Calculating rise time, settling time and overshoot for liquid tank level controller

[topcat123]

Homework Statement

This is the second part my problem. In the first part the Open Loop and Closed loop TF where worked out from design parameters. In later questions a lead or lag commentator is needs to be designed.

Design an appropriate controller to ensure the steady state
error in the liquid level in the tank when it undergoes a step
change is always less than ±0:5%. The settling time and
overshoot of the system response should also be less than
1:5 seconds and 5%, respectively.

I am unsure on how to calculate these parameters.

Homework Equations

The system is a negative unity feedback.

The Attempt at a Solution

Open loop TF
$$G(s)=\frac{0.213}{s(0.66s+3.5)+1}$$
Closed Loop TF
$$G(s)=\frac{0.213}{s(0.66s+3.5)+1.213}$$

Using the Steady Stat Error $(e_{ss})=0.005$to work out the gain for the controler
$$e(s)=\frac{R(s)}{1+KpG(s)}$$
With A step $\frac{1}{s}$
$$e(s)=\frac{\frac{1}{s}}{1+KpG(s)}$$
As $\lim_{ss \rightarrow \infty} e(t)=\lim_{s \rightarrow 0} se(s)=0.005$
$s=0$
Therefor
$$0.005=\frac{s\frac{1}{s}\left[s(0.66s+3.5)+1\right]}{s(0.66s+3.5)+1+0.213Kp}$$
Giving A $Kp=934.27$
How do I calculate the rise time, peak overshoot and the settling time.

Any tips or help would be appreciated.
Thanks
Tim

 

[FactChecker]

The only thing I have ever seen is to plot its time response to a step input and determine those numbers from the graph.

 

[topcat123]

Plot it how? Bode, Root locus.

 

[FactChecker]

Plot it how? Bode, Root locus.

No. Plot the response signal versus time. Feed a step function into the transformation and measure how it responds in time. All the requirements you listed in your post #1 can be measured by looking at the plot of response versus time.