AE$452/$ME$452$: Control System Design

Homework Assignment #$2$

Due date: $\frac{10}{02}\frac{?}{2024},11$:$59pm$ MT

MATLAB Problem $2(500$ pts$)$: Repeat Problem $1$ using MATLAB, assume $K=K_2=1$ and $K_l=10.$

a$)$ Determine the closed$-$loop transfer function $T(s)=Y\frac{s}{R}(s),$ assume $T_d(s)=0.$

b$)$ Determine the sensitivity of the transfer function with respect to small changes in $K_l$ and $K.$

c$)$ Determine the steady$-$state error for a step input $R(s)=\frac{1}{s}.$

d$)$ Determine the steady$-$state error due to a disturbance $T_d(s)=\frac{1}{s}($assume $R(s)=0).$

e$)$ Calculate the response $y(t)$ for a unit step input when $K=K_2=1$ and $K_l=10,$ assume $T_d(s)=0.$

Nict...hhanna

rigure $1$: Depth control system. Please help with MATLAB code. AE$452/$ME$452$: Control System Design

Homework Assignment #$2$

Due date: $\frac{10}{02}\frac{?}{2024},11$:$59pm$ MT

MATLAB Problem $2(500$ pts$)$: Repeat Problem $1$ using MATLAB, assume $K=K_2=1$ and $K_l=10.$

a$)$ Determine the closed$-$loop transfer function $T(s)=Y\frac{s}{R}(s),$ assume $T_d(s)=0.$

b$)$ Determine the sensitivity of the transfer function with respect to small changes in $K_l$ and $K.$

c$)$ Determine the steady$-$state error for a step input $R(s)=\frac{1}{s}.$

d$)$ Determine the steady$-$state error due to a disturbance $T_d(s)=\frac{1}{s}($assume $R(s)=0).$

e$)$ Calculate the response $y(t)$ for a unit step input when $K=K_2=1$ and $K_l=10,$ assume $T_d(s)=0.$

Nict...hhanna

rigure $1$: Depth control system.