Uncertain Mechanical Systems Research Articles

Adaptive Control of Mechanical Systems Using Neural Networks

In this paper, we consider the decentralized adaptive control design problem for uncertain mechanical systems, where uncertainty may arise due to isolated subsystem and/or interconnections among subsystems. Radial basis function neural networks are used to approximate the nonlinear functions to include both dynamic and interconnection uncertainties in each subsystem. The stability of the thus designed control system can be guaranteed by a rigid proof. Finally, a simulation example is given to illustrate the effectiveness of the proposed algorithm.

A Simple Nonlinear Observer for a Class of Uncertain Mechanical Systems

A simple nonlinear observer is proposed for a class of uncertain nonlinear multiple-input-multiple-output (MIMO) mechanical systems whose dynamics are first-order differentiable. The global asymptotic observation of the proposed observer is proved. Thus, the observer can be designed independently of the controller. Furthermore, the proposed observer is formulated without any detailed model knowledge of the system. These advantages make it easy to implement. Numerical simulations are included to illustrate the effectiveness of the proposed observer.

Design sensitivity and reliability-based structural optimization by univariate decomposition

This paper presents a new univariate decomposition method for design sensitivity analysis and reliability-based design optimization of mechanical systems subject to uncertain performance functions in constraints. The method involves a novel univariate approximation of a general multivariate function in the rotated Gaussian space for reliability analysis, analytical sensitivity of failure probability with respect to design variables, and standard gradient-based optimization algorithms. In both reliability and sensitivity analyses, the proposed effort has been reduced to performing multiple one-dimensional integrations. The evaluation of these one-dimensional integrations requires calculating only conditional responses at selected deterministic input determined by sample points and Gauss–Hermite integration points. Numerical results indicate that the proposed method provides accurate and computationally efficient estimates of the sensitivity of failure probability, which leads to accurate design optimization of uncertain mechanical systems.

Fuzzy Analysis of Geometric Tolerances Using Interval Method

The quality and performance of any mechanical system are greatly influenced by the GD&T (geometric dimensioning and tolerancing) used in its design. A proper consideration of the various types of tolerances associated with different components could not only satisfy the assembly requirements, but also minimize the manufacturing cost. To satisfy the design and functional specifications, one has to know how various tolerance patterns affect the manufacturability and assemblability of the designed parts. Therefore, a thorough understanding of how different forms of mechanical tolerances interact with each other becomes a must for designers and manufacturers. The effects of form, orientation, and position tolerances on the kinematic features and dimensions of mechanical systems are analysed using a new approach, based on fuzzy logic, in this article. In this approach, the α-cut method is used with the mechanical tolerances concerned as intervals. The proposed approach represents a more natural and realistic way of dealing with uncertain properties like geometric dimensions. A typical mechanical assembly system involving form, orientation, and position tolerances is used as an illustrative example. As the fuzzy approach leads to systems of non-linear interval equations, a modified Newton-Raphson method is developed for the solution of these equations. The current approach is found to be effective, simple, and accurate and can be extended to the analysis and synthesis of any uncertain mechanical system where the probability distribution functions of the uncertain parameters are unknown.

Second-order sliding-mode observer for mechanical systems

The super-twisting second-order sliding-mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems. The finite time convergence of the observer is proved. Thus, the observer can be designed independently of the controller. A discrete version of the observer is considered and the corresponding accuracy is estimated.

Adaptive motion tracking control of uncertain nonholonomic mechanical systems including actuator dynamics

The design of position tracking control of mechanical systems with classical nonholonomic constraints incorporating actuator dynamics is discussed. An adaptive controller is designed at the actuator level and the controller guarantees that the configuration state of the system tracks the desired trajectory. A detailed numerical example is presented to illustrate the developed method.

Intelligent robust tracking controls for holonomic and nonholonomic mechanical systems using only position measurements

Intelligent robust tracking control designs are proposed in this paper for both uncertain holonomic and nonholonomic mechanical systems. A unified and systematic procedure, that is based on an adaptive fuzzy (or neural network) system and a linear observer, is employed to derive the controllers for these two constrained mechanical systems. Adaptive fuzzy-based (or neural network-based) position feedback tracking controllers can be constructed such that all the states and signals of the closed-loop systems are bounded and the tracking error locally converges to a small region around zero. Only position measurements are required for feedback. The implementation of the fuzzy (or neural network) basis functions depends only on the desired reference information and so once a set of desired trajectories is given, the required basis functions can be explicitly preassigned. Consequently, the intelligent robust position feedback tracking controllers developed here possess the properties of computational simplicity and easy implementation. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed control algorithms.

H∞ disturbance attenuation for uncertain mechanical systems with input delay

The paper deals with the robust H disturbance attenuation problem for uncertain mechanical systems with input delay. The parameter uncertainties for the mass, damping and stiffness matrices take an additive a priori norm-bounded form. The time delay for the input is time-invariant but has a known constant bound. A robust static H state-feedback controller is designed to attenuate the disturbance on the controlled output to a prescribed level for all admissible parameter uncertainties and input delay. The design approach is formulated in terms of the feasibility of certain delay-dependent linear matrix inequalities. A numerical example is employed to illustrate the effectiveness of the approach.

A robust feedback linearization control for constrained mechanical systems

A robust control approach is developed for the tracking problem of uncertain constrained mechanical systems. The dynamic model is modified to contain two sets of state variables, where one describes the constrained motion and the other describes the unconstrained motion. The controller consists of two control elements. The first is based on the input-output decoupling approach in non-linear control theory; it is used to achieve exponential global tracking of both position and constraint forces on the constrained manifold of the nominal system. The second is a robust loop that ensures asymptotic stability of the uncertain system under parameters as well as environmental uncertainties. This control element consists of a class of continuous state feedback control. The only required information about the uncertainties is their Euclidean norm bound function. System stability is investigated using Lyapunov stability theory and it is shown that global stability holds for both system state vectors.

Adaptive Control—A Departure from the Certainty-Equivalence Paradigm

A fundamental study of indirect adaptive control addressed towards a class of uncertain mechanical and aerospace systems is the subject of this paper. We utilize and build upon certain recent techniques within adaptive control that permit nonlinear parameterization of uncertainty, thereby amounting to a significant shift from the classical certainty equivalence methodology. Instead of the more popular direct adaptive control formulations, our focus is restricted to the indirect methods because imposing prior information on properties of physically meaningful plant parameters is convenient within this framework. For two different types of uncertainty parameterizations, namely scalar parameters and proper orthogonal matrix parameters, we present smooth, non-overparameterized (lower order), and stable adaptive control algorithms that provide improved transient performance while at the same time utilize all the available prior information on the unknown parameters. In the particular case when there exists a single scalar uncertain parameter, the most novel attribute of the proposed controller is that adaptation gets automatically frozen once the parameter estimate reaches the corresponding true value, a highly desirable feature that is clearly missing within all existing certainty equivalence adaptive control schemes. Through both analysis and simulations, we have been able to confirm that this “nice” feature amounts to having a proportional term within the parameter update law; and is in fact enabled by a crucial role played by the introduction of certain design functions that are embedded within the new controller. All technical descriptions will be further elaborated by illustrative physical examples as well as numerical simulations of the resulting closed-loop dynamics to demonstrate the potential advantages of this new approach.

Design and Realtime Implementation of an Adaptive Variation Absorber for Uncertain Mechanical Systems Subjected to Unknown Disturbances

Design and Realtime Implementation of an Adaptive Variation Absorber for Uncertain Mechanical Systems Subjected to Unknown Disturbances

Design and Realtime Implementation of an Adaptive Variation Absorber for Uncertain Mechanical Systems Subjected to Unknown Disturbances

Design and Realtime Implementation of an Adaptive Variation Absorber for Uncertain Mechanical Systems Subjected to Unknown Disturbances

Adaptive Tracking Control of Linear Uncertain Mechanical Systems Subjected to Unknown Sinusoidal Disturbances

The design and implementation of an adaptive disturbance rejection approach is presented for single-input-single-output linear-time-invariant uncertain mechanical systems subject to sinusoidal disturbances with unknown amplitudes and frequencies. The proposed technique suggests construction of a set of stabilizing tuning functions via a state estimate observer in a backstepping fashion to achieve asymptotic disturbance rejection. The tuning functions design is based on a single Lyapunov function incorporating both the error states and update law, and hence, global stability and improved transient performance are readily achieved. Utilizing only the system output, a virtual control input is used in place of non-measurable and unknown signals. The performance of the adaptation algorithm is demonstrated through both simulations and experiments for a single-degree-of-freedom system with unknown parameters and subject to an unknown sinusoidal disturbance. Significant matching between the simulation and experimental results is observed.

Robust adaptive motion/force tracking control of uncertain nonholonomic mechanical systems

The position/force tracking control of Lagrangian mechanical systems with classical nonholonomic constraints is addressed in this paper. The main feature of this paper is that 1) control strategy is developed at the dynamic level and can deal with model uncertainties in the mechanical systems; 2) the proposed control law ensures the desired trajectory tracking of the configuration state of the closed-loop system; 3) the tracking error of constraint force is bounded with a controllable bound; and 4) a global asymptotic stability result is obtained in the Lyapunov sense. A detailed numerical example is presented to illustrate the developed method.

Robust Frequency-Shaping Optimal Active Vibration Control of Uncertain Flexible Mechanical Systems with Persistent Excitation

ABSTRACTBased on the frequency-shaping optimal control method, this paper proposes a time-domain robust disturbance rejection design approach for a class of uncertain flexible mechanical systems subject to persistent disturbances and time-varying parameter perturbations. In the approach, a frequency-shaping output filter is first employed to combine with the mechanical system and a Kalman filter to form an augmented system. Some eigenvalues of the frequency-shaping output filter coincide with the unstable poles of the disturbance dynamics to perform disturbance rejection. Then, for the designed closed-loop system to have asymptotic stability, a new robust stability condition is proposed. It is shown that, using the proposed stability condition, the resulting controller can suppress the persistent disturbance and keep the flexible mechanical system from the possibility of instability caused by spillover and time-varying parameter perturbations. Finally, two examples are given to demonstrate the use of the design approach.

Stability chart for the delayed Mathieu equation

In the space of system parameters, the closedform stability chart is determined for the delayed Mathieu equation defined as (t)(cost)x(t) bx(t2). This stability chart makes the connection between t...

Optimum Design of Mechanical Systems Involving Interval Parameters

The imprecision or uncertainty present in many engineering systems can be modeled using probabilistic, fuzzy or interval methods. This work presents the optimum design of uncertain mechanical systems using interval analysis for the prediction of system response. Each of the uncertain parameters is defined by a range of values. Since the interval ranges of response parameters is found to increase with an increase in the number and/or ranges of input interval parameters with the use of interval arithmetic operations, a truncation procedure is used to obtain approximate but reasonably accurate response of the system. This procedure is found to be simple, economical and fairly accurate. The optimum design of a brake is considered to illustrate the computational aspects of the methods. The procedures outlined in this work are quite general and can be used for the design of any uncertain mechanical system when either the probability distribution functions or the preference information of uncertain parameters are unknown.

Adaptive realization of desired constraint stabilization dynamics in the control of multibody systems

This paper presents a novel way of stabilizing the constraint drift dynamics in the numerical simulation of multibody systems. This formulation is applicable for a large class of uncertain mechanical systems described by nonlinear differential algebraic equations that are subject to holonomic constraints. In the absence of uncertainty in the system inertia parameters, it is possible to develop stabilization relationships that suppress the accumulation of error in the constraint equations during the time integration process. In order to account for ignorance in the parameters, we propose a model reference adaptive control scheme that ensures the asymptotic realization of the desired (reference) constraint violation dynamics. Special attention is given to the case of redundantly actuated systems, as is typical for robotics. For this class of problems, we direct special attention to optimization criteria that achieve any desired manoeuvre using minimum control effort and coordination between the redundant set of actuators. An example application demonstrates the effectiveness and practicality of the proposed adaptive control formulation.

Second order sliding mode control for robot arms with time base generators for finite-time tracking

A novel chattering-free dynamic sliding mode controller for a class of uncertain mechanical systems is proposed in order to account globally for a time-varying sliding regime for all time and for any initial condition. The new sliding surface, parametrized by a time base generator, plays the role of moving, and rotating continuously the nominal sliding surface, while shifting is done through a known, state-independent, vanishing vector to eliminate the reaching phase for any initial condition, a weaker assumption in comparison to some moving sliding surface designs. In this way, the closed-loop system yields finite-time convergence of tracking errors, whose convergence time can be fixed independently of initial conditions, in contrast to terminal sliding mode wherein convergence time depends on initial conditions. To implement the controller, the upper bound of the derivative of the sliding surface is required, a weaker assumption in contrast to some dynamic sliding mode controllers. The performance of the closed-loop system is visualized through simulation.

Finite attraction for nonlinear uncertain mechanical systems

Finite attraction for nonlinear uncertain mechanical systems