Uniform semiglobal practical asymptotic stability for non-autonomous cascaded systems and applications

It is due to the modularity of the analysis that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on ``adding integrators''. Nevertheless, the standing assumptions in most of the present literature on cascaded systems is that, when decoupled, the subsystems constituting the cascade are uniformly globally asymptotically stable (UGAS). Hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable (USPAS). This situation is often encountered in control practice, e.g., in control of physical systems with external perturbations, measurement noise, unmodelled dynamics, etc. This paper generalizes previous results for cascades by establishing that, under a uniform boundedness condition, the cascade of two USPAS systems remains USPAS. An analogous result can be derived for USAS systems in cascade. Furthermore, we show the utility of our results in the PID control of mechanical systems considering the dynamics of the DC motors.Comment: 16 pages. Modifications 1st Feb. 2006: additional requirement that links the parameter-dependency of the lower and upper bounds on the Lyapunov function, stronger condition of uniform boundedness of solutions, modification and simplification of the proofs accordingl

Limiting performance analisys of a head protection helmet using multicriteria control optimization

In this paper the limiting performance analysis of a head protection helmet is performed. A discrete model of the human head is used. A multicriteria optimum control problem is formulated in order to minimize the risk of injuries in case of impact. Several injury criteria are minimized and are required to remain below a safety threshold value. The optimal control force acting on the head is found. The optimal control force is determined by nonlinear programming. The equations of motion are integrated at-once, as it is typical for static response, instead of the traditional step-by-step integration.info:eu-repo/semantics/publishedVersio

Time-frequency energy analysis of chaotic mechanical system affected by additive impulses

Chaotic vibrations in elastic mechanical systems are not stationary. In the considered case a transient induced vibration is discussed. Here the energy is concentrated in different varying frequency ranges. This contribution considers an experimental investigation of jumping phenomena in this system under chaotic vibrations, driven by cart under harmonic excitation. Using this system, the data of jumping phenomenon during the chaotic vibration are collected and analyzed. Here, time-frequency energy method can effectively show the characteristics of energy in time domain and perform the component analysis in specific frequency range. Applying a comparative study of jumping phenomenon discussing different equilibria, frequency range recognition, and energy characterization, the jumping phenomenon of the pendulum signal induced by chaotic vibration is characterized. A state transition model is established. Further, an additive impulsive control on the elastic system is considered to validate the model

MATLAB-based Tools for Modelling and Control of Underactuated Mechanical Systems

Underactuated systems, defined as nonlinear mechanical systems with fewer control inputs than degrees of freedom, appear in a broad range of applications including robotics, aerospace, marine and locomotive systems. Studying the complex low-order nonlinear dynamics of appropriate benchmark underactuated systems often enables us to gain insight into the principles of modelling and control of advanced, higher-order underactuated systems. Such benchmarks include the Acrobot, Pendubot and the reaction (inertia) wheel pendulum. The aim of this paper is to introduce novel MATLAB-based tools which were developed to provide complex software support for modelling and control of these three benchmark systems. The presented tools include a Simulink block library, a set of demo simulation schemes and several innovative functions for mathematical and simulation model generation

CONTROL OF THE DOUBLE INVERTED PENDULUM ON A CART USING THE NATURAL MOTION

This paper deals with controlling the swing-up motion of the double pendulum on a cart using a novel control. The system control is based on finding a feasible trajectory connecting the equilibrium positions from which the eigenfrequencies of the system are determined. Then the system is controlled during the motion between the equilibrium positions by the special harmonic excitation at the system resonances. Around the two equilibrium positions, the trajectory is stabilized by the nonlinear quadratic regulator NQR (also known as SDRE – the State Dependent Riccati Equation). These together form the control between the equilibrium positions demonstrated on the double pendulum on a cart