# What is Step response: Definition and 39 Discussions

The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from zero to one in a very short time. The concept can be extended to the abstract mathematical notion of a dynamical system using an evolution parameter.
From a practical standpoint, knowing how the system responds to a sudden input is important because large and possibly fast deviations from the long term steady state may have extreme effects on the component itself and on other portions of the overall system dependent on this component. In addition, the overall system cannot act until the component's output settles down to some vicinity of its final state, delaying the overall system response. Formally, knowing the step response of a dynamical system gives information on the stability of such a system, and on its ability to reach one stationary state when starting from another.

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1. ### Engineering First Order RL Circuit: Finding a Current I2(0-)

I shorted the inductor and performed mesh analysis. The solutions to the linear system were done using a calculator. The book says that the value for i2(0-) should be 15 mA but I'm getting -2mA. What am I doing wrong? I'm completely confused. Maybe mesh isn't the most efficient way to find I2...
2. ### Engineering Step response of RC circuit with independent voltage and current sources

Dear PF, In the figure down below is Q7.47 which asks to determine the voltage v(t) across the capacitor for t > 0. Since it is given that V(0) = 0 there are two scenario's which is between time interval 0 < t < 1 and t > 1 according to the independent sources. For the scenario 0 < t < 1 the...
3. ### Physical/conceptual reason for inductor voltage step response

I'm trying to understand the physical reason why when you drive an ideal inductor (no series resistance) with an ideal voltage step input (no series resistance), e.g. some Vin(t) = V0u(t), the output current will be a linear ramp. I can see how to derive this from the inductor equation, v = L...
4. ### MATLAB Ltiview and negative step response of a linear system

Hi, my professor gave me I code where he used to evaluate the answer of a linear system to a step increase in the input variables like this: MySystem = ss(A, B, C, D); ltiveiw('step', MySystem, 'r-', 300); My problem is that with this code I get the response only for a positive step. I'd...
5. ### Step Response Characteristics in Simulink

I have a system that I have built in Simulink with a step input and scope output. I would like to measure the peak overshoot, settling time etc. In Matlab this can be done using the 'step' command and generating the characteristics from the Figure window. Is there a way of getting the same...
6. ### Impulse reponse from step response

Homework Statement Homework Equations Derivative of step response is impulse response The Attempt at a Solution [/B] I marked A cause it matches the other coefficients. But where does 9 come from in the last term. I tried with laplace and got the last term as 9. But how to get that in time...
7. ### Step Response from the Impulse Response

Homework Statement Homework Equations Use Laplace then multiply in laplace domain then do laplace inverseThe Attempt at a Solution Book answer is A I don't get the first term of eat in option A.[/B]
8. ### Calculating the time taken for the step response of a system

Homework Statement I have worked out the transfer function of a block diagram in 1st order form To = (K/1+ts) and the 2nd part of the question asks to calculate the time for the output temperature to change by 80% when k1=1, k2=2, k3=3 and k4=4 Homework Equations where K = (k1k2)/(k1k2k4+k2k3)...
9. ### Understanding Root Locus Method: Stability and Response of Control Systems

Good afternoon people; recently I decided to give a study break from control engineering; now I'm back. I'm studying again control theory and I see some good results. By the way I got stuck in a topic called root locus method. Now my issue is not about how to sketch the root loci graph (BTW I...
10. ### Need help in step response circuit diagram

This isn't a homework question! I posted the question for context purpose. So I understand that at t>0 the switch moves to b. Hence the first circuit diagram (pictured) I understand. However for the 2nd circuit diagram (picture 2) when asked to transform to s domain. Why does this answer...
11. ### Impulse and step response related to the angular position of a spacecraft

Hi! I don't know if I'm in the right forum of this site but I'm trying anyway. I was just wondering if someone could explain how the step- and impulse response is related to an angular position (of e.g. a spacecraft )? Just a little about the theory since I am trying to actually understand...
12. ### Matlab step response. Just need a quick check

Homework Statement Could someone just quickly check my Step Reponse diagram which I made using Matlab. It does not look like the usual shape for a step response system which is making me a bit worried. I'm a fairly new to Matlab and Control Engineering Homework Equations G(s) = 3 / ((s^2) +3)...
13. ### Response of a system (Control theory)

Hi everyone. I'm studying for the exam of control theory, and now I'm having an hard time with the response of a system, in particular when we have oscillations. Suppose you have a system, with a transfer function, say, G(S), in the form: G(S) = 1 -------------------...
14. ### Use convolution integral to find step response of a system

Homework Statement An electrical network has the unit-impulse response :h(t)=3t⋅e-4t .If a unit voltage step is applied to the network, use the convolution integral to work out the value of the output after 0.25 seconds. Homework Equations Convolution integral: y(t)=f(t)*h(t) Unit step...
15. ### Step response of LC circuit

Hi All , I was thinking about the time domain unit step response of ideal series LC crcuit. If both cap and inductor are ideal and unchrged initially and I am looking at voltage across capacitor. Connecting a battery to LC circuit at t=t1 , would the circuit oscillate ? I am not able to...
16. ### Step response time of control system

Homework Statement I'm having a slight problem with the question below. A temperature control process has a first-order response with a step response time of 12 seconds. In selecting a temperature sensor for the control system for the process, for what maximum value of sensor time-constant...
17. ### Why does this step response overshoot?

I have this transfer function which i don't know why it is overshooting due to an step input. http://snag.gy/Vh1SM.jpg Could someone explain why it does that. It's it a close loop transfer function, where I've designed a controller for it, but for some reason, eventhoug all my poles...
18. ### First order unit step response

I think I mostly understand how this works, and it makes intuitive sense. However, I'm a little bit confused by one step in the proving of this. On the second page of the attached PDF, there is this statement: x' + kx = (r/k + c2)δ(t) ... (followed by the cases of t<0 and t>0 What comes...
19. ### Engineering Finding the step response of RL circuit

Homework Statement Homework Equations The Attempt at a Solution I understand everything except how they got i(∞). It seems like they used current division on 3A. But where are they applying current division and where did they get 3A? Also, in the last step, they magically added u(t). Where...
20. ### Use Simulink to check the step response of a control system

1. I have to use Simulink to check the step response of a state feed-back design (controller) and state estimator (observer). I did the problem and got matrices that I need for the desired poles but I'm not sure how to use Simulink to do them.3. I really don't want to post the exact vales to my...
21. ### Natural and step response RLC find iL(t)

Homework Statement The switch in the circuit in the figure has been open a long time before closing at t=0. Find iL(t) t>0 Express your answer in terms of t, where t is in milliseconds. https://www.flickr.com/photos/84781786@N03/8899251427/ The Attempt at a Solution We simplify...
22. ### Engineering Laplace Step Response Circuit Analysis

Homework Statement Shown in attachment Homework Equations The Attempt at a Solution I'm trying to analyze the circuit in the attached picture. This is a step response with a 3V input or 3u(t). What I've done so far is: 1. convert all of the components to the s-domain. R = R, L = sL, C =...
23. ### Drawing the step response of a second order system

Homework Statement I have to draw the step response of the following two systems. G1 = (4+3s)/(s^2+4s+4) G2 = 3/(s^2+4s+4) So I started to draw the step response of the second system first. It has to be in the funky standard form: \frac{ω2}{s2 + 2ζωs + ω2} EDIT: Seems like the above doesn't...
24. ### Unit step response of RC high pass filter

what is the unit step response of a high pass RC filter ? I want to calculate using transfer function approach. My solution : Y(s)/X(s) = RCs/(1+sRC) X(s)=1/s Y(s)=RC/(1+sRC) taking inverse laplace transform we should get y(t)=exp(-t/RC) But if we consider Y(s)=RC/(1+sRC) RCsY(s)...
25. ### Step response to an impulse response

Hi all, I'm having a lot of trouble understanding this step response: Problem statement: Consider an LTIC system with impulse response given by: h(t) = u(t) - u(t-2) Sketch the step response s(t). I've already sketched h(t)...but, I know that the step response is found by...
26. ### Finding Tau and K from unit step response

Homework Statement Simulate the system to look at the output response with a unit step input applied i.e. use the step command. Confirm the values of K and τau from the simulated response are the same as those you have entered into the simulation. Note that the step command can be used with...
27. ### Step response of a LTI system

Homework Statement Calculate the step response of the system (i.e. response to x(n) = u(n) Previously calculated the impulse response becomes h(n) 3/11 (5/8)^{n} u(n) + 5/22(1/8)^{n}u(n) Homework Equations H(z) =\frac{Y(z)}{X(z)} u(n) =\frac{1}{1-z^{-1}} The Attempt at a...
28. ### Unit step response and unit impulse response

In my ODE course I learned that for a time invariant operator p(D), if p(D)x=q(t) then p(D)\dot{x}=\dot{q}(t). Then the professor "justified" that the derivative of the unit step response, v(t), is the unit impulse response, w(t), because the derivative of unit step function is the Dirac...
29. ### Voltage step response of impedance frequency response

Hi I am a bit unsure about terminology and method, so I would like to discuss this with anyone who knows anything about this. I'm examining the properties of a network of parallel capacitors. I have calculated an impedance versus frequency curve, Z(f), using complex impedance of the...
30. ### Step response of a RC circuit asking for i(t)

Homework Statement In attachment Homework Equations i don't understand why it would be asking for the current going through the capcitor, in a dc circuit it should be an open circuit but there will be a voltage over it... after searching through lecture notes and textbook can't find...
31. ### Step response and peak response of a transfer function

Homework Statement The open loop transfer function to a unity negative feedback system is given as: G(s)=50/s(s+10) Homework Equations Unity feedback is used in this problem, and the system input is a step function. Y(s)=50/s(s^2+10s+50) The Attempt at a Solution I have...
32. ### Engineering Help with Step Response of an RC circuit

Homework Statement Derive the Voltage and Current equations for Step Response of an RC circuit. Homework Equations End products will be Vc(t) = i(s)R + (Vo - i(s)R)e^(-t/RC) and i(t) = (Is - (Vo/R))e^(-t/RC) The Attempt at a Solution Using KCL on a hypotetical RC circuit with a...
33. ### Natural response and step response

ok i need some clarification if you have a circuit where a current source is in parallel with an inductor a resistor and a capacitor is this considered a natural response or a step response. I guess i thought a step response is if a switch is switched and a source is added then it is a step...
34. ### Step Response of System with Pole in s = 0 at Infinity

Homework Statement A contininous time system has when laplace transformed, a pole in s = 0. What is de stepresponse for the system when t goes to infinity Homework Equations H(s) is infinity in 0 (H(s) is unit response laplace transformed) s(t) = h(t) * u(t) (the stepresponse is the...
35. ### Step Response of an LTI system

Hi lads, need help with this question from a signals and systems course. LTI system is defined as follows H(s) = \frac{1}{ s^2 - 2rs cos(theta) + r^2} where r = 20pi, theta = 1.47. Find an expression for the step response of the system I think...
36. ### Integration and RC Step response

Integration Homework Statement Hi everyone, I'm new here. This is my first post. I found physicsforums when researching on google a solution for a doubt I've had when trying to solve rc step response. Basically, the RC analyse showed at...
37. ### Step response of a first order system

Homework Statement Find the unit step response of the transfer function... a) G(s)\,=\,\frac{4}{s\,+\,4} b) G(s)\,=\,\frac{2}{0.2s\,+\,1} Homework Equations General first order step response equation... C(s)\,=\,R(s)\,G(s)\,=\,\frac{a}{s(s\,+\,a)}, where R(s)\,=\,\frac{1}{s} then do an...
38. ### Engineering RLC circuit step response time domain

This is more of a math question but i feel like i will get more help among Electrical Engineers. I successfully found the step response of an RC circuit in the time domain using Laplace Transforms. But i can't seem to figure out how to do it with an RLC transfer function. I have the following...
39. ### Unit Step Response: Solving s(t) = e^{-t}u(t) for u(t) - u(t-2)

The step response of an LTI system is given by s(t) = e^{-t}u(t) . Find its response to the input u(t) - u(t-2) . Note: u(t) is the unit step function. So I have the solution, but I do not understand it. y(t) = s(t) - s(t-2) = e^{-t}u(t) - e^{-(t-2)}u(t-2) I really don't...