Class Of Underactuated Mechanical Systems Research Articles

Enhanced free reaching phase SMC for UMS

In this paper, a new design method for sliding mode control (SMC) is presented for nonlinear underactuated mechanical systems. The aim is to eliminate the reaching phase in SMC and avoid the chattering phenomenon while achieving fast and robust tracking for a class of underactuated mechanical systems (UMS). An alternative method is presented to express the sliding domain equations by incorporating tracking errors. The fundamental concept behind the suggested control scheme is to adjust the tracking errors, enabling the system response to commence on the sliding surface regardless of the initial conditions. This modification guarantees the elimination of the reaching phase, avoiding the chattering phenomenon, and ensuring that the tracking error converges to zero. The stability analysis of the proposed approach is conducted using the Lyapunov method. Through numerical simulations, the validity of the approach is confirmed by implementing the control scheme on a crane system. Subsequently, the performance of the proposed approach is compared with other control methods, emphasizing its effectiveness in handling uncertainties. This comparative analysis aims to emphasize the advantages and efficiency of the proposed control strategy over alternative methods, in particular, to address uncertainties and achieve the desired control objectives.

Online Trajectory Planning Control for a Class of Underactuated Mechanical Systems

Efficient control of underactuated systems has always been a great challenge, since one has to stabilize both actuated and unactuated states with fewer control inputs. During the past decades, great efforts have been devoted to improving the transient performance and robustness of the system, which are very crucial in plenty of application scenarios. To motivate corresponding research, an online trajectory planning method is proposed for a class of underactuated mechanical systems in this paper. Specifically, reference trajectories are first generated for actuated states. Based on that, appropriate online adjustments are made to these reference trajectories, so as to realize efficient stabilization of the unactuated states. Different from traditional off-line planning methods, the proposed one utilizes real-time feedback to counteract various unfavorable conditions, which endows it stronger robustness and better transient performance. Rigorous Lyapunov-based analysis is performed to show that the closed-loop system is asymptotically stable around the desired equilibrium point. Finally, the proposed method is applied to two underactuated mechanical systems, with simulation/experiment results provided to demonstrate its superior performance.

Integral IDA-PBC of Underactuated Mechanical Systems with Actuator Dynamics and Uncertain Coupling

This work investigates the passivity-based control of a class of underactuated mechanical systems with first-order actuator dynamics and constant but uncertain coupling. The main contribution is a new dynamic extension of the interconnection-and-damping-assignment passivity-based control methodology that compensates for the effect of the model uncertainty. The effectiveness of the controller is demonstrated with numerical simulations on a ball-on-beam system.

Integral passivity‐based control of underactuated mechanical systems with actuator dynamics and constant disturbances

AbstractThis work investigates the energy shaping control of a class of underactuated mechanical systems with first‐order actuator dynamics and subject to both matched and unmatched constant additive disturbances. To this end, a new nonlinear control law which includes two independent integral actions is presented. The controller design is outlined for systems with first‐order actuator dynamics, and also for systems with direct actuation. The effectiveness of the proposed approach is demonstrated with numerical simulations on an inertia wheel pendulum and on a ball‐on‐beam system, both actuated by electric DC motors and subject to constant disturbances.

Control of a Double-Pendulum Overhead Crane System Based on Hierarchical Sliding Mode Control Techniques

The double-pendulum overhead crane system belongs to a class of underactuated mechanical systems, which is challenging to control due to its strong nonlinearities. This study deals with the nonlinear controller design for a double-pendulum overhead crane based on hierarchical sliding mode control with state-dependent switching gain. The equivalent and switching controls are obtained with the aid of first-level and second-level sliding surfaces. The asymptotic stability of sliding surfaces is proved theoretically and also shown graphically. Numerical simulations show that the proposed controller performs better than conventional hierarchical sliding mode control. The proposed controller effectively suppresses the load and hook swing and precisely controls the trolley’s displacement. It has strong robustness to the payload displacement and the change of the crane parameters.

Energy shaping control of a class of underactuated mechanical systems with high-order actuator dynamics

In this work we present some new results on energy shaping control for underactuated mechanical systems with high-order actuator dynamics. To this end, we propose an extension of the Interconnection and damping assignment Passivity based control methodology to account for actuator dynamics. This brings the following new results: i) a potential and kinetic energy shaping and damping assignment procedure that yields two alternative controllers; ii) a potential energy shaping and damping assignment procedure for a narrower class of underactuated mechanical systems. The proposed approach is illustrated with numerical simulations on three examples: an Acrobot system with a series elastic actuator; a soft continuum manipulator actuated by electroactive polymers; a two-mass-spring system actuated by a DC motor.

Stabilization of Double Inverted Pendulum Systems Based on Hierarchical Sliding Mode Control Techniques

The double rotary inverted pendulum (DRIP) system belongs to the class of under‐actuated mechanical systems, and it is a highly nonlinear, unstable, and benchmark system to test the different control techniques. This paper successfully designed the nonlinear hierarchical sliding mode control (HSMC) techniques to stabilize the DRIP system. We compare the performance of these techniques numerically with each other and with the previously designed control technique. We propose an aggregated HSMC technique as it has a much shorter stabilization time than other designed techniques.

A Constructive Procedure for Orbital Stabilization of a Class of Underactuated Mechanical Systems

In this note, we present a constructive procedure to solve the orbital stabilization problem of a class of nonlinear underactuated mechanical systems with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> degrees of freedom and underactuation degree one using the Immersion and Invariance technique. We define sufficient conditions to solve explicitly the partial differential equations arising in the Immersion and Invariance methodology, so that mechanical systems with gyroscopic terms can be considered. At the end, we use two practical systems as examples to illustrate the design procedure, as well as validating performance via simulations and experiments.

Data-driven passivity-based control of underactuated mechanical systems via interconnection and damping assignment

Since its introduction in the late 1980s, passivity-based control (PBC) has proven to be successful in controlling many robotic systems. The connection between stability and passivity theory is the most attractive feature of controllers designed using this methodology. However, the need to solve nonlinear partial differential equations (PDE) in closed-form has been a major challenge in applying PBC to general robotic systems. Here, we introduce a systematic approach to design controllers for a class of underactuated mechanical systems based on interconnection and damping assignment. Exploiting the universal approximation capability of neural networks, we formulate a data-driven optimisation problem that discovers solutions to the required PDEs automatically. Our approach does not destroy the passivity structure, preserving the inherent stability properties. We demonstrate the efficacy of our framework on two benchmark problems: the inertia wheel pendulum and the ball and beam system.

Stabilization of a class of nonlinear underactuated mechanical systems with 2-DOF via immersion and invariance

In this work, we propose a controller based on the well-known Immersion and Invariance technique to solve the stabilization problem of a class of underactuated mechanical systems with 2-Degree of Freedom (DOF). We define simple conditions such that the ordinary partial equations arising in Immersion and Invariance are solved. The class of systems addressed in this work includes underactuated mechanical systems with gyroscopic forces. Our approach is validated through simulation and experimental results.

Bounded inputs total energy shaping for a class of underactuated mechanical systems

AbstractDesigning control systems with bounded input is a practical consideration since realizable physical systems are limited by the saturation of actuators. The actuators' saturation degrades the performance of the control system, and in extreme cases, the stability of the closed‐loop system may be lost. However, actuator's saturation is typically neglected in the design of control systems, with compensation being made in the form of overdesigning the actuator or by postanalyzing the resulting system to ensure acceptable performance. The bounded input control of fully actuated mechanical systems has been investigated in multiple studies, but it is not generalized for underactuated mechanical systems. This article proposes a systematic framework for finding the upper bound of control effort in underactuated systems, based on interconnection and the damping assignment passivity based control approach. The proposed method also offers design variables for the control law to be tuned, considering the actuator's limit. The primary difficulty in finding the control input upper bounds is the velocity‐dependent kinetic energy‐related terms. Thus, the upper bound of velocity is computed using a suitable Lyapunov candidate as a function of closed‐loop system parameters. The validity and application of the proposed method are investigated in detail through two benchmark systems simulations.

A speed regulator for a force-driven cart-pole system

In this paper, we present a speed regulator for a force-driven cart-pole system. The proposed controller allows bringing the pole towards its upright position, while the cart moves asymptotically at desired constant speed, recovering the position regulation when we assign a desired constant position of the cart. The main motivation for addressing speed regulation is to broaden the scope of control of underactuated mechanical systems, because so far, the control of this class of mechanical systems has been focused primarily on position regulation; and therefore, there is few information and results available on broader control objectives, such as speed regulation. In particular, we design a speed regulator for the cart-pole system, as this system is one of the more representative test benches of underactuated mechanical system found in many automatic control research laboratories. Another novelty is the introduction of an alternative energy shaping approach for the velocity control design of a class of underactuated mechanical systems. A complete asymptotic stability analysis based on the Lyapunov theory and the Barbashin–Krasovskii theorem is presented. Local asymptotic stability is concluded. Simulation results upon a force-driven cart-pole model illustrate the performance of the proposed controller.

Control System Design of an Underactuated Dynamic Body Weight Support System Using Its Stability.

This paper discusses the stability of systems controlling patient body weight support systems which are used in gait re-education. These devices belong to the class of underactuated mechanical systems. This is due to the application of elastic shock-absorbing connections between the active part of the system and the passive part which impacts the patient. The model takes into account properties of the system, such as inertia, attenuation and susceptibility to the elements. Stability is an essential property of the system due to human–device interaction. In order to demonstrate stability, Lyapunov’s theory of stability, which is based on the model of system dynamics, was applied. The stability of the control system based on a model that requires knowledge of the structure and parameters of the equations of motion was demonstrated. Due to inaccuracies in the modeling of the rope (one of the basic elements of the device), an adaptive control system was introduced and its stability was also proved. The authors conducted simulation and experimental tests that illustrate the functionality of the analyzed control systems.

Gain-adapting coupling control for a class of underactuated mechanical systems

While presenting many advantages in application, the loss of actuators also brings about great challenge to the control of underactuated systems. Specifically, the unactuated DOFs (degrees of freedom) cannot be directly controlled, instead, they have to be stabilized indirectly through appropriate regulation of actuated ones. As an unfortunate fact, the natural couplings between actuated and unactuated states are often relatively weak. Hence, in many practical cases, even the actuated states are well regulated, the performance of the unactuated states still fails to meet expectations. Such phenomenon is particularly obvious when the system faces various disturbances, since the unactuated states are more vulnerable to them and more difficult to be re-stabilized. To deal with the aforementioned issues, a nonlinear gain-adapting controller is proposed for a class of underactuated mechanical systems, which incorporates extra unactuated states-related information into the controller to enhance the state couplings. In this way, the closed-loop system reacts more appropriately and efficiently to the unactuated dynamics, which is expected to obtain improved transient performance and robustness. With a relatively concise structure, the proposed strategy imposes few requirements on the system configuration, which makes it more convenient for practical application. Theoretical analysis and experiment results are presented to demonstrate the performance of the proposed method.

Adaptive fractional-order fast terminal sliding mode with fault-tolerant control for underactuated mechanical systems: Application to tower cranes

We develop a robust controller for tracking a class of underactuated mechanical systems (UMSs) that considers many inconveniences, such as actuator faults, parametric uncertainties, and disturbances, by combining a fast terminal sliding mode with fractional derivatives and integrals. Despite these disadvantages and the lack of actuators, such a controller has some advantages, such as robustness, quick transient responses, finite-time convergence, and the flexibility of fractionally derivative orders. However, this control version still requires a complete knowledge of faults, parametric variations, and disturbances. Hence, to overcome these limitations, we improve the controller by integrating an adaptation estimator to approximate the necessary knowledge through an equivalently unique component. We apply the proposed controller to a Liebherr-130-HC tower crane, which is a highly underactuated system, to investigate control quality. Simulation and comparison of the results with the other control approaches, such as sliding mode control (SMC), terminal SMC, and parametric estimator-based SMC, are conducted to highlight the advantages of the proposed controller.

Adaptive Sliding Mode Based Stabilization Control for the Class of Underactuated Mechanical Systems

This article presents a simple stabilizing control algorithm for a class of underactuated mechanical systems for two degrees of freedom (2DoF). In this respect, the adaptive sliding mode based strategy is proposed for the considered class. The controller, along with the adapted laws, is decided in such a way that the time derivative of a Lyapunov function grows negative. The proposed control technique has been applied to three classic benchmark 2DOF systems, the acrobot, pendoubt, and the cart-pole system. The effectiveness of the proposed strategy is proved in the light of simulation results for all said systems considered as an illustrative example.

Joint position regulation of a class of underactuated mechanical systems affected by LuGre dynamic friction via the IDA-PBC method

This paper presents an extension of the IDA-PBC method, addressing the problem of joint position regulation for a class of underactuated mechanical systems with friction, which is modelled by the LuGre dynamic model. An IDA-PBC including friction compensation with the LuGre model is designed to achieve locally asymptotically joint position regulation of a class of underactuated mechanical systems. To the best knowledge of the authors, this is the first original LuGre model-based controller for position regulation of underactuated mechanical systems. More importantly, the proposed theoretical framework allows us to redesign any IDA-PBC originally designed without friction compensation, as long as the parameters of the LuGre model of each actuator are available. Additionally, friction compensation in mechanical systems is known to improve controller performance at low velocities, being an advantage over other controllers that do not consider it. As a case study, an underactuated mechanical system available in numerous automatic control laboratories, called pendubot, is worked out to illustrate its performance through real-time experiments. Finally, a comparison is carried out between the proposed controller and an IDA-PBC with Dahl model friction compensation to test its superiority.

Stabilization of a Class of Underactuated Nonlinear Systems via Underactuated Back-Stepping

The stabilization problem for a class of nonlinear systems is solved via a novel method inspired by back-stepping. The method, that we call underactuated back-stepping, is introduced by solving the stabilization problem for an inertia wheel pendulum and it is then developed for a class of underactuated mechanical systems. The properties of the resulting closed-loop systems are studied in detail and case studies are given to show the effectiveness of the proposed method.

Path following of a class of underactuated mechanical systems via immersion and invariance‐based orbital stabilization

SummaryThis article aims to provide a new problem formulation of path following for mechanical systems without time parameterization nor guidance laws, namely, we express the control objective as an orbital stabilization problem. It is shown that it is possible to adapt the immersion and invariance technique to design static state‐feedback controllers that solve this problem. In particular, we select the target dynamics adopting the recently introduced Mexican sombrero energy assignment method. To demonstrate the effectiveness of the proposed method we apply it to control underactuated marine surface vessels.

Optimal Adaptive Robust Control Based on Cooperative Game Theory for a Class of Fuzzy Underactuated Mechanical Systems.

While designing control for a class of underactuated mechanical systems (UMSs), the uncertainty and the prescribed nonholonomic tracking trajectories should be taken into consideration. Uncertainty considered in this article is time varying and bounded, and the bound of uncertainty is described using the fuzzy set theory, namely, fuzzy UMSs. An analytical dynamics-based view is taken in which the prescribed tracking trajectories are viewed as servo constraints which can be linear, nonlinear, holonomic, and nonholonomic. Using this view, a novel closed form solution of adaptive robust control is found with leakage type adaptive law to guarantee deterministic system performance, including uniform boundedness and uniform ultimate boundedness. In order to find the optimal dual gain parameters of the designed control, a two-player cooperative game is proposed for which the Pareto optimality can always be guaranteed. The effectiveness of the proposed control is shown through numerical simulation of a two-wheeled inverted pendulum vehicle.