# EE 350 Control Systems Assignments

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

1.11 The laser guided missile shown in the figure 1.11 has a pitch moment of $90kgm^2$.
The control fins produce the moment about the pitch mass center of $360Nm$ per radian of fin angle $\beta(t)$.
The fin positional control system is describe by a differential equation $0.2 d\beta/dt + \beta(t) = u(t)$, where $u(t)$
is the control signal. Determine the differential equation relating the control signal $u(t)$ and pitch angle $\theta(t)$.

Fig 1.11 Laser guided missile

1.12 A field control DC motor develop the torque of $T_m(t)$ proportional to the field current $i_f(t)$.
The rotating parts have moment of inertia I of $1.5 kgm^2$ and a viscous damping coefficient $C$ of 0.5Nms/rad.
When a current of 1.0 A is passed through the field coil, the shaft finally settles down to a steady speed $\omega_0(t)$ of 5 rad/s.
a. Determine the differential equation relating $i_f(t)$ and $\omega_0(t)$.
b. What is the value of coil constant $K_c$, and what is the torque developed by a motor when a current of 0.5A flows through the field coil?

1.13 In the following figure the cross sectional area of the water tank is A, and under steady conditions both
the outflow and inflow $V_a$ and the head is $H_a$.

a. Under these conditions find an expression for the linearized valve resistance $R_f$ given that the flow through the valve is
$V=A_vC_d \sqrt{2gH}$, Where V=volumetric flow-rate($m^3/s$), $A_v$=Valve flow area($m^2$), $C_d$=coefficient of discharge,
g=acceleration due to gravity($m/s^2$), H=head across the valve(m).

b. If the steady value of the head $H_a$ is 1.5m, what is the valve resistance $R_f$, when, $A_v= 15\times10^{-3}m^2$,
$g=9.81m/s^2$, $C_d=0.6$.

c. Now if the inflow increases an amount $v_1$ producing an increase in head h and an increase in outflow $v_2$, find the
differential equation relating $v_1$ and $v_2$ when the tank cross sectional area A is $0.75m^2$.

Fig 1.12 Hydraulic system

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