Mass-spring Mechanical System Research Articles

Asynchronous Sliding Mode Control for Nonlinear Markov Jumping Systems With PDT-Switched Transition Probabilities

This paper studies the asynchronous sliding mode control for nonlinear Markov jump systems (NMJSs), whose transition probabilities is piecewise-constant and subjected to the persistent dwell-time (PDT) switching rule. By resorting to the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy set theory, the nonlinearity and uncertainty features of the investigated systems are modeled. Taking the uncertain membership functions (MFs) of IT2 T-S fuzzy systems into consideration, the non-parallel distributed compensation strategy is employed for designing the MFs of the controller such that them do not need to be obtained in time. Furthermore, in view of the difficulty of accurately acquiring the mode of NMJSs with complex transition probabilities, the hidden Markov model is employed to provide a detected mode for constructing the sliding mode law. Afterwards, a novel fuzzy sliding surface is proposed, and an asynchronous IT2-fuzzy-model-based sliding mode control law is designed for forcing the closed-loop systems to move on the predefined sliding surface. Thereafter, a novel two-mode-dependent Lyapunov-like function is conceived for the studied systems, where modes of NMJSs and transition probabilities are permitted to change simultaneously. Through applying an improved technique to handle the parametric matrix inequalities, some less-conservative sufficient conditions in the form of linear matrix inequality are obtained for ensuring the stochastic exponentially asymptotical stability of the sliding mode with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance. Finally, a mass-spring mechanical system is presented to substantiate the validity of the proposed main results.

FLS-Based Nonuniform Trajectory Tracking AILC for Uncertain Nonlinear Systems with Nonsymmetric Dead-Zone Input and Initial State Error

This paper proposes an AILC method for uncertain nonlinear system to solve different target tracking problems. The method uses fuzzy logic systems (FLS) to approximate every uncertain term in systems. All closed-loop signals are bounded on 0 , T according to the Lyapunov theory. A time-varying boundary layer and a typical convergent series are introduced to handle initial state error, unknown bounds of errors, and nonuniform target tracking, respectively. The result is that the tracking error’s norm can converge to a small neighborhood along iteration increasing asymptotically. Finally, the simulation results of mass-spring mechanical system show the correctness of the theory and validity of the method.

RBFNN-Based Nonuniform Trajectory Tracking Adaptive Iterative Learning Control for Uncertain Nonlinear System with Continuous Nonlinearly Input

This paper proposes an adaptive iterative learning control (AILC) method for uncertain nonlinear system with continuous nonlinearly input to solve different target tracking problem. The method uses the radial basis function neural network (RBFNN) to approximate every uncertain term in systems. A time-varying boundary layer, a typical convergent series are introduced to deal with initial state error and unknown bounds of errors, respectively. The conclusion is that the tracking error can converge to a very small area with the number of iterations increasing. All closed-loop signals are bounded on finite-time interval 0 , T . Finally, the simulation result of mass-spring mechanical system shows the correctness of the theory and validity of the method.

Tracking-Based Control for Constrained Nonlinear Systems Under Parametric Uncertainties

The adaptive tracking control is extended to the nonlinear system with multiple uncertainties consisting of input saturation, unknown parameter and full-state constraints. To deal with the input saturation, a distinctive method of introducing an auxiliary system is used instead of directly approximating it by a smooth function. Then, the adaptive backstepping technique is combined with the barrier Lyapunov function (BLF) to solve the parametric nonlinearities and give a systematic design procedure. Based on this design procedure, an adaptive state-feedback controller is obtained with rigourous stability analysis. It is verified that all the signals are uniformly ultimately bounded, the tracking error is bounded in a compact set of the origin, and the full-states are not violated. Finally, the proposed controller is used to a mass-spring mechanical system, and demonstrates the proposed scheme is effective.

Adaptive Finite-Time Control for High-Order Nonlinear Systems With Multiple Uncertainties and its Application

The globally finite-time control issue is concerned in this note for high-order nonlinearly parameterized systems with unknown control gain and external disturbances. A novel control strategy combining adaptive control technique with sign function can well deal with serious uncertainties and unknown control gain. Without any nonlinear growth assumptions, a unified and systematic design procedure is employed to derive an adaptive state-feedback controller with the help of the adding a power integrator method and backstepping technique. Then, by finite-time stability analysis and Lyapunov functions, the proposed controller ensures that the closed-loop system is globally practically finite-time stable (PFTS). Two simulation examples, including a mass-spring mechanical system and a numerical example, are applied to verify the performance and effectiveness of the designed schemes.

A new approach to global stabilization of high-order time-delay uncertain nonlinear systems via time-varying feedback and homogeneous domination

This paper addresses the state-feedback stabilization problem for a class of high-order uncertain nonlinear systems with multiple time-delays. The distinguished feature of the systems to be investigated is the serious coexistence between unknown time-varying parameters and unknown multiple time-delays. Time-varying method combined with adaptive technique is used to capture the possible unknowns and delayed states. The new control strategy is presented based on homogeneous domination idea and the choice of a Lyapunov–Krasovskii functional. Finally, the developed scheme is used to stabilize mass-spring mechanical system with unknown time-delays.

Robust output tracking control for a class of uncertain nonlinear systems using extended state observer

This paper investigates the global robust output tracking control problem via output feedback for a class of nonlinear uncertain systems with the integral input-to-state stable (iISS) dynamic uncertainties. By performing the coordinates transformation and employing an extended state observer (ESO), it can be seen that the robust setpoint tracking control is well solved. The proposed control strategy simplifies the control design procedure. This control scheme finds its application in the mass-spring mechanical system. It is shown that the asymptotic tracking control for any desired displacement can be achieved in the mass-spring mechanical system in the case of unknown parameters. The simulation results demonstrate that the proposed control scheme has a better tracking performance. This verifies the effectiveness of the developed method.

Output tracking control for generalised high-order nonlinear system with serious uncertainties

ABSTRACTThis paper focuses on the problem of output tracking control for a class of generalised high-order uncertain nonlinear systems. Serious uncertainties are composed of unknown high-order terms, unknown nonlinear functions and the signal to be tracked. The new feedback scheme guarantees that the tracking error belongs to a prescribed small neighbourhood of the origin in finite time. Design procedures are presented by combining improved adding a power integrator method with the recursive construction. As an application, the control methodology is used in the tracking control of the mass-spring mechanical system.

Amplitude Controlled Adaptive Feedback Resonance in a Single Degree-of-Freedom Mass-Spring Mechanical System

Many mechanical and micro-mechanical applications utilize artificially generated self-excited oscillations either as the working principle or as the performance enhancer. The present paper investigates a switched damping adaptive feedback control method for inducing artificial controlled self-excited oscillation in a single degree-of-freedom damped mass-spring mechanical system. The adaptive feedback control can generate oscillation at the natural frequency of the system with controlled amplitude and maintain the frequency of oscillation at the natural frequency of the system under parametric variations. The desired amplitude of oscillation even under parametric variations can be achieved when the controller is designed utilizing a frequency detector (used to adapt the natural frequency of the system). Numerical simulations confirm the analytical results.

DESARROLLO DE EXPERIMENTOS VIRTUALES BASADOS EN ADOBE FLASH

El presente trabajo describe el desarrollo de dos experimentos virtuales usando Adobe Flash. El primero consta de un sistema masa-resorte el cual permite a los estudiantes hallar el valor de la gravedad terrestre con la incertidumbre correspondiente. El segundo consta de un sistema compuesto por tres masas y cuatro resortes. Éste experimento permite al alumno visualizar movimientos de sistemas mecánicos complejos, además de darle una visión acerca de la mecánica lagrangeana, así como de los conceptos de valor propio y estado propio de un sistema. Ambos programas son interactivos, permitiendo a los alumnos observen cambios en el sistema físico a medida que realicen cambios en los parámetros correspondientes. Estos experimentos virtuales pueden ser utilizados como complementos en las clases teóricas incrementando el dinamismo en las mismas. Los programas pueden correr directamente desde las computadoras o pueden instalarse en un servidor y ser ejecutados desde cualquier parte del mundo por clases enteras al mismo tiempo, sin importar el sistema operativo que usen.

On the high frequency transfer of mechanical stimuli from the surface of the head to the macular neuroepithelium of the mouse.

Vestibular macular sensors are activated by a shearing motion between the otoconial membrane and underlying receptor epithelium. Shearing motion and sensory activation in response to an externally induced head motion do not occur instantaneously. The mechanically reactive elastic and inertial properties of the intervening tissue introduce temporal constraints on the transfer of the stimulus to sensors. Treating the otoconial sensory apparatus as an overdamped second-order mechanical system, we measured the governing long time constant (Τ(L)) for stimulus transfer from the head surface to epithelium. This provided the basis to estimate the corresponding upper cutoff for the frequency response curve for mouse otoconial organs. A velocity step excitation was used as the forcing function. Hypothetically, the onset of the mechanical response to a step excitation follows an exponential rise having the form Vel(shear) = U(1-e(-t/TL)), where U is the applied shearing velocity step amplitude. The response time of the otoconial apparatus was estimated based on the activation threshold of macular neural responses to step stimuli having durations between 0.1 and 2.0 ms. Twenty adult C57BL/6 J mice were evaluated. Animals were anesthetized. The head was secured to a shaker platform using a non-invasive head clip or implanted skull screws. The shaker was driven to produce a theoretical forcing step velocity excitation at the otoconial organ. Vestibular sensory evoked potentials (VsEPs) were recorded to measure the threshold for macular neural activation. The duration of the applied step motion was reduced systematically from 2 to 0.1 ms and response threshold determined for each duration (nine durations). Hypothetically, the threshold of activation will increase according to the decrease in velocity transfer occurring at shorter step durations. The relationship between neural threshold and stimulus step duration was characterized. Activation threshold increased exponentially as velocity step duration decreased below 1.0 ms. The time constants associated with the exponential curve were Τ(L) = 0.50 ms for the head clip coupling and T(L) = 0.79 ms for skull screw preparation. These corresponded to upper -3 dB frequency cutoff points of approximately 318 and 201 Hz, respectively. T(L) ranged from 224 to 379 across individual animals using the head clip coupling. The findings were consistent with a second-order mass-spring mechanical system. Threshold data were also fitted to underdamped models post hoc. The underdamped fits suggested natural resonance frequencies on the order of 278 to 448 Hz as well as the idea that macular systems in mammals are less damped than generally acknowledged. Although estimated indirectly, it is argued that these time constants reflect largely if not entirely the mechanics of transfer to the sensory apparatus. The estimated governing time constant of 0.50 ms for composite data predicts high frequency cutoffs of at least 318 Hz for the intact otoconial apparatus of the mouse.

Precise tracking of a piezoelectric positioning stage via a filtering-type sliding-surface control with chattering alleviation

A filtering-type sliding-surface control (FTSSC) design with chattering alleviation compared to the traditional sliding-mode control (SMC) is proposed for precise trajectory tracking of a piezoelectric positioning stage (abbreviated by ‘piezo-stage’). First, considering the dynamics of motion of a mass-spring mechanical system, the differential equations of motion system – which contains the parameters of a linear viscous friction, spring-coefficient, and a nonlinear hysteresis function – are proposed to describe the dynamics of motion of the piezo-stage. Then, the frequency-dependent hysteresis responses from both the proposed equations and the practical piezo-stage are illustrated to validate the equations. Based on the equations proposed, a state-space model is developed in which the applied voltage to the stage is defined as an output of a new control variable. According to the state-space model, the FTSSC design is proposed to provide not only the advantages of the traditional SMC, but also chattering improvement. Using the proposed control approach to the trajectory tracking of the piezo-stage, we can obtain that (a) high-performance tracking response, (b) robustness to system uncertainties and (c) chattering alleviation compared with the traditional SMC. Experimental results are illustrated to validate the proposed control approach for practical applications in trajectory tracking.