# Overshoot Control: Determining k to Avoid Overshoot

• peripatein
In summary: Once the closed loop response is boiled down to a quadratic form, it should be straightforward to extract damping.
peripatein
Hello,
Suppose I have the following step response:
ystep(t)=(kP/1+kP)(1-e(-t/τ))
where k is constant and P is the plant.
How may I determine the values of k for which there would be no overshoot?

Last edited:
No takers yet ?

Seems to me you'd have to plug in whatever f(t) describes P and find the damping.

Here are the relevant functions:
P(s)=s^2+a1*s+a0
Y_step(s)=[kP(s)]/[1+kP(s)]
Now, how exactly do I find the values of k which would prevent an overshoot?

you're on the right track...

Laplace Transfer function of plant then is P(s) = s2 + a1s +a0

and when connected to feedback to close the loop takes that form KP/(1+KPh), h being feedback gain

so you'll have to expand that by plugging in P(s) to get Laplace transform of the closed loop,

and multiply that by a step, which in Laplace is 1/s,

which will result in a pretty long fraction
that'll have to be resolved by algebra

but since this looks like a homework problem it'll be quite do-able, for textbooks are that way.

Once the closed loop response is boiled down to a quadratic form it should be straightforward to extract damping.

Now - it was 1965 when i took modern control theory course
and my algebra has grown rusty, if you'll pardon a cheap excuse for not solving this and typing it out in latex.

Above is the approach i'd have used in 1965. I remember struggling with the algebra of this type problems, and still dread them.
Hopefully someone who's fresh will chime in now, i wanted to prime the pump for you. Could be they're teaching an easier method nowadays.

peripatein said:
... Suppose I have the following step response:
ystep(t)=(kP/1+kP)(1-e(-t/τ))
where k is constant and P is the plant ...

This looks an awful lot like you're mixing up frequency- and time-domain expressions. I assume P is a (complex-valued) transfer function. How did you arrive at this expression?

peripatein said:
Here are the relevant functions:
P(s)=s^2+a1*s+a0
Y_step(s)=[kP(s)]/[1+kP(s)] ...
Are you sure you have the right P(s)? I ask because it's not a proper transfer function, i.e. it cannot represent any physically realizable system, which is a tad unusual in introductory control theory.

## 1. What is "Overshoot Control" and why is it important?

"Overshoot Control" is a method used in control systems to prevent a system from exceeding its desired output value. It is important because overshooting can lead to instability and potentially damaging results in a system.

## 2. How is "k" determined in Overshoot Control?

"k" is determined using mathematical calculations and analysis of the system's parameters and desired output. It is typically found through trial and error, adjusting until the desired output is achieved without overshooting.

## 3. What are some factors that can affect Overshoot Control?

The factors that can affect Overshoot Control include the system's initial conditions, the system's gain, and the desired output value. Changes in any of these factors can impact the amount of overshoot in the system.

## 4. Can Overshoot Control be completely eliminated?

No, Overshoot Control cannot be completely eliminated. In most systems, some level of overshoot is necessary for proper functionality. However, it can be minimized through careful tuning and adjustments.

## 5. How can Overshoot Control be optimized?

Overshoot Control can be optimized by fine-tuning the system's parameters and using advanced control techniques such as PID (Proportional-Integral-Derivative) control. It is also important to consider the system's response time and adjust accordingly to achieve the desired output without excessive overshoot.

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