Control Tutorials for MATLAB and Simulink (2024)

The step function is one of most useful functions in MATLAB for control design. Given a system representation, the response to a step input can be immediately plotted, without need to actually solve for the time response analytically. A step input can be described as a change in the input from zero to a finite value at time t = 0. By default, the step command performs a unit step (i.e. the input goes from zero to one at time t = 0). The basic syntax for calling the step function is the following, where sys is a defined LTI object.

step(sys)

Contents

  • Changing the magnitude of the step
  • Specifying the time scale
  • Saving the response
  • Step response of discrete-time systems

This command will produce a series of step response plots, all on the same figure. A plot will be made for each input and output combination. Most systems you will come across in the beginning will be SISO or Single-Input, Single-Output. In this case, there will be only one plot generated. However, the step command can also accept MIMO, Multiple-Input, Multiple-Output, systems.

For example, suppose you want to model a mechanical system consisting of a mass, spring, and damper, with an applied force. You can derive the transfer function shown below. You wish to see what the system response to unit step input is (an applied force of 1N). To model this, enter the following code into a new m-file. Running this script in the MATLAB command window will generate a plot like the one shown below.

 M = 1; % units of kg K = 10; % units of N/m B = 2; % units of N-s/m num = 1; den = [M B K]; sys = tf(num,den) step(sys);
sys = 1 -------------- s^2 + 2 s + 10 Continuous-time transfer function.

Control Tutorials for MATLAB and Simulink (1)

This figure shows the output response, which is the position of the mass. You can see that in steady-state the mass has moved 0.1 meters (the spring force balances the applied force). The system is underdamped and has overshoot.

Further details regarding the use of the step command for more advanced situations are given below.

Changing the magnitude of the step

So far, we have only dealt with unit step inputs. Suppose the input to our system was not 1 Newton, but in fact 100 Newtons. The step command can accommodate this by multiplying the system by 100 (since we are only dealing with linear systems). For the example above, this is achieved with the following code, which generates the plot shown below.

step(100*sys);

Control Tutorials for MATLAB and Simulink (2)

The plot looks similar to the one above it except that it has been scaled vertically by a factor of 100.

Specifying the time scale

The step response for any LTI object can be plotted with a user-supplied time vector. This vector will specify the time interval over which the step response will be calculated. If the vector is spaced at small time intervals, the plot will look smoother. Specifcally, a specified time vector can be supplied via the second input to the function as shown below.

step(sys,t);

In the above two plots, only the first 6 seconds of the response are shown. Suppose that the first 10 seconds need to be displayed. A time vector can be created to compute the step response over this range. Adding the following commands to your m-file and running will generate the figure shown below.

t=0:0.1:10;step(sys,t);

Control Tutorials for MATLAB and Simulink (3)

As you can see, the plot goes for 10 seconds.

Saving the response

The final note about the step command is that all of the above variations can be used with lefthand arguments. There are two ways to invoke the lefthand arguments, depending on whether or not the time vector was supplied to the step command.

[y,t] = step(sys);

or

[y,t] = step(sys,t);

If the system is in state-space form, then the time histories of the internal states can also be returned.

[y,t,x] = step(sys);

The y vector contains the output response. It has as many columns as outputs and as many rows as elements in the time vector, t. The x vector contains the state response. It has as many columns as states and as many rows as elements in the time vector, t. When used with lefthand arguments, no plot is drawn when the step function is called. You will usually want to put a semicolon after the step command when you invoke it with lefthand arguments; otherwise, MATLAB will print out the entire output, state, and time vectors to the command window. You can plot the output response using plot(t,y) and the state response using plot(t,x).

Step response of discrete-time systems

If the system under consideration is a discrete-time system, step will plot the output as piecewise constant. If the sampling time is unspecified, the output time scale will be in samples. If the sampling time is specified, the time scale will be in seconds. Consider the following example.

num = 1;den = [1 0.5];Ts = 0.1;sys = tf(num,den,Ts)step(sys)
sys = 1 ------- z + 0.5 Sample time: 0.1 secondsDiscrete-time transfer function.

Control Tutorials for MATLAB and Simulink (4)


Published with MATLAB® 9.2

Control Tutorials for MATLAB and Simulink (2024)

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How do I find answers in MATLAB? ›

To view all of your solutions, go to a Problem page and click View my solutions. You can view your solutions in a list or in the Solution Map. If using the list view, you can review the display by selecting a Sort by option.

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Comprehensive introduction to MATLAB and SIMULINK, covering programming basics, vectors, matrices, loops, and functions through illustrative examples for quick learning.

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If you're a novice programmer, you can expect it to take a little longer than if you were a more seasoned programmer. Someone who can afford to devote all their time to MATLAB can finish learning the language in two weeks. If you have a lot of other responsibilities, however, it will take you longer to complete.

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To format the way numbers display, do one of the following:
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Description. S = solve( eqn , var ) solves the equation eqn for the variable var . If you do not specify var , the symvar function determines the variable to solve for. For example, solve(x + 1 == 2, x) solves the equation x + 1 = 2 for x.

Is MATLAB harder than Python? ›

Learning curve: Python is significantly simpler than Matlab and doesn't require as much background knowledge. Matlab is structured in a very logical and comprehensible way but is aimed at users with a deep knowledge of math.

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Engineering - Software & QA Matlab Simulink Developer Salary 1 - 4 years exp.₹4.3 Lakhs ₹2.9 L/yr - ₹8.1 L/yr
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Is MATLAB enough for a job? ›

Conclusion. The industry has some familiar buzz that learning MATLAB will not be a good opportunity for a better career. But this is not fully true. Yes, it is an acceptable reason that salary or company structure will never be able to touch available popular jobs on other programming technologies.

Does NASA use Simulink? ›

A recent experiment at NASA Ames Research Center's Vertical Motion Simulator (VMS) successfully combined a real-time, human in-the-loop architecture with the flexibility of operating in the Simulink® graphical model-based engineering environment.

What is the disadvantage of Simulink? ›

Simulink's drawback lies in its confinement to pre-existing block functionalities, potentially limiting specific needs or requiring adjustments that might not align with desired behaviors or appearances.

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Engineers use MATLAB and Simulink tools to accelerate the design of embedded systems that have interacting components such as video, and user interface features found in phone or game systems.

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Matlab careers are actually on the rise today. It's a very popular programming language. It can be used by a developer, engineer, programmer, scientist, etc. to collect and sort out data, and develop apps, software, and sites.

Is MATLAB a valuable skill? ›

MATLAB is especially important to engineers and scientists as it allows them to express mathematics.

How to check results in MATLAB? ›

View Results in Command Window

The Summary Report link provides access to the Model Advisor Command-Line Summary report. You can review additional results in the Command Window by calling the DisplayResults parameter when you run the Model Advisor.

How do you find the step response in MATLAB? ›

[ y , tOut ] = step( sys , tFinal ) computes the step response from t = 0 to the end time t = tFinal . [ y , tOut ] = step( sys , t ) returns the step response of a dynamic system model sys at the times specified in the vector t .

How do I find something in MATLAB code? ›

Search Using Find Dialog Box

The Find dialog box opens. The search begins at the current cursor position. MATLAB finds the text you specified and highlights it. MATLAB beeps when a search for Find Next reaches the end of the Command Window, or when a search for Find Previous reaches the top of the Command Window.

What is the ANS command in MATLAB? ›

ans is the variable created when an output is returned without a specified output argument. MATLAB® creates the ans variable and stores the output there. Changing or using the value of ans in a script or function is not recommended, as the value can change frequently. ans is specific to the current workspace.

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