Self-excited periodic motion in underactuated mechanical systems using two-fuzzy inference system

An open loop vibrational control for underactuated mechanical systems with amplitude and frequency modulation is investigated. Since there is no direct external input to an unactuated joint, the dynamic coupling between the actuated and unactuated joint is utilized for controlling the unactuated joint. Feedback linearization has been performed to incorporate fully the known nonlinearities of the underactuated system considered. The actuated joints are firstly positioned to their desired locations, and then periodic oscillatory inputs are applied to the actuated joints to move the remaining unactuated joints to their target positions. The amplitudes and frequencies of the vibrations introduced are determined through the averaging analysis. A systematic way of obtaining an averaged system for the underactuated system via a coordinate transformation is developed. A manipulator in the space where no gravitation exists can be vibrationally controlled in the event of actuator failure. A control design example of a 2R planar manipulator with a free joint with no brake is provided.

Underactuated systems are mechanical systems with fewer actuators than the system degrees of freedom, i.e., some degrees of freedom are not directly driven by actuators. Many benchmark underactuated systems have been developed to study the nature of underactuated dynamics and their possible controller designs. Unlike fully actuated systems where many control strategies are available for an entire class of systems, there are few results applicable to even a small class of underactuated mechanical systems. In this paper, an Adaptive Fuzzy Sliding Mode Controller (AFSMC) is proposed in order to stabilize an inverted pendulum mounted on a ball system, also known as ballbot; this latter an interesting underactuated mechanical system for which the controller designs are a pending task, i.e. the performance for different control strategies could be explored. The performance of our proposal is verified via numerical simulation, showing the robustness against time-varying uncertainties and disturbances.

Underactuated mechanical systems are frequently encountered in several industrial and real-world applications such as robotic manipulators with elastic components, aerospace vehicles, marine vessels, and overhead container cranes. The design of accurate controllers for this kind of mechanical system can become very challenging, especially if a high level of uncertainty is involved. In this paper, an adaptive fuzzy inference system is combined with a sliding mode controller in order to enhance the control performance of uncertain underactuated mechanical systems. The proposed scheme can deal with a large class of multiple-input–multiple-output underactuated systems subject to parameter uncertainties, unmodeled dynamics, and external disturbances. The convergence properties of the resulting intelligent controller are proved by means of a Lyapunov-like stability analysis. Experimental results obtained with an overhead container crane demonstrate not only the feasibility of the proposed scheme, but also its improved efficacy for both stabilization and trajectory tracking problems.

In this paper we use a nonholonomic affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. The class of nonholonomic systems we study in this paper includes, in particular, wheeled-type vehicles, which are important for many robotic locomotion systems. We illustrate our ideas by considering a simple example on a three-dimensional manifold

Due to lack of enough control inputs for system degrees of freedom, the underactuated system is always a challenging problem in the field of control application. For this reason, a growing interest is arising about the design of automatic control systems for underactuated system. In this paper, to achieve the robustness of the system, a new coupling control scheme is applied to obtain a globally asymptotically stable resat parameters for a class of underactuated mechanic system. By utilizing a Lyapunov-based stability analysis, we can achieve asymptotic tracking of desired reference signal which is subject to both underactuation and parametric uncertainties. To demonstrate the effectiveness of the proposed controller, results are applied to the Furuta pendulum system and a planar flexible joint robot.

In this work, first we estimate all the system’s state vector, with guarantied precision, for a category of second order underactuated mechanical systems (UMS), exploiting the triangular observer (TO) model that suits to the structure of these systems. Then we propose a sliding mode controller (SMC). The latter uses the estimated states given by the observer. The underactuated system is decomposed into two subsystems, where the sliding surface is constructed in two levels for each subsystem. The proposed controller guaranties the tracking performances, with minimization of chattering phenomenon, due to the constructed observer, even for system with uncertainties. Simulation results show the effectiveness of this strategy of control.

Model-Following Control of Nonlinear Systems based on Virtual Constraints

Sliding mode control has been shown to be a robust and effective control approach for stabilization of nonlinear systems. However the dynamic performance of the controller is a complex function of the system parameters, which is often uncertain or partially known. This paper presents an adaptive fuzzy sliding mode control for a class of underactuated nonlinear mechanical systems. An adaptive fuzzy system is used to approximate the uncertain parts of the underactuated system. The adaptive law is designed based on the Lyapunov method. The proof for the stability and the convergence of the system is presented. Robust performance of the adaptive fuzzy sliding mode control is illustrated using a gantry crane system. Simulation results demonstrate that the system output can track the reference signal in the presence of modelling uncertainties, external disturbances and parameter variation.

In this paper, we introduce a new approach in generating a periodic motion for underactuated mechanical systems using continuous sliding-mode (SM) algorithms as a feedback loop, particularly with super-twisting algorithm and Power-Fractional Sliding-Modes (PFSM), without computing a reference trajectory. Periodic solutions of the closed-loop system are found by mean of the describing function method which allows to tune the amplitude and frequency of the oscillations via corresponding gain parameters. Performance issue of a self-excited system, applied to 3-DOF underactuated robot, is illustrated by simulations.

Stabilization of underactuated mechanical systems is one of the fundamental benchmark problem in the field of control theory. In this article, a hierarchical sliding mode control based on state-dependent switching gain is proposed for stabilization of underactuated mechanical systems. This controller is based on the so called first-level and second-level sliding surfaces. The asymptotic stability of these surfaces is proved by the Lyapunov stability theory. The proposed control technique is applied to two nonlinear underactuated mechanical systems and its feasibility is verified by numerical simulation. The proposed controller efficiently tackles the bounded external disturbance and shows robust performance. The convergence rate of the proposed controller is much faster as compared with the conventional decoupled sliding mode control and the integral sliding mode control.

ABSTRACTRobust control of under-actuated mechanical systems (UMSs) with model uncertainty is still a challenging problem. For UMSs, the model parametric uncertainties make it difficult to precisely calculate the isolated equilibrium point corresponding to a fixed input. Without an accurate destination state, many set-point control methods cannot eliminate the positioning errors. An improved sliding mode control (ISMC) method is proposed to solve the robust control problem for a class of UMSs with model uncertainty and input disturbance. A balance variable is introduced in the sliding surface design to compensate for the disturbance caused by the inaccurate destination state, and the ISMC method is proposed to make the system state reach the sliding surface in finite time. Linear matrix inequality approach and particle swarm optimisation algorithm are applied to design the sliding mode surface parameters. The simulation results on an UMS are presented to show the effectiveness of the proposed scheme.

It is shown that the flat output of the single input underactuated mechanical system can be obtained by finding a smooth output function such that the system has relative degree equals to the dimension of the state space. Assuming the flat output of an underactuated system can be solved explicitly, an optimization method is proposed for the motion planning of the differentially flat underactuated mechanical systems by constructing a shape adjustable curve with satisfying specific boundary conditions in flat output space. The inertia wheel pendulum is used to verify the proposed optimization method and some numerical simulation results are included.

Distributed Control of Heterogeneous Underactuated Mechanical Systems

This paper presents an approach to show global controllability of a class of underactuated mechanical systems. This class of systems include gymnastic robots and the classic cart-pole system. For this class of systems, we can define a connection point, and design a damping controller u(t) with the Lyapunov method to drive all states to the connection point. Further by exploiting the time reversal symmetry of the system and spline interpolation, a controller u(-t) can be obtained to drive the system from the connection point to any other state. The system is thus shown completely controllable, i.e., there exists an admissible trajectory from any given state to any given final state. Swing-up control designs for a pendubot, cart-pole system and triple pendulum are given as illustrative examples.

This paper investigates a Takagi-Sugeno fuzzy descriptor approach for designing a input delay controller for a rotary inverted pendulum. The rotary inverted pendulum, under-actuated system, is considered a benchmark for verifying the performance of linear or nonlinear control laws in control system theory because this system has nonlinearities, such as gravity and centripetal force. The Takagi-Sugeno fuzzy modeling technique transformed the rotary inverted pendulum system into several local linear models, and a parallel distributed compensation (PDC) based fuzzy controller was designed. By constructing suitable Lyapunov-Krasovskii functionals and utilizing some mathematical techniques, a stabilization criterion for a T-S fuzzy system with input delay was derived in linear matrix inequalities. Finally, the designed controller was experimented on the ‘Quanser SRV-02’ platform compared to the linear controller designed using LMI Toolbox of MATLAB under the same conditions.