Research Papers

Variable Structure Control of a Mass Spring Damper Subjected to a Unilateral Constraint: Application to Radio-Frequency MEMS Switches

[+] Author and Article Information
Amer L. Allafi

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: allafiam@msu.edu

Premjeet Chahal

Department of Electrical and
Computer Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: chahal@egr.msu.edu

Ranjan Mukherjee

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: mukherji@egr.msu.edu

Hassan K. Khalil

Department of Electrical and
Computer Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: khalil@msu.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received February 12, 2017; final manuscript received December 5, 2017; published online March 7, 2018. Assoc. Editor: Tesheng Hsiao.

J. Dyn. Sys., Meas., Control 140(8), 081004 (Mar 07, 2018) (7 pages) Paper No: DS-17-1081; doi: 10.1115/1.4039153 History: Received February 12, 2017; Revised December 05, 2017

A feedback control strategy is presented for improving the transient response of the ubiquitous mass-spring-damper (MSD) system; the closed-loop system has a small settling time with no overshoot for a step input. This type of response is ideal for MSD systems subjected to a unilateral constraint such as radio-frequency micro-electro-mechanical-system (RF MEMS) switches, which are required to close in a short period of time without bouncing. The control strategy switches the stiffness of the MSD between its nominal value and a negative value, resulting in a hybrid dynamical system. A phase portrait analysis of the hybrid system is carried out to establish the asymptotic stability property of the equilibrium and quantify the transient response. Simulation results are presented using parameter values of a real RF MEMS switch from the literature. As compared to open-loop strategies that are currently used, the proposed feedback control strategy promises to provide comparable switch-closing times with robust performance and eliminate bouncing.

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Grahic Jump Location
Fig. 1

Phase portrait of the mass-spring damper system described by Eqs. (6) and (7) with (a) positive stiffness (α=+1) and (b) negative stiffness (α=−β2)

Grahic Jump Location
Fig. 2

(a) Phase portrait of the hybrid MSD system described by Eqs. (6) and (7) with μ1<λ<0. (b) Phase plane in (a) showing the lines L1, L2, and L3 and zones Z1, Z2, and Z3.

Grahic Jump Location
Fig. 3

Asymptotic convergence of the states (y,y′) of the hybrid MSD system to the origin from different regions in the phase plane: “ftc” and “ac” denote finite time convergence and asymptotic convergence, respectively

Grahic Jump Location
Fig. 4

Variation of nondimensional settling time Ts with ζ for the linear controller in Eq. (2) and the VSC in Eq. (4) with β∈{1.0,2.0,3.0}

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Fig. 5

(a) A metal-to-metal contact RF MEMS switch comprised of a fixed electrode and a cantilevered electrode and (b) equivalent MSD model of the cantilevered electrode

Grahic Jump Location
Fig. 6

Displacement of the cantilevered electrode of the RF MEMS switch for the control input in Eq. (2) with parameter values in Eq. (25) and ζ∈{0.02,1.00}

Grahic Jump Location
Fig. 7

Modified RF MEMS switch: Forces on the cantilevered electrode can be generated in the positive and negative x direction by placing the SPDT switch in configurations A and B, respectively

Grahic Jump Location
Fig. 8

Block diagram for simulation of closed-loop control of RF MEMS switch

Grahic Jump Location
Fig. 9

(a) and (b) Displacement and velocity of the cantilevered electrode in Fig. 7; (c) and (d) voltage applied to the two fixed electrodes to generate a positive and negative force on the cantilevered electrode; and (e) phase plane trajectory of the electrode



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