Theįigure below illustrates the control architecture we will employ. In order to stabilize this system and eventually meet our given design requirements, we will add a feedback controller.
Its output continues to grow to infinity in the same manner that an integral of a constant would grow to infinity as the upper Therefore, when the system is given a step input This particular case, the pole at the origin behaves like an integrator. This fact is in agreement with what we have already seen. Unbounded when given an input, even when the input is bounded.
Area between two functions in matlab symbolic toolbox free#
Even though the free response will not grow unbounded, a system with a pole on the imaginary axis can grow A pole on the imaginary axis indicates that the free response of the system will not grow unbounded, but also will Two poles are in the left-half of the complex s-plane. Stability of a system can be determined by examining the poles of the transfer function where the polesĬan be identified using the MATLAB command pole as shown below.Īs indicated by this function, one of the poles of the open-loop transfer function is on the imaginary axis while the other Add the following commands onto the end of the m-file and run it in the MATLAB command windowĪnd you will get the associated plot shown below.įrom the above plot, we see that the open-loop response does not satisfy the design criteria at all. Specifically, we will use the MATLAB command step to analyze the open-loop step response where we have scaled the input to represent an elevator angle input ( ) of 0.2 radians (11 degrees). Now let's see how the uncompensated open-loop system performs. First create a new m-file and type in the following commands (refer to the main problem for the details of getting these commands).
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