Dynamics and control of a class of underactuated mechanical systems

This paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom. Control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the results; these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable

Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.Comment: 9 page

Adaptive fuzzy sliding mode control for uncertain nonlinear underactuated mechanical systems

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. © 2013 IEEE

Sliding mode control of a class of underactuated system with non-integrable momentum

In this paper, a sliding mode control scheme is developed to stabilise a class of nonlinear perturbed underactuated system with a non-integral momentum. In this scheme, by initially maintaining a subset of actuated variables on sliding manifolds, the underactuated system with the non-integrable momentum can be approximated by one with the integrable momentum in finite time. During sliding, a subset of the actuated variables converge to zero and a physically meaningful diffeomorphism is systematically calculated to transform the reduced order sliding motion into one in a strict feedback normal form in which the control signals are decoupled from the underactuated subsystem. Furthermore, based on the perturbed strict feedback form, it is possible to find a sliding mode control law to ensure the asymptotic stability of the remaining actuated and unactuated variables. The design efficacy is verified via a multi-link planar robot case study

Control of a class of multibody underactuated mechanical systems with discontinuous friction using sliding-mode

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.This paper studies sliding-mode control of a class of multibody underactuated systems with discontinuous friction presenting on the unactuated configuration variable with consideration of parametric uncertainties. Global motion for this class system including sticking, stick-slip, and slip regimes are analyzed, and their corresponding equilibria are identified. Our control objective is to avoid the sticking and stick-slip regimes while track a desired velocity in the slip regime. The proposed sliding-mode controllers are robust to parametric uncertainties, and their stabilities are proved by using the Lyapunov direct method. Two examples, a mass-spring-damping system and a drill-string system, are used to demonstrate the validity of the proposed controllers.The author(s) received no financial support for the research, authorship, and/or publication of this articl

Modelling and control of offshore crane systems

University of Technology Sydney. Faculty of Engineering and Information Technology.Cranes are widely used in transportation, construction and manufacturing. Suspended payloads in crane system are caused to swing due to actuator movement, external disturbance such as wind flows, and motion of the crane base in the case of portable cranes. Recently, offshore cranes have become a new trend in stevedoring and in offshore construction as they can help to avoid port congestion and also to exploit ocean engineering applications. For crane operations, it is important to satisfy rigorous requirements in terms of safety, accuracy and efficiency. One of the main challenges in crane operations has been identified as the sway motion control, which is subject to underactuation of crane drive systems and external disturbances. Particularly in offshore cranes, the harsh conditions can produce exogenous disturbances during the load transfer at various scenarios of offshore crane operations in practice. Therefore, it is interesting as to how to design robust controllers to guarantee high performance in the face of disturbances and parameter variations in offshore cranes. The motivation for this thesis is based on recent growing research interest in the derivation of dynamic models and development of control techniques for offshore cranes in the presence of, for example, the rope length variation, sway, ocean waves and strong winds in offshore crane systems. Accordingly, the work for this thesis has been conducted in the two main themes, namely analytical modelling and control design, for which new results represent its contributions. Dynamic models of two types of offshore crane systems, namely the offshore gantry crane and offshore boom crane, are derived in the presence of vessel’s ocean wave-induced motion. The effect of wind disturbances on the payload sway is also considered in the modelling. In the control context, sliding mode control techniques for a generic form of underactuated mechanical Lagrangian systems are presented, including the conventional first-order, second-order and adaptive fuzzy sliding mode controllers. The major component in this part of the thesis is the design of sliding mode control laws based on the developed offshore crane models for trajectory tracking problems, in the presence of persistent disturbances in severe open-sea conditions. Extensive simulation results are presented to demonstrate the efficacy of the models and robustness of the designed controllers

Robust Control Methods for Nonlinear Systems with Uncertain Dynamics and Unknown Control Direction

Robust nonlinear control design strategies using sliding mode control (SMC) and integral SMC (ISMC) are developed, which are capable of achieving reliable and accurate tracking control for systems containing dynamic uncertainty, unmodeled disturbances, and actuator anomalies that result in an unknown and time-varying control direction. In order to ease readability of this dissertation, detailed explanations of the relevant mathematical tools is provided, including stability denitions, Lyapunov-based stability analysis methods, SMC and ISMC fundamentals, and other basic nonlinear control tools. The contributions of the dissertation are three novel control algorithms for three different classes of nonlinear systems: single-input multipleoutput (SIMO) systems, systems with model uncertainty and bounded disturbances, and systems with unknown control direction. Control design for SIMO systems is challenging due to the fact that such systems have fewer actuators than degrees of freedom to control (i.e., they are underactuated systems). While traditional nonlinear control methods can be utilized to design controllers for certain classes of cascaded underactuated systems, more advanced methods are required to develop controllers for parallel systems, which are not in a cascade structure. A novel control technique is proposed in this dissertation, which is shown to achieve asymptotic tracking for dual parallel systems, where a single scalar control input directly affects two subsystems. The result is achieved through an innovative sequential control design algorithm, whereby one of the subsystems is indirectly stabilized via the desired state trajectory that is commanded to the other subsystem. The SIMO system under consideration does not contain uncertainty or disturbances. In dealing with systems containing uncertainty in the dynamic model, a particularly challenging situation occurs when uncertainty exists in the input-multiplicative gain matrix. Moreover, special consideration is required in control design for systems that also include unknown bounded disturbances. To cope with these challenges, a robust continuous controller is developed using an ISMC technique, which achieves asymptotic trajectory tracking for systems with unknown bounded disturbances, while simultaneously compensating for parametric uncertainty in the input gain matrix. The ISMC design is rigorously proven to achieve asymptotic trajectory tracking for a quadrotor system and a synthetic jet actuator (SJA)-based aircraft system. In the ISMC designs, it is assumed that the signs in the uncertain input-multiplicative gain matrix (i.e., the actuator control directions) are known. A much more challenging scenario is encountered in designing controllers for classes of systems, where the uncertainty in the input gain matrix is extreme enough to result in an a priori-unknown control direction. Such a scenario can result when dealing with highly inaccurate dynamic models, unmodeled parameter variations, actuator anomalies, unknown external or internal disturbances, and/or other adversarial operating conditions. To address this challenge, a SMCbased self-recongurable control algorithm is presented, which automatically adjusts for unknown control direction via periodic switching between sliding manifolds that ultimately forces the state to a converging manifold. Rigorous mathematical analyses are presented to prove the theoretical results, and simulation results are provided to demonstrate the effectiveness of the three proposed control algorithms

Geometric Surface-Based Tracking Control of a Quadrotor UAV

New quadrotor UAV control algorithms are developed, based on nonlinear surfaces composed of tracking errors that evolve directly on the nonlinear configuration manifold, thus inherently including in the control design the nonlinear characteristics of the SE(3) configuration space. In particular, geometric surface-based controllers are developed and are shown, through rigorous stability proofs, to have desirable almost global closed loop properties. For the first time in regards to the geometric literature, a region of attraction independent of the position error is identified and its effects are analyzed. The effectiveness of the proposed "surface based" controllers are illustrated by simulations of aggressive maneuvers in the presence of disturbances and motor saturation.Comment: 2018 26th Mediterranean Conference on Control and Automation (MED