Constraint-Following Based Adaptive Robust Control for Underactuated Mechanical Systems

In this book, we collected recent results on the control of underactuated mechanical systems subject to internal uncertainties and external disturbances. The strategy developed is so universal that it is not restricted to a specific system but a large class of underactuated systems. Several benchmark systems are studied in this book, including detailed literature review, system dynamics derivation, control problem formulation, and simulation verification. The control strategy developed in chapter 4 is able to stabilize all these benchmark systems with satisfactory performance regardless of the underactuated dynamics and various uncertainties. The book is written as a text suitable for graduate students in the advanced course for the control of underactuated systems. It also provides valuable tools for researchers and practicing engineers working on the control of underactuated mechanical systems.

Passivity-based control of underactuated mechanical systems with nonlinear friction effects is analyzed. The port-controlled-Hamiltonian equations of the mechanical system are extended by incorporating a novel dynamic friction model, whose internal states are included as generalized coordinates. The extended Hamiltonian model preserves passivity properties of the LuGre model for the velocity-force pair, with no extra conditions on the friction model parameters. Simulation results are presented for an underactuated double pendulum.

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.

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.

In this paper we discuss the partial feedback linearization control of underactuated mechanical systems. We consider an n degree of freedom system having m actuated, or active, degrees of freedom and l=n-m unactuated, or passive, degrees of freedom. It is known that the portion of the dynamics corresponding to the active degrees of freedom may be linearized by nonlinear feedback. In this paper we show, alternatively, that the portion of the dynamics corresponding to the passive degrees of freedom may be linearized by nonlinear feedback under a condition that we call strong inertial coupling. We derive and analyze the resulting zero dynamics which are crucial to an understanding of the response of the overall system. Simulation results are presented showing the performance of two link underactuated robots under partial feedback linearization control. >

This 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.

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.

Control of underactuated mechanical systems via energy shaping is a well-established, robust design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations (PDEs). In this technical note a new, fully constructive, procedure to shape the energy for a class of mechanical systems that obviates the solution of PDEs is proposed. The control law consists of a first stage of partial feedback linearization followed by a simple proportional plus integral controller acting on two new passive outputs. The class of systems for which the procedure is applicable is identified imposing some (directly verifiable) conditions on the systems inertia matrix and its potential energy function. It is shown that these conditions are satisfied by three benchmark examples.

A non-linear Euler-Lagrange (EL) controller is proposed for underactuated mechanical Euler-Lagrange systems. The rationale is that mimicking the process structure in the controller will lead to improved performance. The tuning of the controller can be rather intuitive as it can be seen as an auxiliary mechanical system that is connected to the process, also called the main system. The tuning methodology used here finds its roots in the vibration absorber technology: transfer the energy from the main to the auxiliary system and dissipate the energy in the additional structure. Energy, in the form of the Hamiltonian, is used to examine stability of the compound system using Lyapunov’s direct method. To evaluate the performance of the controller, the Hamiltonian of the main system is used. A planar manipulator with two and three degrees-of-freedom (DOF) shows the effectivity of the proposed tuning method

On closed-loop vibrational control of underactuated mechanical systems

Adaptive robust control for fuzzy underactuated mechanical systems: A Stackelberg game-theoretic optimization approach

SummaryAt the present time, there is a great deal of interest in the adaptive control of systems with rapidly varying parameters. Such problems arise in different forms and in many disciplines including finance, sociology, biology, and engineering. In general, these problems are intractable mathematically and the time variations have to be classified in some form to obtain rigorous results. In this paper, we consider the adaptive identification and control of linear systems with periodically varying parameters (referred to as linear time‐varying periodic (LTP) systems). The class of systems with known periodic parameters has been investigated widely since the pioneering work of Floquet and lends itself to rigorous mathematical analysis. However, very little was known until the early years of the last decade concerning the adaptive control of such systems. The problem was introduced by Xu and explored in detail by Narendra and Zhiling in 2006 and 2009, respectively. In 2012, a new method was introduced in adaptive control by Han and Narendra and is referred to as second‐level adaptation. In this paper, the adaptive identification and control of LTP systems using second‐level adaptation is discussed.

The performance of a damping-controllable dynamic damper was investigated with an adaptive neural net control system. The damping controllability of the dynamic damper was accomplished by introducing the Electro-Rheological (ER) fluid, which is known as one of the highly functional materials and whose apparent viscosity can be varied in accordance with applied electric field strength in a wide range as well as in a short time. As a control system for the present dynamic damper, an adaptive neural net control system was developed ; it was composed of a forward model network and a controller network. With the proposed neural net control system, the damping-controllable dynamic damper can be tuned by itself even if response of a structure shows nonlinearity to input disturbances or varies its own dynamic characteristic. Moreover, the vibration amplitude corresponding to several natural frequencies can be reduced with only a single dynamic damper. Numerical and experimental investigations were performed, and the results shows the superiority of the present adaptive vibration control system.

Adaptive traffic control systems continuously monitor traffic conditions on an arterial and adjust traffic signal timings to accommodate variation in traffic volume and minimize stops and delays. This paper describes currently practical adaptive control systems which have been used in the United States and worldwide, which include Adaptive Control System-Lite (ACS-Lite), Optimization Policies for Adaptive Control (OPAC), Real-Time Hierarchical Optimized Distributed and Effective System (RHODES), Sydney Coordinated Adaptive Traffic System (SCATS) and Split Cycle Offset Optimization (SCOOT). The comparisons of the benefits from past experiences, cost and hardware requirements will help the traffic engineers and decision makers a guideline to select the optimized adaptive control system based on research objectives.

SummaryIn this study, we present a reinforcement learning (RL)‐based flight control system design method to improve the transient response performance of a closed‐loop reference model (CRM) adaptive control system. The methodology, known as RL‐CRM, relies on the generation of a dynamic adaption strategy by implementing RL on the variable factor in the feedback path gain matrix of the reference model. An actor‐critic RL agent is designed using the performance‐driven reward functions and tracking error observations from the environment. In the training phase, a deep deterministic policy gradient algorithm is utilized to learn the time‐varying adaptation strategy of the design parameter in the reference model feedback gain matrix. The proposed control structure provides the possibility to learn numerous adaptation strategies across a wide range of flight and vehicle conditions instead of being driven by high‐fidelity simulators or flight testing and real flight operations. The performance of the proposed system was evaluated on an identified and verified mathematical model of an agile quadrotor platform. Monte‐Carlo simulations and worst case analysis were also performed over a benchmark helicopter example model. In comparison to the classical model reference adaptive control and CRM‐adaptive control system designs, the proposed RL‐CRM adaptive flight control system design improves the transient response performance on all associated metrics and provides the capability to operate over a wide range of parametric uncertainties.