Class Of Underactuated Systems Research Articles

Attitude optimization by extremum seeking for rigid bodies actuated by internal rotors only

SummaryIn this paper, we investigate the stabilizing effect of an extremum seeking control law on a class of underactuated Lagrangian control systems with symmetry. Our study is motivated by the problem of attitude optimization for satellites with reaction wheels. The goal is to minimize the value of an analytically unknown configuration‐dependent objective function without being reliant on measurements of the current configuration and velocity. This work extends our previous work on extremum seeking control for fully actuated mechanical systems on Lie groups in the absence of dissipation. We show that the earlier method for fully actuated systems can also be successfully applied to a certain class of underactuated systems, which are controlled by internal momentum exchange devices (reaction wheels) so that the total momentum is conserved. Conservation of momentum allows us to reduce the control system to a system on a smaller state manifold. The reduced control system is not of Lagrangian form but fully actuated. For the reduced control system we prove that the extremum seeking method leads to practical uniform asymptotic stability. We illustrate our findings by the example of a rigid body with internal rotors.

Backstepping control for a class of underactuated nonlinear mechanical systems with a novel coordinate transformation in the discrete-time setting

In this technical note, a combined discrete-time controller, consisting of a partial feedback linearization controller and a backstepping controller, is proposed to manage the stabilization for a class of underactuated nonlinear mechanical systems. The traditional backstepping control method is impracticable to directly apply it to underactuated systems since they are generally not in the lower triangular form. First, a feedback controller that partially linearizes the underactuated mechanical systems is derived to facilitate the backstepping controller design. In the design, discrete-time system dynamics obtained utilizing the Euler approximation are considered. Afterward, a novel coordinate transformation is introduced for a class of underactuated systems that transform the mathematical model of the partially linearized underactuated mechanical systems into the strict-feedback form. After these steps, the conventional backstepping approach is structured in discrete-time setting. The stability of the closed-loop system dynamics with the proposed combined discrete-time controller is shown utilizing Lyapunov theory. Several computer-based simulations are executed to depict the performance and the applicability of the proposed method on the Cart–Pole system and the Inertia Wheel Pendulum. Moreover, the effectiveness of the proposed nonlinear controller is verified by numerical simulation results in comparison with a discrete-time chattering-free sliding-mode controller.

Sliding mode control based on RBF neural network for a class of underactuated systems with unknown sensor and actuator faults

ABSTRACT A sliding mode control method is developed in this study for application to a class of underactuated systems with bounded unknown disturbance and sensor and actuator faults. In the proposed method, a robustness item compensates for the bounded unknown disturbance and a Nussbaum function realises sensor and actuator faults tolerance simultaneously, and all signals of the system are proven to be bounded. A radial basis function (RBF) neural network is developed to estimate the unknown functions of the system. Finally, Hurwitz stability analysis is conducted to guarantee the stability of the closed-loop system. Simulations are conducted wherein a coupled motor driving system is placed under the proposed control laws to validate this approach.

Cascade Delayed Controller Design for a Class of Underactuated Systems

In this paper, a delayed control strategy for a class of nonlinear underactuated fourth-order systems is developed. The proposal is based on the implementation of the tangent linearization technique, differential flatness, and a study of the σ-stabilization of the characteristic equation of the closed-loop system. The tangent linearization technique allows obtaining a local controllability property for the analyzed class of systems. Also, it can reduce the complexity of the global control design, through the use of a cascade connection of two second-order controllers instead of designing a global controller of the fourth-order system. The stabilizing behavior of the delayed controller design is supported by the σ-stability criterion, which provides the controller parameter selection to reach the maximum exponential decay rate on the system response. To illustrate the efficiency of the theoretical results, the proposal is experimentally assessed in two cases of study: a flexible joint system and a pendubot.

Nonlinear Motion Control of Complicated Dual Rotary Crane Systems Without Velocity Feedback: Design, Analysis, and Hardware Experiments

As a class of underactuated systems, cooperative dual rotary crane systems (DRCSs) are widely used to complete the task of large payload transportation in complex environments, since the working capacity of single cranes is quite limited. However, the control issues of DRCS fail to receive enough attention at present. Compared with single cranes, DRCSs contain more state variables, geometric constraints, and coupling relationships. Therefore, the complex kinematic and dynamic characteristics make controller design/stability analysis very challenging for DRCS. In order to solve these problems, based on the dynamic model of DRCS established by Lagrange’s method, an output feedback control method with consideration for actuator constraints is designed to realize accurate dual boom positioning and rapid elimination of payload swings. The stability of the equilibrium point for the closed-loop system is analyzed by using Lyapunov techniques and LaSalle’s invariance principle. To the best of our knowledge, this article yields the first solution for effective control of DRCS, which needs no velocity feedback, respects the actuator constraints, and is designed and analyzed without linearizing the complicated nonlinear dynamic equations. Finally, a series of hardware experiments on a self-built experimental platform is carried out to illustrate the effectiveness of the proposed controller. Note to Practitioners —This article is motivated by the control problem of dual rotary boom crane systems. In order to meet industrial requirements, the masses and volumes of to-be-hoisted cargoes are larger than before, and consequently, dual-crane systems are more frequently needed to fulfill transportation tasks. For such systems, although they improve the load capacity, greater challenges are caused when eliminating cargo swings in the transportation process. To the best of our knowledge, current control methods are mainly designed based on linearized/reduced models, whose performance may be not satisfactory when swing angles are large. Moreover, most methods use velocity signals with unexpected noises and ignore the constraints of actuators’ amplitudes, which may not be feasible in practical applications. To solve these problems, this article presents an output feedback controller, which can simultaneously solve the problems of saturation constraints and velocity signal unavailability. The proposed controller can guarantee accurate boom positioning and cargo swing elimination with guaranteed theoretical proof. Furthermore, the control performance is verified experimentally on a self-built testbed. In future efforts, we intend to apply the presented control method to industrial applications.

Approximate Linearization of a Class of Underactuated System and its Application in the Ball and Beam System

In this paper, we consider the dynamical model of a class of underactuated systems. By combination of the partial fedback linearization and Yamada’s global linearization, we deduced a global approximate linearization method for underactuated systems. By using this method, the dynamical equations can be transformed into an state eqution that is expressed as a pseudolinear term with Brunovsky canonical form plus a high order nonlinear term, where the nonlinear term is high order on the equilibrium manifold of the system. By standard nonlinear feedback method, the system is transformed into the sum of a stable linear term and a high order nonlinear term. Take proper feedforward value as the input to reduce the influence of the nonlinear term to the system and thus the underactuated system can be regulated. This method is applied to the ball and beam system and simulation results show that the proposed approximate linearization method is effective for setpoint control.

Neuro-Fuzzy Sliding Mode Control of Inverted Pendulum

In this paper we develop a robust controller based on sliding mode, neural network and fuzzy logic for the control of a class of under-actuated systems. The stability of the proposed controller is proved with the Lyapunov function method. Simulation results are made on an inverted pendulum.

Sliding mode control for an underactuated slosh-container system using non-linear model

This work mainly deals with the sliding mode control for non-linear model of sloshing liquid in a container. Slosh coupled with container dynamics represents a class of underactuated systems with coupled non-linear equations. A pendulum model is used to model the lateral slosh. A linear sliding surface-based sliding mode control is derived. The reduced order system equation during sliding mode becomes non-linear when the non-linear system is constrained to the linear surface. Here a new method is proposed for the stability analysis of the reduced order non-linear system using Lyapunov stability theory. Simulations are carried out to validate the method. Experimental work is carried out to implement the designed sliding mode control strategy on the slosh-container system and corresponding results are also reported.

Adaptive Backstepping Control for Uncertain Underactuated Systems with Input Constraints

Considering a class of underactuated systems with functional uncertainties, an adaptive backstepping controller is presented. By applying backstepping control strategy and online approximation of uncertainties with wavelet networks, the desired tracking performance in presence of actuator constraints is assured. Singularity due to adaptation is tackled by incorporating a switching scheme. Proposed controller guarantees the ultimate upper boundedness of all closed loop signals. Effectiveness of proposed scheme is illustrated through simulation.

Sliding mode control for slosh-free motion-A class of underactuated system

Underactuated systems are the representative of a large class of systems. This paper presents a new method for the design of sliding surface for a class of second order underactuated system in which a virtual input is considered in unactuated subsystem. A sliding mode controller is proposed to ensure sliding along the sliding surface. A problem of slosh free-motion of a container is considered as representative of a typical class of underactuated system. A simple pendulum model is considered to represent the lateral slosh. Extensive simulation studies are conducted with the controller to demonstrate the proposed approach.

Improving the Performance of Orbitally-Stabilizing Controls for the Furuta Pendulum

This paper presents an approach to compute suboptimal nonlinear H∞ controls for orbital stabilization of a certain class of underactuated systems. The control objective is to locally asymptotically stabilize the system around a predefined target orbit with a certain degree of L2-Gain disturbance attenuation. Additionally, to solve the Hamilton-Jacobi-Bellman equation (HJBE) arising in the nonlinear H∞ framework, an approximate solution is provided, based on a Galerkin-like approximation scheme. In particular, the methodology is applied to the well-known Furuta Pendulum system and simulation results are shown

Steering a class of redundant mechanisms through end-effector generalized forces

A particular class of underactuated systems is obtained by considering kinematically redundant manipulators for which all joints are passive and the only available inputs are forces/torques acting on the end-effector. Under the assumption that the degree of redundancy is provided by prismatic joints located at the base, we address the problem of steering the robot between two arbitrary equilibrium configurations. By performing a preliminary partial feedback linearization, the dynamic equations take a convenient triangular form, which is further simplified under additional hypotheses. We give sufficient conditions for controllability of this kind of mechanisms. With a PPR robot as a case study, an algorithm is proposed for computing end-effector commands that produce the desired reconfiguration in finite time. Simulation results and a discussion on possible generalizations are given.