Developing A Viscoelastic Model and Controller for the MRE Isolator Over A Wide Frequency Range

Abstract

Passive rubber isolators are designed to isolate vibrations for a fixed set of operating frequencies. To design an isolator over broadband frequency, it must change its property to adapt depending upon the frequency of excitation. The semi-active isolator has the desired qualities to achieve the required vibration isolation over broadband frequency. Among the available semi-active isolators, MRE (Magnetorheological Elastomer) isola- tor is one such isolator where the dynamic properties of the active element are varied by applying magnetic field. The active element MRE consists of ferromagnetic filler parti- cles dispersed in an elastomer matrix. Other than magnetic influence, the MRE dynamic properties are influenced by amplitude of excitation and frequency under passive and magnetized conditions, due to its physical structure being particulate composite. This complex behaviour of MRE makes it challenging to develop a mathematical model for an MRE isolator considering all the operating parameters. Furthermore, because the mathematical model for the isolator is unknown, developing control for such conditions becomes more difficult. Present work focused on the design of MRE isolator to regulate micron-level vibra- tions in electronic circuit boards application. The initial methodology involved design- ing the MRE isolator to operate in shear mode. The performance of the isolator was then evaluated through a displacement transmissibility test over a frequency range of 15 Hz to 80 Hz. The test involved varying the input current to the isolator from 0 A to 3 A, as well as the excitation amplitudes from 1.25 mm to 2.25 mm. Performance results show that MRE isolator changes its stiffness under magnetic field, and increases the overall natural frequency of the system. On the other hand, under passive and active conditions, the change in stiffness decreases with the amplitude of excitation. This is due to Payne effect which exists in the particle filled elastomer. Overall, the shift in the natural frequency and relative increase in stiffness decreased from 21.07 Hz to 16.09 Hz and 190.09% to 154.78%, with increasing the amplitude of excitation from 1.25 mm to 2.25 mm. The damping ratio of the MRE isolator increases with increasing current in- put but decreases with increasing excitation amplitude. This behaviour was observed in the passive and active states of the MRE isolator. The decrease or increase in damping is primarily caused by the decrease or increase in friction between the particle and the matrix. According to the results of the performance tests, the designed isolator providesmaximum vibration isolation of approximately 74.12% at 2.25 mm excitation ampli- tude and minimum vibration isolation of approximately 39.04% at 1.25 mm excitation amplitude under 3 A current input. The conventional methods of developing the viscoelastic model involves the estima- tion of the parameters for the steady-state response of the isolator for a single frequency of excitation. To develop a complete mathematical model using this method involves a larger number of experiments as well as time. To overcome this problem, a state- space approach was introduced, which involves the estimation of model parameters for steady-state response of MRE isolator under multiple sweep frequency of excitation. In this approach, initially, a viscoelastic model consisting of Zener and Bouc-Wen elements arranged parallelly was considered. Here, the Zener element in the model was used to predict the viscoelastic properties of the MRE isolator, and the Bouc-Wen element, on the other hand, was used to predict the hysteresis behaviour of the MRE isolator. Once the mathematical model was defined, in the second stage, a linear second-order state- space equation was extracted from experimental data using the MATLAB system iden- tification toolkit. Once the linear state space was determined, the unknown parameter values of the viscoelastic model were estimated by minimising the mean square error between the linear state space and the model response using MATLAB optimization toolkit. Using the known model parameters with respect to current input, a polynomial equation was used to establish a relationship between the viscoelastic model parameter and the current input to the isolator. This state-space approach modelling reduces the number of experiments required to develop the mathematical model for the MRE isolator over a wide frequency range. The model parameters for the different excitation ampli- tudes were estimated based on the Controller Stopping frequency (CS frequency). This reduces the further amount of experimentation, and the polynomial equation was used to establish the relationship between the current input to the isolator and the amplitude of excitation. This relationship equation was used to calculate the viscoelastic model parameter values with respect to excitation amplitude. Hence, the complete mathemat- ical model which consists of all the influencing operating parameter is ready for use in the control development. For effective use of the MRE isolator, a superior control strategy was implemented, and the superior controller chosen based on the following characteristics:• The designed controller should be robust and adaptive to ensure the stability of the system. • Should consider uncertainty in the model parameters. • Should consider the uncertainty in the external environment changes. The previously developed fuzzy controller has the problem of producing control output even when it is isolated. To overcome this problem, a control condition was developed based on the model to control the output of the Fuzzy controller. Another controller, a model-based sliding mode controller (MBSM controller), was also devel- oped in addition to the fuzzy controller to produce the desired response at the receiver end. In the simulation, the performance of both model-based controllers was tested us- ing random excitation signals. The test results confirm that the MBSM controller works more efficiently than the fuzzy controller to control the amplitudes of the vibrations. Another model-free controller, the radial basis function neural network sliding mode controller (RBSM controller), was also developed. The unknown model was estimated by a radial basis neural network in this controller, and the sliding mode controller was the primary controller that produced the control input to the isolator. Ten neurons were considered for ten conditions, and the desired output was generated using the radial basis function neural network sliding mode controller (RBSM controller). The simulation re- sults show that the RBSM controller works properly in all ten conditions. An additional set of conditions were also considered when testing the effectiveness of the controller; the results confirm that the RBSM delivers the desired output as expected.