎｏｖ直接稳定性理论和ＬａＳａｌｌｅ不变性原理证明了闭环系统的全局渐近稳定性．两自由度机器人系统数值仿真结果表明了所提出的ＮＰＤ＋控制具有良好的控制品质．     

Composite quadratic Lyapunov functions for constrained control systems

A Lyapunov function based on a set of quadratic functions is introduced in this paper. We call this Lyapunov function a composite quadratic function. Some important properties of this Lyapunov function are revealed. We show that this function is continuously differentiable and its level set is the convex hull of a set of ellipsoids. These results are used to study the set invariance properties of continuous-time linear systems with input and state constraints. We show that, for a system under a given saturated linear feedback, the convex hull of a set of invariant ellipsoids is also invariant. If each ellipsoid in a set can be made invariant with a bounded control of the saturating actuators, then their convex hull can also be made invariant by the same actuators. For a set of ellipsoids, each invariant under a separate saturated linear feedback, we also present a method for constructing a nonlinear continuous feedback law which makes their convex hull invariant.     

Algebraic separation in realizing a linear state feedback control law by means of an adaptive observer

Based on a novel adaptive observer, which does not require signal boundedness in its stability proof, an algebraic separation property of linear state feedback control and adaptive state observation is established. This means, whenever a linear, stabilizing state feedback control law is realized with the state replaced by the state estimate of the given stable adaptive observer, then the resulting nonlinear control system is also globally asymptotically Lyapunov stable with respect to the initial state and parameter observation error of the adaptive observer. In particular, no assumptions on the system dynamics nor on the speed of the adaptation are made.     

On linearization of nonlinear singularity perturbed systems

This note considers external (feedback) linearization of nonlinear singularly perturbed systems. When more accurate representation of some dynamic systems is taken into account. The necessary condition for linearization may be violated. In these cases the slow manifold theory is shown to provide a practical tool for solving this problem. Furthermore, for a class of systems with fast actuators, direct application of present methodology in the literature is shown to be valid provided the linear equivalent system contains fast dynamics as well.     

Global stabilization of partially linear composite systems using homogeneous method

A linear feedback control scheme to globally stabilize a class of partially linear composite systems is proposed from the point view of homogeneity. Assume that the global stability of the zero dynamics of the nonlinear subsystem can be tested by using a homogeneous Lyapunov function. It is shown that the stabilization of the linear controllable subsystem from its own states equals to the stabilization of the whole systems if the nonlinearities satisfy a homogeneous inequality condition. Then we assume that the states are not measurable and also extend the method developed for state‐feedback control to the output‐feedback case. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

An approach to stability criteria of neural-network control systems

This paper discusses stability of neural network (NN)-based control systems using Lyapunov approach. First, it is pointed out that the dynamics of NN systems can be represented by a class of nonlinear systems treated as linear differential inclusions (LDI). Next, stability conditions for the class of nonlinear systems are derived and applied to the stability analysis of single NN systems and feedback NN control systems. Furthermore, a method of parameter region (PR) representation, which graphically shows the location of parameters of nonlinear systems, is proposed by introducing new concepts of vertex point and minimum representation. From these concepts, an important theorem, which is useful for effectively finding a Lyapunov function, is derived. Stability criteria of single NN systems are illustrated in terms of PR representation. Finally, stability of feedback NN control systems, which consist of a plant represented by an NN and an NN controller, is analyzed.     

Output tracking problem for systems with input saturations via nonlinear integrating actions

In this paper we synthesize nonlinear state feedback controllers for locally stabilizing linear systems with both saturating actuators and additive disturbances when the output must track a certain reference level. The objective is to bring the steady‐state error due to disturbances to zero by using a saturated controller that contains a nonlinear integrating action. The objective is two‐fold since we want to determine both a stabilizing controller and a region of the state space over which the stability of the resulting closed‐loop system is ensured, when the controls are allowed to saturate. The controller gains and the associated domain of stability are synthesized by using either Riccati equations (ARE) or linear matrix inequalities (LMIs). Copyright © 2000 John Wiley & Sons, Ltd.     

Feedback passivity‐based control of discrete nonlinear systems with time‐delay for variable geometry truss manipulator

In this paper, the feedback passivity‐based control of nonlinear discrete time‐delay systems for variable geometry truss manipulators is investigated. To determine an appropriate communication channel in the sense of feedback passivation, we first model the dynamics of the variable geometry truss manipulator as a generalized discrete nonlinear system with time‐delay. Then we further prove that when the infinite norm of estimated error is bounded, as long as there is a controller enables the closed‐loop system to be input‐strictly passive, there must be a deterministic equivalent controller to ensure that the system is stochastically quasi passive. After that, on the basis of the conclusion obtained, a more conclusive corollary is addressed for linear plants. Though passivity is a stricter condition than stability, feedback passivation does not impose more restrictions on estimate errors, and therefore does not require more communication channel information than mean square stability. Finally, we simplify the variable geometry truss dynamics to a linear plant to simulate to verify the validity of our method, and also compared the experimental results with the methods in the existing literature.