Fully-actuated Systems Research Articles

Robust control of uncertain fully actuated systems with nonlinear uncertainties and perturbed input matrices

Robust control of uncertain fully actuated systems (FASs) with nonlinear uncertainties and perturbed input matrices is considered. Motivated by the recent work on this issue, two novel robust controllers are further developed for two cases under different assumptions. For both cases, the assumption on the perturbation input matrix in the previous work is relaxed to a significant extent, which allows many typical perturbation input matrices, such as constant ones, to be handled, while the previous method cannot. Moreover, for the first case, the assumption on the system uncertainty is further relaxed, and the states of the closed-loop system are globally bounded and converge into an arbitrarily small spherical domain centered at the origin. For the second case, with another requirement on the system nonlinearity imposed, the global exponential stability of the closed-loop system is achieved. The successful application in an electromechanical system verifies the effectiveness of the method.

A fully actuated system approach: Desired compensation adaptive robust control for uncertain nonlinear systems

A desired compensation adaptive robust control (DCARC) framework is presented for two types of fully actuated systems (FASs) subject to both parametric and nonlinear uncertainties based on the Lyapunov theory. The designed controller consists of three parts: (i) a fundamental linear state error feedback term; (ii) an adaptive feedforward compensation term; (iii) a robust compensation term. Different from the existing FAS approaches, the adaptive compensation in the proposed controller relies on the noise-free desired trajectory and online parameter estimate only. A better overall tracking performance with an accelerated transient response is expected, arising from significantly reducing interaction between the robustness part and the adaptation part. Through theoretical analysis, the proposed controller ensures that the estimation error of the unknown parameter vector and the tracking error finally converge to a bounded ellipsoid. The comparative simulation of a permanent magnet (PM) stepper motor demonstrates the effectiveness of the presented approach.

Controllability and control for discrete periodic systems based on fully-actuated system approach

The problem of controllability and control of linear discrete-periodic systems is investigated in this paper. The high-order fully-actuated models for linear discrete periodic time-varying systems are constructed, and a controllability criterion based on fully-actuated system models is proposed. On this basis, stabilization as the fundamental issue is studied and periodic state-feedback control laws are designed via fully-actuated systems approach and parametric design, which converted the original problem into the pole assignment problem for linear constant systems. Finally, a numerical example is given to verify the validity and feasibility of the proposed method.

An active fault tolerance framework for uncertain nonlinear high-order fully-actuated systems

This paper presents a novel active fault tolerance framework for uncertain high-order fully-actuated systems (HOFASs). Starting from the uncertain faulty HOFAS model with nonlinear measurement, the advantages of this description are revealed via Lie Derivatives. A HOFAS adaptive observer and controller integration is established and further a closed-loop HOFAS dynamic data modeling structure is derived. This structure uncovers the dynamic characteristics including fault features, and naturally yields a fault detectability condition. Based on the fault information from the dynamic data model, an active fault tolerant control strategy for HOFASs is proposed, which enriches HOFAS control theory. The uniformly bounded stability of the HOFAS model is proved theoretically and illustrated experimentally.

Fault-tolerant tracking control for nonlinear observer-extended high-order fully-actuated systems

In the paper, a fault-tolerant tracking control strategy is proposed for a class of nonlinear high-order fully-actuated systems (HOFASs) with multiplicative and additive actuator faults. Different from general state space methods, HOFAS approaches can achieve global stability through specific nonlinear control laws, and maintain the fully-actuated and uncoupled characteristics of most physical objects. Starting from the HOFAS tracking error dynamics, a tracking differentiator is designed to solve the reference signal and its derivatives numerically. Furthermore, a specific extended state observer is firstly embedded into the HOFAS, which expands the application scenarios of the HOFAS theory. Based on Lyapunov stability theory, a fully-actuated fault-tolerant control technique is presented to ensure the uniformly ultimately bounded stability of the tracking error. A numerical comparative experiment fully illustrates the effectiveness of the proposed strategy.

Adaptive fault-tolerant control for nonlinear high-order fully-actuated systems

In this paper, an adaptive fault-tolerant control (FTC) strategy is proposed for a class of high-order fully-actuated (HOFA) systems. A pre-closed-loop treatment is presented to simplify the observer design for the nonlinear system with actuator faults but it leads to a new problem that faults may not satisfy the observation matching conditions. Thus, an intermediate variable observer is introduced to adaptively estimate system states and actuator faults simultaneously. Then the influence of observation errors on system stability is analyzed by analyzing matrix singular value perturbation. Under the proposed adaptive FTC method, the closed-loop global uniformly ultimately bounded stability is achieved by Lyapunov synthesis. Finally, the effectiveness of the proposed FTC method is verified by simulations.

INVERTED PENDULUM WITH LINEAR SYNCHRONOUS MOTOR SWING UP USING BOUNDARY VALUE PROBLEM

Research in the field of underactuated systems shows that control algorithms which take the natural dynamics of the system’s underactuated part into account are more energy-efficient than those utilizing fully-actuated systems. The purpose of this paper to apply the two-degrees-of-freedom (feedforward/feedback) control structure to design a swing-up manoeuver that involves tracking the desired trajectories so as to achieve and maintain the unstable equilibrium position of the pendulum on the cart system. The desired trajectories are obtained by solving the boundary value problem of the internal system dynamics, while the optimal state-feedback controller ensures that the desired trajectory is tracked with minimal deviations. The proposed algorithm is verified on the simulation model of the available laboratory model actuated by a linear synchronous motor, and the resulting program implementation is used to enhance the custom Simulink library Inverted Pendula Modeling and Control, developed by the authors of this paper.

Optimal structured static state-feedback control design with limited model information for fully-actuated systems

We introduce the family of limited model information control design methods, which construct controllers by accessing the plant’s model in a constrained way, according to a given design graph. We investigate the closed-loop performance achievable by such control design methods for fully-actuated discrete-time linear time-invariant systems, under a separable quadratic cost. We restrict our study to control design methods which produce structured static state feedback controllers, where each subcontroller can at least access the state measurements of those subsystems that affect its corresponding subsystem. We compute the optimal control design strategy (in terms of the competitive ratio and domination metrics) when the control designer has access to the local model information and the global interconnection structure of the plant-to-be-controlled. Finally, we study the trade-off between the amount of model information exploited by a control design method and the best closed-loop performance (in terms of the competitive ratio) of controllers it can produce.

Control of Manipulators with some Unactuated Joints

A mobile-based robot, a robot with an actuator failure, a manipulator with structural flexibility, and robots grasping an articulated object are systems with unactuated or "passive" joints. The dynamics and control of these robot systems is more complex than fully-actuated systems because unactuated joints may lead to uncontrollability. Based on a recursive formulation of the inverse dynamics for manipulators with some unactuated joints, control laws are developed for joint space control and task space control. Important in the task space control law for underactuated systems is the inversion of the generalized Jacobian. Spatial operator algebra techniques are used to develop computationally efficient algorithms for the inverse generalized Jacobian and the control laws.