Since real chaotic systems have undesired randomlike behaviors which have also been deteriorated by environmental noise, chaotic systems are modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of wiener process which. Nonlinear control of underactuated mechanical systems with. Starting from a simple, marginally stable model considered for lyapunov based boundary control of flexible mechanical systems, we add a term driving an instability and prove that for an. The presentation of adaptive control results will mostly be at the level of examples, not general theory. This book includes nonlinear design topics such as feedback linearization, lyapunov based control, adaptive control, optimal control and robust control.
Warren dixon university of florida gainesville, florida, u. Pdf anthropomorphic mechanical design and lyapunovbased. Control lyapunov function, lyapunov design, model reference adaptive. Wal l a new approach to adaptive model reference control, based on lyapunovs direc methodt, is presented. A trend of investigation of nonlinear control systems has been present over the last few decades. A new lyapunov based robust control for uncertain mechanical systems zhen shengchao 1, 2 zhao han 1 chen yehwa 2 huang kang 1 abstract we design a new robust controller for uncertain mechanical systems. The ones marked may be different from the article in the profile. The control lyapunov function is used to test whether a system is feedback stabilizable, that is whether for any state x there exists a control. However, such relaxations were achieved in the absence of discrete states. Since most practical scenarios require the design of nonlinear controllers to work around uncertainty and measurementrelated issues, the authors use lyapunovs direct method as an effective tool to design and. Nonlinear dynamical systems and control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on lyapunovbased methods. It has been the subject of extensive studies for centuries, with the. A design procedure for single output systems has been developed and the re. Adaptive neural dynamic surface control of mechanical.
Recent advancements in lyapunovbased design and analysis techniques have applications to a broad class of engineering systems, including mechanical, electrical, robotic, aerospace, and underactuated systems. Bin xian is a professor in the school of electrical engineering and automation at tianjin university. Hence, numerous control methods are proposed for the tracking problem of fullyactuated mechanical systems. Lyapunovbased control of robotic systems automation and. The focus in this dissertation is the further development and application of switched systems methods for uncertain nonlinear networked systems. Lyapunovbased control of mechanical systems semantic scholar. Lyapunovbased control of saturated and timedelayed nonlinear systems by nicholas fischer december 2012 chair. Dynamical system theory lies at the heart of mathematical sciences and engineering. The proposed controller takes into account the dynamics of both the object and the manipulators. Nagarkatti fumin zhang with 89 figures birkhauser boston basel berlin. Stabilization of nonlinear systems with state and control constraints using lyapunovbased predictive control prashant mhaskar, nael h. Averaging consider the general class of nonlinear systems. Based on recent surveys, control of general underactuated systems is a major. Dawson clemson university clemson, south carolina, u.
Sharma, 2012 presented a predictor based compensation method to control systems with known constant input delay. Lyapunov design for safe reinforcement learning journal of. These properties are then exploited to design aset point regulation controller. Lyapunovbased control of mechanical systems springerlink. Lyapunov based nonlinear control the research is focused on the development and application of a lyapunov based control methodology, which incorporates the full nonlinear system dynamics in the design and analysis without requiring the solution of the nonlinear equations of motion. In special cases, this allows construction of hamiltoniantype lyapunov. In chapter 3, a nonlinear control technique for cascaded nonlinear systems with inputs entering at different dynamic orders is presented.
Lyapunov based control design for multiple robots handling. Lyapunovbased pd linear control of the oscillatory. Lyapunovbased control of mechanical systems marcio s. Lyapunov design encyclopedia of life support systems. Discontinuous discretetime systems kellett and andrew r. Lyapunov based model reference adaptive control for aerial manipulation matko orsag, christopher korpela, stjepan bogdan, and paul oh abstractthis paper presents a control scheme to achieve dynamic stability in an aerial vehicle with dual multidegree of freedom manipulators using a lyapunov based model reference adaptive control. Lyapunov analysis for controlled systems we now want to use lyapunov analysis to study the stability of systems with control inputs.
The proposed framework is lyapunov based and unlike standard neural network nn controllers guaranteeing ultimate bounded. Lyapunovbased control methods for neuromuscular electrical stimulation by nitin sharma august 2010 chair. Introduction mechanical systems electric machines robotic systems aerospace systems. Elfarra control of nonlinear and hybrid process systems. Nonlinear dynamical systems and controlpresents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on lyapunovbased methods. Lyapunov based control of saturated and timedelayed nonlinear systems by nicholas fischer december 2012 chair. A control lyapunov approach to predictive control of hybrid systems 1 discrete states. Set that the eigenvalues of are, and the corresponding eigenstates are. The class of continuous nonlinear controllers that are based on control lyapunov functions clfs can be understood graphically as continuous selections from a setvalued map that takes states and maps them to control value sets. Lyapunovbased fault tolerant control of quadrotor unmanned aerial vehicles xiaobing zhang a thesis in the department of mechanical and industria engineerinl g presented in partia fulfillmenl t of the requirements for the degree of master of engineering at concordi universita y montreal, quebec canad, a march 2010 xiaobing zhang 201, 0. Lyapunovbased model predictive control of an input. Lyapunovbased tracking control in the presence of uncertain. Restoration of arm function is necessary to resuming activities of daily living adl.
This is a new textreference on advanced nonlinear controllers for mechanical systems that are based on a lyapunovtype design and analysis methodology. Design of lyapunov based nonlinear position control of electrohydraulic servo systems deticek, e. In order to shorten the time required to reach the target state, we propose two designs to optimize lyapunov control in this paper. Mechatronic control of distributed noise and vibration.
Hamiltons principle is applied to model the dynamics of the gantry crane system. Lyapunov functions for nonlinear discretetime systems. This thesis presents the theoretical development, simulation study and flight tests of a lyapunovbased control approach for the fault tolerant control ftc of a quadrotor unmanned aerial vehicle uav. The control strategy is based on partial feedback linearization, in a first stage, to linearize only the actuated coordinate of the inverted pendulum, and then, a suitable lyapunov function is formed to obtain a stabilizing feedback controller. It will then proved, by means of lyapunov energy functions, that this law can also be used to bound the original nonlinear nonautonomous system. Mechanical engineering neuromuscular electrical stimulation nmes is the application of a potential.
Lyapunovbased control of robotic systems aman behal university of central florida orlando, florida, u. On the other hand, recent technological advances have produced many realworld engineering applications that require the automatic con trol of mechanical systems. Lyapunovbased control of mechanical systems by marcio s. Lyapunovbased approach introduces advanced tools for stability analysis of nonlinear systems. A new lyapunov based robust control for uncertain mechanical. Edvard deticek mitja kastrevc university of maribor, faculty of mechanical engineering, slovenia this paper studies the nonlinear closed loop control of an electrohydraulic servo system. Lyapunov based generic controller design for thrustprop elled underactuated systems pedro o. This cited by count includes citations to the following articles in scholar. Energy based control of a class of underactuated mechanical systems. The design of nonlinear controllers for mechanical systems has been an ex tremely active area of research in the last two decades.
Download it once and read it on your kindle device, pc, phones or tablets. Mechanical engineering the focus of this research is an examination of the interplay between di. Request pdf lyapunovbased control of mechanical systems friction is a natural phenomenon that affects almost all motion. With the proposed boundary control laws, the states of the moving strip system are proven to converge to a neighbourhood of the equilibrium points, namely, the stability of the moving strip system. Our design techniques combine nonlinear partial feedback linearization with lyapunov methods based on saturation functions, switching and energy shaping. Request pdf lyapunovbased control of mechanical systems the synthesis of controllers basically involves two steps. Lyapunovbased pd linear control of the oscillatory behavior of a nonlinear mechanical system. Stabilization of nonlinear systems with state and control. Lyapunovbased control of mechanical systems control engineering kindle edition by queiroz, marcio s. In this article, we address the problem of controlling multiple robots manipulating a rigid object cooperatively.
Lyapunovbased generic controller design for thrustpropelled. Lyapunov based model reference adaptive control for aerial. More formally, suppose we are given an autonomous dynamical system. This book provides a practical yet rigorous development of nonlinear, lyapunovbased tools and their use in the solution of control theoretic problems. The title of this book is lyapunovbased control of mechanical systems control engineering and it was written by marcio s. Anthropomorphic mechanical design and lyapunovbased. Designs for uncertainty, constraints and time delays.
The function in can be interpreted as the lyapunov function v x. Lyapunov based control of robotic systems aman behal university of central florida orlando, florida, u. Lyapunov based optimal control of a class of nonlinear systems. Lyapunovbased control of a robot and massspring system undergoing an impact collision by chienhao liang may 2007 chair. The first design makes the lyapunov function decrease as fast as possible with a constraint on the total power of control fields, and the second design has the same purpose but with a constraint on each control field. Dimarogonas abstract we present a controller for an underactuated system which is driven by a one dimensional linear accelerationthrust along a direction vector, by a timevarying gr avity. Full text of nonlinear control of engineering systems. A new lyapunov based robust control for uncertain mechanical systems. From the invariant principle lemma 1, the quantum systems with impulsive control fields will converge to. Stability criteria for nonlinear systems first lyapunov criterion reduced method. Kellett and teel, on the robustness of klstability for difference inclusions. A graphical understanding of lyapunovbased nonlinear control. Lyapunovbased control of mechanical systems ebook, 2000. The lyapunov functionbased control approach is designed and modeled for the dcac inverter to serve the functions.
Mechanical engineering time delays and actuator saturation are two phenomena which affect the performance of dynamic systems under closedloop control. Lyapunovbased control of mechanical systems request pdf. The design of nonlinear controllers for mechanical systems has been an ex. Abstractthis paper deals with control of a solar photovoltaic pv power generating system interfaced with the grid. We claim that v x is a constrained control lyapunov function. Request pdf lyapunovbased control of mechanical systems the design of nonlinear controllers for mechanical systems has been an ex tremely active area of research in the last two decades. A sliding mode control approach smc is used for achieving maximum power tracking mpt control of solarpv array. Lyapunovbased nonlinear missile guidance journal of. First we propose and prove a few fundamental properties of the multirobot dynamical system. Before we state our controller specifically, we formalize the properties of this. Abstractin this paper, a neuroadaptive control framework for continuous and discretetime nonlinear uncertain dynamical systems with inputtostate stable internal dynamics is developed. Lecture notes in control and information sciences, vol 170. A nonlinear control force is presented to stabilize the underactuated inverted pendulum mounted on a cart. A control lyapunov approach to predictive control of hybrid.
Citeseerx document details isaac councill, lee giles, pradeep teregowda. Control lyapunov functions for adaptive nonlinear stabilization. Lyapunovbased control of mechanical systems control. From a theoretical point of view, this attention can be attributed to their interesting dynamic behavior, which makes them suitable benchmarks for nonlinear control the oreticians. Dawson is mcqueen quattlebaum professor and chair of the holcombe department of electrical and computer engineering at clemson university. Constrained control lyapunov functionbased control of. Mechanical and aerospace engineering the problem of controlling a robot during a noncontact to contact transition has been a historically challenging problem that is practically motivated by. Arts lab, scuola superiore santanna, pisa, italy department of information engineering, univ. For mechanical systems energy of a free mechanical system with friction always decreases unless the system is at rest, equilibrium. Lyapunov control of quantum systems with impulsive control fields.
Nonlinear dynamical systems and control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on lyapunov based methods. Lyapunov stability analysis for feedback control design. Lyapunovbased control of robotic systems describes nonlinear control design solutions for problems that arise from robots required to interact with and manipulate their environments. A detailed description of the system s dynamics is also presented. Lyapunovbased controller for a class of stochastic chaotic. Lyapunovbased impact time control guidance laws against stationary targets. Nonlinear dynamical systems and controlpresents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on lyapunov based methods. Lyapunovbased control design for multiple robots handling a. In this regard, the control problems of mechanical systems have been extensively studied in the literature, in the context of either eulerlagrange systems or robotics. Lyapunovbased fault tolerant control of quadrotor unmanned aerial vehicles. Lyapunovbased controller for the inverted pendulum cart. Lyapunovbased control design for multiple robots handling.
Lyapunovbased control of robotic systems automation and control engineering book 36 kindle edition by behal, aman, dixon, warren, dawson, darren m. A lyapunovbased approach for the control of biomimetic robotic systems with periodic forcing inputs domenico campolo. As a result the methods for its analysis and design have improved rapidly. Anthropomorphic mechanical design and lyapunovbased control of a new shoulder rehabilitation system mahdieh babaiasla, ahmad ghanbaria,b, and smrs noorania aschool of engineering emerging technologies, university of tabriz, tabriz, iran bfaculty of mechanical engineering, university of. Lyapunovbased control of mechanical systems book, 2000. An important and particularly nice property of v x is that the level sets v x c are equal to the set boundaries. This study presents a general control law based on lyapunovs direct method for a group of wellknown stochastic chaotic systems. A mechanical wristwatch winds down as the potential energy stored in its spring is expended. The twodegreeoffreedom control system consists of a feed forward controller based on an inverse system and a feed back controller with suppressing the vibration effectively and stabilizing. Lyapunov function and sliding mode control approach for. Lyapunov based optimal control of a class of nonlinear systems by hassan zargarzadeh a dissertation presented to the faculty of the graduate school of the missouri university of science and technology in partial fulfillment of the requirements for the degree doctor of philosophy in electrical engineering 2012 approved jagannathan sarangapani. Lyapunovbased robust and adaptive control of nonlinear systems using a novel feedback structure by parag patre august 2009 chair. The primary qualitative technique we use is lyapunov control design.
Proceedings of the institution of mechanical engineers, part i. Xiii lyapunov design shuzhi ge encyclopedia of life support systems eolss lyapunov design shuzhi ge department of electrical and computer engineering, the national university of singapore, singapore keywords. Mechanical engineering switched systems theory consists of tools developed for systems containing a combination of continuous and discrete dynamics. Outputfeedback design for nonsmooth mechanical systems. Kokotovi6 department of electrical and computer enoineerino, university of california, santa barbara, ca 93106, usa received 6 august 1994. Department of mechanical and aerospace engineering, university of florida, gainesville, fl 326116250. Use features like bookmarks, note taking and highlighting while reading lyapunovbased control of robotic systems automation and control engineering book 36. This result was further relaxed in 2,3 towards using a terminal inequality constraint on the continuous states. Lyapunovbased tracking control in the presence of uncertain nonlinear parameterizable friction c. Energy based control of a class of underactuated mechanical.