EEE $441$

DISCRETE TIME CONTROL SYSTEMS

ASSIGNMENT

A discrete$-$time digital controller for a DC motor system is required to be designed. The motor's dynamics are represented by the following transfer function:

$\frac{(s)}{V(s)}=\frac{k_b}{(sL+R)(sJ+B)+k_b{k}_m}$

Where:

$(s)$ is the Laplace transform of output signal $(t),$ where $$ is the angular velocity of motor,

$,V(s)$ is the Laplace transform of input signal $v(t),$ where $v$ is the voltage applied to the motor,

$k_b$ is the back EMF constant,

$k_m$ is the torque constant,

$L$ is the inductance of the motor,

$,R$ is the resistance of the motor windings,

$J$ is the moment of inertia of the rotor,

$,B$ is the damping coefficient.

The parameters of the DC motor to be controlled are as follows: $R=1\mathrm{.}0,L=0\mathrm{.}5H,k_b=0\mathrm{.}02,k_m=0\mathrm{.}02,J=0\mathrm{.}02kg.m^2,B=0\mathrm{.}2Nms.$

You are required to design a discrete$-$time digital controller that will regulate the DC motor system such that the following performance criteria are met for a unit step input:

Overshoot $(M_p)$ : The maximum overshoot should not exceed $4\mathrm{.}3\%.$

Peak Time $(t_p)$ : The peak time should not exceed $2$ seconds.

Steady$-$State Error $(e_{ss})$ : The steady$-$state error must be less than $0\mathrm{.}01.$

Once the controller is designed, use MATLAB to simulate the closed$-$loop system with a unit step input. You should:

Plot the step response of the closed$-$loop system.

Evaluate the system's performance, including the overshoot, peak time, and steady$-$state error.

Ensure that the system satisfies the required specifications.