Simple Approximate Solutions for Dynamic Response of Suspension System

An approximate simplified analytic solution is proposed for the one DOF (degree of freedom) static and dynamic displacements alongside the stiffness (dynamic and static) and damping coefficients (minimum and maximum/critical values) of a parallel spring-damper suspension system connected to a solid mass-body gaining its energy by falling from height h. The analytic solution for the prescribed system is based on energy conservation equilibrium, considering the impact by a special G parameter. The formulation is based on the works performed by Timoshenko (1928), Mindlin (1945), and the U. S. army-engineering handbook (1975, 1982). A comparison between the prescribed studies formulations and current development has led to qualitative agreement. Moreover, quantitative agreement was found between the current prescribed suspension properties approximate value - results and the traditionally time dependent (transient, frequency) parameter properties. Also, coupling models that concerns the linkage between different work and energy terms, e.g., the damping energy, friction work, spring potential energy and gravitational energy model was performed. Moreover, approximate analytic solution was proposed for both cases (friction and coupling case), whereas the uncoupling and the coupling cases were found to agree qualitatively with the literature studies. Both coupling and uncoupling solutions were found to complete each other, explaining different literature attitudes and assumptions. In addition, some design points were clarified about the wire mounting isolators stiffness properties dependent on their physical behavior (compression, shear tension), based on Cavoflex catalog. Finally, the current study aims to continue and contribute the suspension, package cushioning and containers studies by using an initial simple pre – design analytic evaluation of falling mass- body (like cushion, containers, etc.).

Applying Set Membership Strategy in State of Charge Estimation for Lithium-ion Battery

As state of charge is one important variable to monitor the later battery management system, and as traditional Kalman filter can be used to estimate the state of charge for Lithium-ion battery on basis of probability distribution on external noise. To relax this strict assumption on external noise, set membership strategy is proposed to achieve our goal in case of unknown but bounded noise. External noise with unknown but bounded is more realistic than white noise. After equivalent circuit model is used to describe the Lithium-ion battery charging and discharging properties, one state space equation is constructed to regard state of charge as its state variable. Based on state space model about state of charge, two kinds of set membership strategies are put forth to achieve the state estimation, which corresponds to state of charge estimation. Due to external noise is bounded, i.e. external noise is in a set, we construct interval and ellipsoid estimation for state estimation respectively in case of external noise is assumed in an interval or ellipsoid. Then midpoint of interval or center of the ellipsoid are chosen as the final value for state of charge estimation. Finally, one simulation example confirms our theoretical results.

Application of Interval Predictor Model Into Model Predictive Control

In this paper, interval prediction model is studied for model predictive control (MPC) strategy with unknown but bounded noise. After introducing the family of models and some basic information, some computational results are presented to construct interval predictor model, using linear regression structure whose regression parameters are included in a sphere parameter set. A size measure is used to scale the average amplitude of the predictor interval, then one optimal model that minimizes this size measure is efficiently computed by solving a linear programming problem. The active set approach is applied to solve the linear programming problem, and based on these optimization variables, the predictor interval of the considered model with sphere parameter set can be directly constructed. As for choosing a fixed non-negative number in our given size measure, a better choice is proposed by using the Karush-Kuhn-Tucker (KKT) optimality conditions. In order to apply interval prediction model into model predictive control, the midpoint of that interval is substituted in a quadratic optimization problem with inequality constrained condition to obtain the optimal control input. After formulating it as a standard quadratic optimization and deriving its dual form, the Gauss-Seidel algorithm is applied to solve the dual problem and convergence of Gauss-Seidel algorithm is provided too. Finally simulation examples confirm our theoretical results.

Stability Analysis of Pressure and Penetration Rate in Rotary Drilling System

The purpose of this paper is to stabilize the annular pressure profile throughout the wellbore continuously while drilling. A new nonlinear dynamical system is developed and a controller is designed to stabilize the annular pressure and achieve asymptotic tracking by applying feedback control of the main pumps. Hence, the paper studies the control design for the well known Managed Pressure Drilling system (MPD). MPD provides a closedloop drilling process in which pore pressure, formation fracture pressure, and bottomhole pressure are balanced and managed at the surface. Although, responses must provide a solution for critical downhole pressures to preserve drilling efficiency and safety. Our MPD scheme is elaborated in reference to a nontrivial backstepping control procedure and the effectiveness of the proposed control laws are shown by simulations.

Efficient Intersection Computation of the Bezier and Hermite Curves with Axis Aligned Bounding Box

Cubic parametric curves are used in many applications including the CAD/CAM systems. Especially the Hermite, Bezier and Coons formulations of a cubic parametric curve are used in E2 and E3 space. This paper presents efficient algorithm for the intersection computation of a cubic parametric curve with the Axis Aligned Bounding Box (AAB Box). Usual solution is to represent the cubic curve by a polyline, i.e. actually by sampled points of the given curve. However, this approach is dependent on the sampling frequency and can lead to problems especially in CAD/CAM systems and numerically controlled machines use.

Robust Exponential Stabilization for a Class of Nonlinear Uncertain Systems with Time-varying Delays

This paper is concerned with the problem of robust exponential stabilization for a class of nonlinear uncertain systems with time-varying delays. By using appropriately chosen Lyapunov-Krasovskii functional, together with the Finsler’s lemma, sufficient conditions for exponential stability of nonlinear uncertain systems with time-varying delays are proposed in terms of linear matrix inequality (LMI). Then, novel sufficient conditions are developed to ensure the nonlinear uncertain system with time-varying delay is robust exponentially stabilizable in terms of linear matrix inequality with state feedback control. Finally, a numerical example is given to illustrate the efficiency of proposed methods.

Additive Mixed Sensitivity Design of PID Controllers for Continuous-Time System with Uncertain Time-Delay

This paper presents an algorithm for all achievable coefficients of Proportional Integral Derivative (PID) controllers in an integral-derivative plane that stabilizes and satisfies additive mixed sensitivity constraint with an uncertain time delay for a continuous-time system. This algorithm solves the singularity problem of designing PID controllers in the integral and derivative plane and estimates achievable ranges of proportional gain of the PID controllers. A numerical cascaded ball and beam with unity feedback control of an SRV-DC motor and uncertain communication time delays in the system process demonstrate the application of this methodology. In this application, the additive weight bounds the additive errors for the cascaded ball and beam and the closed-loop SRV-DC motor system transfer function with the internal communication time delays

Reliability Analysis of Hydrodynamic System for Robot Configuration

The failure tree and J-M model method are lack of analysis of the importance of each component model, which leads to the low reliability of the analysis results. In view of this problem, a Monte Carlo method based on the shape of the English long-distance robot is proposed. In view of the configuration of the robot, the realization process of the robot shape fluid dynamics system is analyzed. The frequency of accident is determined by Monte Carlo simulation, which is used as the reliability index of the system. In MATLAB, the reliability of the shape fluid dynamic system of robot is analyzed by Monte Carlo method. The system importance name and parameters are determined. The parameter conforms to the statistical function of random variables of each corresponding probability distribution function. According to the parameters, the function of the structure is established. The system is divided into reliable state, failure state and limit state with 0 as the dividing point, and the actual failure probability of the system is calculated. The numerical solution of log domain is simulated by the method of statistical calculation of random variables, and the actual failure probability is expressed by normal distribution function. The experimental results show that the actual failure probability of the method is lower than 5% under any working load, and the reliability of the analysis results is high.

Robust Controller Design for Descriptor-type Time-delay Systems

Linear time-invariant descriptor-type time-delay systems are considered. A robust stabilizing controller design approach for such systems is introduced. Uncertainties both in the time-delays and in other system parameters are considered. A frequency-dependent scalar bound on such uncertainties is first derived. Once this bound is found, the controller design is completely based on the nominal model. However, satisfying a scalar frequency-dependent condition, which uses the derived bound, guarantees robust stability. An example is also presented to illustrate the proposed approach

Stability Analysis and Robust H∞ Filtering for Discrete-time Nonlinear Systems with Time-varying Delays

In this paper, we investigate the problem of robust H∞ filter design for a class of discrete-time nonlinear systems. The systems under consider involves time-varying delays and parameters uncertainties. The main objective is to design a linear full-order filter to ensure that the resulting filtering error system is asymptotically stable with a prescribed H∞ performance level. By constructing an appropriate Lyapunov-Krasovskii functional, some novel sufficient conditions are established to guarantee the filter error dynamics system is robust asymptotically stable with H∞ performance γ , and the H∞ filter is designed in term of linear matrix inequalities. Finally, a numerical example is provided to illustrate the efficiency of proposed method.