Jian-Qiao Sun

Passive, Adaptive and Active Tuned Vibration Absorbers—A Survey

An overview of the recent development of tuned vibration absorbers (TVAs) for vibration and noise suppression is presented. The paper summarizes some popular theory for analysis and optimal tuning of these devices, discusses various design configurations, and presents some contemporary applications of passive TVAs. Furthermore, the paper also presents a brief discussion on the recent progress of adaptive and semi-active TVAs along with their on-line tuning strategies, and active and hybrid fail-safe TVAs.

The Generalized Cell Mapping Method in Nonlinear Random Vibration Based Upon Short-Time Gaussian Approximation

This scheme provides a very efficient and accurate way of computing the one-step transition probability matrix of the previously developed generalized cell mapping (GCM) method in nonlinear random vibration

First-passage time probability of non-linear stochastic systems by generalized cell mapping method

In this paper, the first-passage time probability of linear and non-linear dynamical systems subjected to white noise excitation is studied by the generalized cell mapping method. A wide range of the damping and non-linear parameters is examined in the study. The results of the first-passage time probability for the systems with large damping and non-linear parameters are difficult to obtain by other methods and they do not seem to have been previously available. The results obtained by the generalized cell mapping method are found to be in good agreement with those obtained by direct simulation.

Stochastic Optimal Control of Nonlinear Systems via Short-Time Gaussian Approximation and Cell Mapping

A novel strategy to obtain global solutions of stochasticoptimal control problems with fixed state terminal conditions and controlbounds is proposed in this paper. The solution is global in the sense that theoptimal control solutions for all the initial conditions in a region of thestate space are obtained. The method makes use of Bellmans principle ofoptimality, the cumulant neglect closure method and the short-time Gaussianapproximation. A Markov chain with a control dependent transition probabilitymatrix is built using the generalized cell mapping method. This allows toevaluate the transient and steady state response of the controlled system. Themethod is applied to several linear and nonlinear systems leading to excellentcontrol performances.

Neural networks for prediction of acoustical properties of polyurethane foams

Abstract This paper presents a study of neural networks for prediction of acoustical properties of polyurethane foams. The proposed neural network model of the foam uses easily measured parameters such as frequency, airflow resistivity and density to predict multiple acoustical properties including the sound absorption coefficient and the surface impedance. Such a model is quite robust in the sense that it can be used to develop models for many different classes of materials with different sets of input and output parameters. The current neural network model of the foam is empirical and provides a useful complement to the existing analytical and numerical approaches.

Stability and Optimal Feedback Controls for Time-Delayed Linear Periodic Systems

An effective numerical method for stability analysis of feedback controls with time delay and for identifying optimal gains of the control is presented. The method develops a mapping of the system response in a finite dimensional state space. Minimization of the largest absolute value of eigenvalues of the mapping leads to optimal control gains. Numerical examples of both time-invariant and periodic linear systems are presented to demonstrate the method. We have found that the proposed method provides accurate stability boundaries and performance contours in the parametric space of control gains.

Solution of Fixed Final State Optimal Control Problems via Simple Cell Mapping

A strategy is proposed to solve the fixed final state optimalcontrol problem using the simple cell mapping method. A non-uniform timestep simple cell mapping is developed to create a general database fromwhich solutions of various optimal control problems can be obtained. Atwo-stage backward search algorithm is proposed to eliminate degeneratedpaths often associated with the simple cell mapping. The proposed methodcan accurately delineate the switching curves and eliminate false limitcycles in the solution. The method is applied to two optimal controlproblems with bang-bang control. The well-known minimum time controlproblem of moving a point mass from any initial condition to the originof the phase plane is studied first. This example has exact solutionsavailable which provide a yardstick to examine the accuracy of themethod. The cell size dependence of the solution accuracy is studiednumerically. The second example is a variable stiffness feedback controlproblem with tuning range saturation. The strategy proposed is able toprovide the switching curves in the phase plane. This result has notbeen obtained before.

A stiffness-varying model of human gait

We report on a conceptual two degrees of freedom (2 DOF) human gait model, which incorporates nonlinear joint stiffness as a stabilizing agent. Specifically, muscle spring-like property provides inherent stability during gait movement using a nonlinear angular spring and dash pot at each joint. The instability problem of the gait model in direct dynamic analysis is overcome by simulating the human co-contraction muscle function. By developing dynamic system stability requirements and hypothesizing a minimum joint stiffness criterion, we determine time-varying joint stiffness. Optimum joint stiffnesses are present for varying gait pattern, stride lengths and cadences. We conclude that nonlinear joint stiffness can be incorporated into gait models to overcome stability problems inherent in such linkage models.

Adaptive force regulation of muscle strengthening rehabilitation device with magnetorheological fluids

In rehabilitation from neuromuscular trauma or injury, strengthening exercises are often prescribed by physical therapists to recover as much function as possible. Strengthening equipment used in clinical settings range from low-cost devices, such as sandbag weights or elastic bands to large and expensive isotonic and isokinetic devices. The low-cost devices are incapable of measuring strength gains and apply resistance based on the lowest level of torque that is produced by a muscle group. Resistance that varies with joint angle can be achieved with isokinetic devices in which angular velocity is held constant and variable torque is generated when the patient attempts to move faster than the device but are ineffective if a patient cannot generate torque rapidly. In this paper, we report the development of a versatile rehabilitation device that can be used to strengthen different muscle groups based on the torque generating capability of the muscle that changes with joint angle. The device is low cost, is smaller than other commercially available machines, and can be programmed to apply resistance that is unique to a particular patient and that will optimize strengthening. The core of the device, a damper with smart magnetorheological fluids, provides passive exercise force. A digital adaptive control is capable of regulating exercise force precisely following the muscle strengthening profile prescribed by a physical therapist. The device could be programmed with artificial intelligence to dynamically adjust the target force profile to optimize rehabilitation effects. The device provides both isometric and isokinetic strength training and can be developed into a small, low-cost device that may be capable of providing optimal strengthening in the home.

Feedback Controls and Optimal Gain Design of Delayed Periodic Linear Systems

In this paper we present an application of a semi-discretization method to the stability analysis of PID feedback controls of linear systems with time delay. The method develops a mapping of the system response in a finite-dimensional state space. Minimization of the largest absolute value of the eigenvalues of the mapping leads to optimal control gains. Numerical examples of both time-invariant and periodic linear systems are presented to demonstrate the method. The tracking control problem of linear systems with time delay is also discussed. We have found that the semi-discretization method provides accurate stability boundaries and performance contours in the parametric space of control gains, and offers an alternative to the classic design approaches of feedback controls.