Now repeat the process on a different data set that potentially has different system

parameters $($n$1,$ d$3$ d$2$ and d$1).$ Read the SEA$\_$speed.csv data and repeat Tasks $4\mathrm{.}3$ and $4\mathrm{.}4$ for this

data. Record your estimated parameter values.

i need help doing this. $\%$ Define a function to compute the step response error for given parameters

function err $=$ cost$\_$function$($params$,$ SEA$\_$time, SEA$\_$speed$)$

N$1=$ params$(1)$;

D$3=$ params$(2)$;

D$2=$ params$(3)$;

D$1=$ params$(4)$;

$\%$ Define the transfer function based on these parameters

s $=$ tf$(\text{'}$s$\text{'})$;

TF$\_$speed $=($N$1*$ s$)/($s$^4+$ D$3*$ s$^3+$ D$2*$ s$^2+$ D$1*$ s$)$;

$\%$ Simulate the response to a $2$V step input

$[$y$,$ ~$]=$ step$(2*$ TF$\_$speed, SEA$\_$time$)$;

$\%$ Compute the error $($sum of squared differences between simulated and actual$)$

err $=$ sum$(($y $-$ SEA$\_$speed$).^2)$;

end

$\%$ Initial guess for the parameters $($based on "near" values$)$

initial$\_$guess $=[4600,150,900,40000]$;

$\%$ Load the experimental speed response data

load$(\text{'}$SEA$\_$speed.mat'$)$; $\%$ Loads SEA$\_$speed and SEA$\_$time

$\%$ Perform parameter estimation using fminsearch

opt$\_$params $=$ fminsearch$($@$($params$)$ cost$\_$function$($params$,$ SEA$\_$time, SEA$\_$speed$),$ initial$\_$guess$)$;

$\%$ Display the optimized parameters

disp$(\text{'}$Estimated Parameters:$\text{'})$;

disp$([\text{'}$N$1=\text{'},$ num$2$str$($opt$\_$params$(1))])$;

disp$([\text{'}$D$3=\text{'},$ num$2$str$($opt$\_$params$(2))])$;

disp$([\text{'}$D$2=\text{'},$ num$2$str$($opt$\_$params$(3))])$;

disp$([\text{'}$D$1=\text{'},$ num$2$str$($opt$\_$params$(4))])$;

$\%$ Now simulate the response using the optimized parameters and plot the result

N$1\_$opt $=$ opt$\_$params$(1)$;

D$3\_$opt $=$ opt$\_$params$(2)$;

D$2\_$opt $=$ opt$\_$params$(3)$;

D$1\_$opt $=$ opt$\_$params$(4)$;

$\%$ Define the optimized transfer function

s $=$ tf$(\text{'}$s$\text{'})$;

TF$\_$speed$\_$opt $=($N$1\_$opt $*$ s$)/($s$^4+$ D$3\_$opt $*$ s$^3+$ D$2\_$opt $*$ s$^2+$ D$1\_$opt $*$ s$)$;

$\%$ Simulate the system's response with optimized parameters

$[$y$\%\%$ Task $4\mathrm{.}4$: Comparing Step Responses

s $=$ tf$(\text{'}$s$\text{'})$;

TF$\_$speed$\_$opt $=($N$1\_$opt $*$ s$)/($s$^4+$ D$3\_$opt $*$ s$^3+$ D$2\_$opt $*$ s$^2+$ D$1\_$opt $*$ s$)$;

$\%$ Simulate the system's response with optimized parameters

$[$y$\_$opt, t$\_$opt$]=$ step$(2*$ TF$\_$speed$\_$opt, SEA$\_$time$)$;

$\%$ Plot the optimized response and experimental data

figure;

plot$($t$\_$opt, y$\_$opt, $\text{'}$r$\text{'},$ 'LineWidth', $1)$; $\%$ Optimized response in red

hold on;

plot$($SEA$\_$time, SEA$\_$speed, $\text{'}$b$\text{'},$ 'LineWidth', $1)$; $\%$ Experimental data in blue dashed line

legend$(\text{'}$Optimized Simulated Response', 'Experimental Data'$)$;

xlabel$(\text{'}$Time $($s$)\text{'})$;

ylabel$(\text{'}$Speed $($rad$/$s$)\text{'})$;

title$(\text{'}$Comparison of Optimized Simulated Response and Experimental Data'$)$;

grid on;

$\%$ Plot the response from Task $4\mathrm{.}2$ for comparison

$\%$ Redefine the near system transfer function

TF$\_$speed$\_$near $=($N$1*$ s$)/($s$^4+$ D$3*$ s$^3+$ D$2*$ s$^2+$ D$1*$ s$)$;

$\%$ Simulate the response for the near system

$[$y$\_$near, t$\_$near$]=$ step$(2*$ TF$\_$speed$\_$near, SEA$\_$time$)$;

$\%$ Plot the near system response

figure;

plot$($t$\_$near, y$\_$near, $\text{'}$g$\text{'},$ 'LineWidth', $1)$; $\%$ Near system response in green

hold on;

plot$($SEA$\_$time, SEA$\_$speed, $\text{'}$b$\text{'},$ 'LineWidth', $1)$; $\%$ Experimental data in blue dashed line

plot$($t$\_$opt, y$\_$opt, $\text{'}$r$\text{'},$ 'LineWidth', $1)$; $\%$ Optimized response in red

legend$(\text{'}$Near System Response', 'Experimental Data', 'Optimized Simulated Response'$)$;

xlabel$(\text{'}$Time $($s$)\text{'})$;

ylabel$(\text{'}$Speed $($rad$/$s$)\text{'})$;

title$(\text{'}$Comparison of Near System, Optimized Simulated Response, and Experimental Data'$)$;

grid on;