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# EE 350 Control Systems Assignments

## Assignment 1: Modeling of a dynamic system (cont'd...)

1.7 Obtain the transfer function $E_0(s)/E_i(s)$.

Fig 1.7 Electronics circuit with impedance

1.8 Derive the transfer function of the following systems.

Fig 1.8 Electronics realization of control blocks

1.9 Obtain the TF of the following systems.

Fig 1.9 Electronics circuits

1.10 A Solenoid valve is shown in the figure below. The coil has the electric resistance of $4\Omega$ and an inductance of 0.6H and produce the electromagnetic force $F_c(t)=K_c\times i(t)$. The valve has the mass of 0.125kg and the liner bearings produce a resistive force of $C\times u(t)$. The value of $K_c$ and $C$ are 0.4N/A and 0.25Ns/m respectively. Deduce the over all differential equation relating the input voltage $v(t)$ to the output velocity $u(t)$.

Fig 1.10 Solenoid valve