![]() Select a choice from the menu to the left for further details. It is apparent from the analysis above that some sort of control will need to be designed to improve the response of the system.įour example controllers are included with these tutorials: PID, root locus, frequency response, and state space. The above results confirm our expectation that the system's response to a step input is unstable. You can also identify some important characteristics of the response using the lsiminfo command as shown. The SI unit of impulse is kg m s1 or N s. Adding the following code to your m-file and running it in the MATLAB command window will generate the plot Impulse is the product of the force F acting on a body and the time t for which the force acts. This using the lsim command which can be employed to simulate the response of LTI models to arbitrary inputs. Since the system has a pole with positive real part its response to a step input will also grow unbounded. In other words, the pole is in the right half of the complex s-plane. The pole at 5.5651 indicates that the system is unstable Likewise, the zeros and poles of the system where the cart position is the output are found as follows: = zpkdata(P_cart, 'v')Īs predicted, the poles for both transfer functions are identical. The zeros and poles of the system where the pendulum position is the output are found as shown below: = zpkdata(P_pend, 'v') ![]() The parameter 'v' shown below returns the poles and zeros as column vectors rather than as cell arrays. We will specificallyĮxamine the poles and zeros of the system using the MATLAB function zpkdata. (MIMO) system will have the same poles (but different zeros) unless there are pole-zero cancellations. In general, all transfer functions from each input to each output of a multi-input, multi-output Since our system has two outputs and one input, it is describedīy two transfer functions. The poles of a system can also tell us about its time response. You can also see that the cart's position moves infinitely far to the right, though there is no requirement on cart position The pendulum's position is shown to increase past 100 radians (15 revolutions), the model is only valid for small. ![]() Add the following commands onto the end of the m-file and run it in the MATLAB command window to get the associated plotĪs you can see from the plot, the system response is entirely unsatisfactory. Specifically, we will examine how the system responds toĪn impulsive force applied to the cart employing the MATLAB command impulse. We can now examine the open-loop impulse response of the system. Create a new m-file and type in the following commands to create the system model (refer to the main problem for the details of getting these We will begin by looking at the open-loop response of the inverted pendulum system.
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