Application of an SMA Spring for Vibration Screen Control

Abstract

Use of springs made of an alloy with shape memory (SMA) to shape the dynamic characteristics of a resonance vibration screen is proposed in this paper. These springs change spring constant as a result of temperature changes. Thus it is possible to change their resonance frequency in real time. In the paper a mathematical model of a controlled SMA spring was formulated and its parameters were identified. In the model both the effect of spring coefficient changes and damping changes depending upon alloy temperature and spring vibration frequency were taken into consideration. Experimental investigations of the examined spring and screen physical model were carried out and selected characteristics were also included. The investigations were carried out at the Dynamics and Control of Structures Laboratory of AGH University of Science and Technology. The control law was formulated. Simulation investigations of the mathematical vibration screen model in both open and closed loop systems were made. It was shown that the elaborated control system is robust of vibration mass changes by as much as ±30%.

Optimal control based on a modified quadratic performance index for systems disturbed by sinusoidal signals

“…In the optimization problem with the weighted multitone performance index, another restriction has been imposed on the set of admissible controls (15). It follows from part (ii) of Theorem 2 that restriction (15) on the set of admissible controls does not change the set of optimal solutions.…”

“…Since the function u t ð ÞAŨ , the existence of decomposition (16)- (19) is an immediate conclusion of condition (15). The uniqueness of the decomposition has been proved from equalities (21) and (22).…”

“…The set of controlsŨ contains functions u t ð Þ that are bounded and satisfy condition (15) for any frequency ω40 and phase shift φAℝ. This condition means that there exists a finite limit of the average of the product of the function u t ð Þ and a sinusoidal function with the frequency ω and phase shift φ.…”

“…An example of such a function is shown at the end of this section. From condition (15) and the properties of operations on function limits, it follows immediately that the setŨ is a vector space. Later in this section we show that the vector spaceŨ contains bounded periodic functions and functions tending to zero at infinity.…”

Design of natural frequency adjustable electromagnetic actuator and active vibration control test

“…With the purpose of solving this problem, there has been much recent interest in the design of natural frequency adjustable devices whose natural frequency can be adjusted by changing the inertial mass or stiffness. [3][4][5][6] A wide variety of design solutions have recently been proposed, and a common factor in most of the designs is the introduction of varying stiffness. An approach for controlling the link position and stiffness of a variable stiffness actuator has been proposed by Sardellitti et al, 7 in which the stiffness perceived at the output link is adjusted to match the varying task requirements through a combination of positioning gains and mechanical stiffness.…”