Predefined-time control for free-floating space robots in task space

This work mainly studies the position and attitude tracking control of a free-floating space robot. With the attitude represented in modified Rodrigues parameters (MRPs), a task-space controller with predefined-time stability is developed considering the external disturbance. The tuning parameters of a predefined-time controller can be formulated as functions of the prescribed upper bound of the stabilization time. Based on the backstepping technique and a novel predefined-time stabilizing function, a predefined-time control scheme is designed for the space robot system. Moreover, to avoid ’explosion of terms’, an auxiliary variable is introduced such that the controller is independent of the derivative of the virtual control law. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.     

Predefined-time tracking of nonlinear strict-feedback systems with time-varying output constraints

In this paper, the problem of the predefined-time tracking with time-varying output constraints (TVOC) is investigated for a class of nonlinear strict-feedback systems. First, the sufficient conditions for the studied problem are presented. Then, a recursive design algorithm of the controller is proposed by backstepping technique. A novel stabilizing function is constructed by adding a fractional term, which is capable of decreasing the asymmetric time-varying Barrier Lyapunov Function (BLF) to the origin within any desired settling time. After that, it is shown that under our proposed control, all the closed-loop signals are bounded, and the tracking error converges to zero within any desired settling time and remains zero thereafter without the violation of the output constraint. The settling time in this paper is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will. Finally, two examples are given to illustrate the effectiveness of the proposed method.     

Predefined-time hierarchical controller-estimator time-varying formation-containment tracking for multiple Euler-Lagrange systems with two-layer leaders

This paper mainly discusses the problem of the predefined-time time-varying formation-containment tracking (TVFCT) for the multiple Euler-Lagrange systems (MELSs), where the external disturbances are taken into consideration. To cope with the above problem, a two-layer formation-containment tracking (FCT) framework is established, namely, the real leaders’ formation layer and the followers’ containment layer, where the analysis of the system is executed step by step. Meanwhile, the corresponding hierarchical control algorithms based on nonsingular terminal sliding mode are designed for different layers to facilitate the implementation of the TVFCT control problem. With the help of the Lyapunov function and predefined-time stability theory, some sufficient criteria for the convergence of the proposed algorithms are provided. In the end, the simulation results demonstrate the effectiveness of the theoretical results and the designed controller.     

Practical predefined-time attitude coordination control for multiple rigid spacecraft

This paper investigates the practical predefined-time attitude cooperation control problem for a group of rigid spacecraft under an undirected communication graph. First, since the leader is accessible to only a subset of the group members, a distributed practical predefined-time state observer is proposed to estimate the leader’s states by using a time-varying scaling function. Second, a distributed practical predefined-time attitude coordination controller is designed to guarantee that the attitude tracking errors of all follower spacecraft converge to the neighborhood of the origin within a preset time. Finally, the effectiveness of the proposed control law is demonstrated by illustrative numerical examples.     

Robust motion control of quadrotors

In this paper, the robust motion control problem is investigated for quadrotors. The proposed controller includes two parts: an attitude controller and a position controller. Both the attitude and position controllers include a nominal controller and a robust compensator. The robust compensators are introduced to restrain the influence of uncertainties such as nonlinear dynamics, coupling, parametric uncertainties, and external disturbances in the rotational and translational dynamics. It is proven that the position tracking errors are ultimately bounded and the boundaries can be specified by choosing controller parameters. Experimental results on the quadrotor demonstrate the effectiveness of the robust control method.     

Predictor-based optimal robust guaranteed cost control for uncertain nonlinear systems with completely tracking errors constraint

In this paper, a novel composite controller is proposed to achieve the prescribed performance of completely tracking errors for a class of uncertain nonlinear systems. The proposed controller contains a feedforward controller and a feedback controller. The feedforward controller is constructed by incorporating the prescribed performance function (PPF) and a state predictor into the neural dynamic surface approach to guarantee the transient and steady-state responses of completely tracking errors within prescribed boundaries. Different from the traditional adaptive laws which are commonly updated by the system tracking error, the state predictor uses the prediction error to update the neural network (NN) weights such that a smooth and fast approximation for the unknown nonlinearity can be obtained without incurring high-frequency oscillations. Since the uncertainties existing in the system may influence the prescribed performance of tracking error and the estimation accuracy of NN, an optimal robust guaranteed cost control (ORGCC) is designed as the feedback controller to make the closed-loop system robustly stable and further guarantee that the system cost function is not more than a specified upper bound. The stabilities of the whole closed-loop control system is certified by the Lyapunov theory. Simulation and experimental results based on a servomechanism are conducted to demonstrate the effectiveness of the proposed method.     

Robust output feedback attitude tracking control for rigid-flexible coupling spacecraft

This paper investigates the robust attitude tracking control problem for a rigid-flexible coupling spacecraft. First, the dynamic model for a rigid-flexible coupling spacecraft is established based on the first-order approximation method to fully reveal the coupling effect between rigid movement and flexible displacement when the spacecraft is in rapid maneuver. In the condition that flexible vibration measurements are not available, an robust output feedback controller which is independent of model is presented using Lyapunov method with considering state-independent disturbances. To resolve the chattering problem caused by the discontinuous sign function, a modified continuous output feedback controller is proposed by introducing functions with continuous property. Rigorous proof is achieved showing that the proposed control law ensures asymptotic stability and guarantees the attitude of a rigid-flexible spacecraft to track a time-varying reference attitude based on angle and angular velocity measurements only. Finally, simulations are carried out to verify the simplicity and effectiveness of the proposed control scheme.     

Dual terminal sliding mode control design for rigid robotic manipulator

This paper proposes a dual terminal sliding mode control scheme for tracking tasks of rigid robotic manipulators. As a significant novelty, the presented design technique integrates the individual sliding mode surfaces to achieve the finite time convergence of tracking errors utilizing specially designed construct, and accordingly the convergence time is easily obtained due to the integral design. The underactuated issue and input limitation are specially considered in this paper, i.e., the underactuated issue is solved by introducing the hierarchical methodology into the basic dual sliding mode controller. The proposed method can easily combine with the adaptive technique to eliminate the negative effect caused by the input limitation in the rigorous stability analysis. These newly proposed methods also have the characteristics of nonsingularity and chattering suppression, and the effectiveness and high efficiency are verified by stabilizing the motions of the overhead crane and the tracking tasks of the rigid robotic manipulator. Simulation results validate the theoretical analyses about the proposed method.     

Robust trajectory tracking control of non-holonomic wheeled mobile robots using an adaptive fractional order parallel fuzzy PID controller

Non-holonomic wheeled mobile robots (WMRs) are highly uncertain, multi-input multi-output (MIMO), non-linear dynamic systems that are expected to perform under varying environment and structural reservations. An Adaptive Fractional Order Parallel Fuzzy Proportional-Integral-Derivative (AFO?PFPID) controller is proposed and investigated on WMR to meet the above challenges. Computer simulations were carried out under the effects of dynamic parameter variations, noise, forced displacement, time delay, and uncertainty in the pose to thoroughly assess the controller's performance. Further, to evaluate its relative assessment, the AFO?PFPID controller's performance is compared with its integer counterpart Adaptive Integer Order Parallel Fuzzy Proportional-Integral-Derivative (AIO?PFPID) controller. Both the controllers were tuned with the Multi-Objective Grey Wolf Optimization Algorithm to minimize the positional and velocity profile errors with an overall goal to attain effective trajectory tracking. Though both the controllers effectively performed tracking goals, the AFO?PFPID controller has offered a significantly robust performance even under the model uncertainties and disturbances. Therefore, based on the presented investigations, it is concluded that the AFO?PFPID controller is a superior control technique for non-holonomic WMRs trajectory tracking application.     

Leader-following rendezvous for uncertain Euler–Lagrange multi-agent systems by output feedback

In this paper, we investigate the problem of output feedback tracking for a class of Euler–Lagrange multi-agent systems with unmeasurable velocity and input disturbances. By proposing a novel dynamic velocity observer, an adaptive output feedback consensus algorithm is proposed such that the tracking errors of all agents can converge to an arbitrarily small neighborhood of zero by tuning the design parameters. A numerical example is presented to illustrate the effectiveness of the controller.     

Three-dimensional predefined-time impact angle control guidance law with field-of-view limit

In this paper, an impact angle control guidance (IACG) law with predefined convergence time and seeker’s field-of-view (FOV) limit is proposed in three-dimensional (3D) scenario. First, a predefined-time error dynamic is developed whose significance is revealed by comparison with conventional methods. Second, based on coupled engagement dynamics, a 3D predefined-time IACG law is derived by applying the proposed error dynamic. To tackle the FOV limit, two auxiliary functions are introduced into the IACG law. The robustness against disturbances and uncertainties is further improved by utilizing the terminal sliding mode technique. With the proposed guidance law, the impact-angle error can converge to zero exactly at a tunable predefined time. Finally, the effectiveness and performance of the proposed IACG law are shown by several simulations with comparative study.     

High dynamic adaptive robust control of load emulator with output feedback signal

This paper is concerned with the high performance adaptive robust control problem for an aircraft load emulator (LE). High dynamic capability is a key performance index of load emulator. However, physical load emulators exist a lot of nonlinearities and modeling uncertainties, which are the main obstacles for achieving high performance of load emulator. To handle the modeling uncertainty and achieve adjustable model-based compensation, firstly, the mathematical model of the load emulator is built, and then a nonlinear adaptive robust controller only with output feedback signal is proposed to improve the tracking accuracy and dynamic response capability. The controller is constructed based on the adaptive robust control framework with necessary design modifications required to accommodate uncertainties and nonlinearities of hydraulic load emulator. In this approach, nonlinearities are canceled by output feedback signal; and modeling errors, including parametric uncertainties and uncertain nonlinearities, are dealt with adaptive control and robust control respectively. The resulting controller guarantees a prescribed disturbance attenuation capability in general while achieving asymptotic output tracking in the absence of time-varying uncertainties. Experimental results are obtained to verify the high performance nature of the proposed control strategy, especially the high dynamic capability.     

串级型迭代学习交叉耦合轮廓误差控制方法

针对两轴伺服系统的研究轮廓误差控制问题,提出了一种串级型迭代学习交叉耦合轮廓误差控制方法,设计了控制器结构并且给出了两轴迭代学习交叉耦合控制算法的收敛条件.仿真结果表明此方法可以实现跟踪误差和轮廓误差的有效补偿.     

Data-driven iterative feedforward control with rational parametrization: Achieving optimality for varying tasks

In precision motion systems, well-designed feedforward control can effectively compensate for the reference-induced error. This paper aims to develop a novel data-driven iterative feedforward control approach for precision motion systems that execute varying reference tasks. The feedforward controller is parameterized with the rational basis functions, and the optimal parameters are sought to be solved through minimizing the tracking error. The key difficulty associated with the rational parametrization lies in the non-convexity of the parameter optimization problem. Hence, a new iterative parameter optimization algorithm is proposed such that the controller parameters can be optimally solved based on measured data only in each task irrespective of reference variations. Two simulation cases are presented to illustrate the enhanced performance of the proposed approach for varying tasks compared to pre-existing results.     

Robust hierarchical control of a laboratory helicopter

This paper deals with the robust position control problem for a three degree-of-freedom (3DOF) laboratory helicopter. The 3DOF helicopter system is a nonlinear multiple-input multiple-output (MIMO) uncertain system, and has the elevation, pitch, and travel angles. The proposed robust controller is a hierarchical controller including an attitude controller and a position controller. The position controller generates the desired reference of the pitch angle based on the tracking error of the travel angle, while the attitude controller achieves the reference tracking of the pitch and elevation angles. It is proven that the tracking errors of the three angles can converge into the given neighborhoods ultimately. Experimental results on the laboratory helicopter demonstrate the effectiveness of the proposed hierarchical control strategy.     

Combined Observer-Controller Synthesis for Electro-Hydraulic Servo System with Modeling Uncertainties and Partial State Feedback

Modeling uncertainties including parameter uncertainty and unmodeled dynamics hinder the development of high-performance tracking controller for hydraulic servo system. The observation for the unknown state is another issue worthy of attention. In this paper, a new seamless observer-controller scheme for hydraulic servo system is proposed with partial feedback. The position signal and the pressure signal are firstly used to build an extended structure estimation system for the unknown state. The advantage of this estimation system is that the state observer provides an extended structure for the parameter adaptation compared to other state observers. Thus the parameter uncertainty can be handled. An adaptive robust controller is synthesized in this paper which includes the adaptive part and the robust part. The adaptive part is used to eliminate the parameter uncertainty. Then the residuals coming from the parameter adaption and the errors coming from the state observation are taken into consideration in the robust part. Moreover, the unmodeled dynamics is also handled by the robust part. Theoretical analysis proves that a prescribed transient performance and the final tracking accuracy can be guaranteed by the proposed observer-controller scheme in the presence of both parameter uncertainty and unmodeled dynamics. Furthermore, the convergence of the closed-loop controller-observer system is achieved with the parametric uncertainty existed only. Extensive comparative experiments performed on a hydraulic actuator demonstrate the effectiveness of the proposed observer-controller scheme.     

Finite-time cooperative circumnavigation control of multiple second-order agents with desired formations

This paper investigates the finite-time cooperative circumnavigation control of multiple second-order agents, in which the agents should surround a moving target with desired formation and circular velocity based on local information. Firstly, the controller design is transformed into design control parameters such that the error system, including distance error, speed error and angle error, is finite-time consensus. The error system is viewed as a cascaded system containing two second-order subsystems, and then a distributed finite-time controller composed of two parts is delivered. The finite-time stability of the entire system is given by employing cascaded control theory. One significant advantage of the proposed controller is that it allows the agents to converge to desired trajectory in a finite time instead of asymptotically. Another merit is that the desired formation is an extensive case and unlimited, including different tracking radii and angular spacing. Furthermore, the proposed controller can be implemented by each agent in its local frame, utilizing only local information. These properties significantly extend the application scope of cooperative circumnavigation. Finally, simulations are carried out to validate the effectiveness of the proposed method.     

Finite-time unknown observer based coordinated path-following control of unmanned underwater vehicles

In this paper, a coordinated path-following control (CPFC) scheme is proposed for multiple unmanned underwater vehicles (UUVs) under undirected communication links. Each UUV is subject to complex unknowns involving model parameter perturbations and time-varying external disturbances. In light of individual path-following control, the coordinated guidance laws are developed to guide UUV surge velocities and yaw velocities, simultaneously. By virtue of graph theory, the neighbor information based path update laws are further employed to achieve synchronized tracking. Within the kinetics controller design, a finite-time unknown observer (FTUO) is utilized to assist in cancelling the lumped unknowns within a short time. Additionally, the FTUO-based distributed robust controllers are developed for UUVs and guarantee the guidance velocity signals generated by coordinated guidance can be successfully tracked. Strict stability analysis is proved in the sense of Lyapunov. Finally, simulation results and comparisons substantiate the efficacy and superiority of the developed CPFC scheme.     

Design of a H∞ model reference tracking control for interconnected nonlinear systems by decentralized dynamic output-feedback

This study investigates the problem of robust tracking control for interconnected nonlinear systems affected by uncertainties and external disturbances. The designed H_∞ dynamic output-feedback model reference tracking controller is parameterized in terms of linear matrix inequalities (LMIs), which is formulated within a convex optimization problem readily implementable. The resolution of such a problem, guarantying not only the quadratic stability but also a prescribed performance level of the resulting closed-loop system, enables to calculate concurrently the robust decentralized control and observation gain matrices. The established LMI conditions are computed in a single-step resolution to obtain all the controller/observer parameters and therefore to overcome the problem of iterative algorithm based on a multi-stage resolution leading in most cases to conservative and suboptimal solutions. Numerical simulations on diverse applications ranging from a numerical academic example to coupled inverted double pendulums and a 3-strongly interconnected machine power system are provided to corroborate the merit of the proposed control scheme.     

A case study on the universal compensation-improvement mechanism: A robust PID filter-shaped optimal PI tracker for systems with/without disturbances

Many dynamical systems are continuous-time non-square with unknown mismatched input and output disturbances. For such systems, a universal on-line robust optimal tracking control is often desirable. In this paper, the conventional proportional-integral-differential (PID) controller is utilized as a fictitious PID filter to shape the tracking error in the frequency-domain using a quadratic performance index as a weighting function, such that the robust PID-shaped PI tracker integrated with the equivalent input disturbance (EID) estimator is established to carry out the on-line robust optimal tracking control of the general disturbed system. The benefits and discrepancies of the proposed compensation improvement mechanism over the conventional optimal trackers for continuous-time non-square systems with/without unknown mismatched input and output disturbances are listed as follows: (i) It develops a new net EID estimator without any previously established constraints on the dimensions of the system and on the disturbances; (ii) It provides an efficient estimated-state-feedback-based EID estimator in contrast to the conventional output-feedback-based EID estimators; (iii) It is able to carry out on-line EID estimation of the tracking errors for systems with endogenous/exogenous output disturbances; (iv) It is a universal tracker which can be simply implemented as a plug-in EID estimator for most servo systems, to improve the performance of any existing observers/trackers which are not allowed to be removed from the system. The advantages of the proposed method over two existing outstanding approaches reported in the literature are pointed out using illustrative examples.