Active DVA

Now, we will consider another active DVA commonly known as proof mass actuator. The basic system is described in Fig. 19.2.

Figure 19.2: Proof mass actuator

A proof mass m_p is connected to a magnetic base with spring k and damper c. The proof mass is placed over a solenoid in which magnetic field could be generated by passing current through coils. The resistance of the coil is R, inductance L, current passing through the coil is i and the proportionality constant corresponding to back EMF is k_b. The EOM are provided below.

Governing equation for electric system

(19.4)

Governing equation for mechanical system

(19.5)

where k_a is the current constant

Converting Equation 19.4 into frequency domain,

	(19.6)

Similarly, from 19.5

Using Equation 19.6 we get

Denoting,
	(19.7)

Also, force exerted by the proof mass actuator on the base is  ,   therefore,  .

Using Equation 19.7

(19.8)

This relationship tells us how force F will be generated by the proof mass accelerator upon application of voltage .