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# EE 350 Control Systems Assignments

## Assignment 1: Modeling of a dynamic system

1.1 The figure 1.1 describes a schema (physical realization) of a room temperature control system. Draw the block diagram of it.

Fig 1.1 Room temperature control system

1.2 Figure 1.2 shows physical realization of elevator control of a high speed jet. Draw the block diagram of it.

Fig 1.2 Elevator control system of high speed jet

1.3 The figure shows a reduction gearbox being driven by a motor that develops a torque $T_m(t)$. It has gear reduction ratio of $n$ and the moments of inertia on the motor and output shafts are $I_m$ and $I_0$, and the respective damping coefficients $C_m$ and $C_0$. Find the differential equation relating the motor torque $T_m(t)$ and the output angular potential $\theta_0(t)$. Gear box parameters are $I_m=5\times10^{-6}kgm^2$, $I_0=0.01kgm^2$, $C_m=60\times10^{-6}Nms/rad$, $C_0=0.15Nms/rad$, $n=50:1$. $a$ and $b$ are pitch circle radii of the gears. Hence the gear reduction ration $n=b/a$.

Fig 1.3 Gear box reduction