Open Loop Analysis For Aircraft Pitch Control
With Pitch angle input of 0.15 radians
Below is the Simulink model for the open-loop control system given in the question.
By running the simulation multiple numbers of times, it is observed that the output reaches a steady state value somewhere around 650-700seconds. So, the simulation is run for 1000 seconds.
Below are the block parameters for the Actuator and aircraft blocks.
The block parameters for the block theta_dot_d for pitch angle input of 0.15 radians is
Since the simulation is run for a very long duration, we need to set the configuration parameters appropriately to view the desired results.
Below is the output on the scope window for the 1000 second duration.
The steady state value is found to be at 0.7424 on the display block of the Simulink model.
In order to get the accurate results, we need to zoom in to the data of the scope and check the values by using the 'Cursor Measurement' option on the scope window.
Rise Time (tr)
It is the time taken for the output to rise from 10% to 90% of the steady-state value.
In order to properly measure the rise time, we will zoom into five to six seconds and measure the times when the output is 10% and 90% of the steady state value and obtain the difference. From the below figure, we can see that the rise time is around 860 milliseconds.
Settling Time (ts)
It is the time by which the output settles within the 2% envelope of the steady-state value. In our case, the 2% envelope is 0.7276 to 0.7572. From the below figure, we can see that the settling time is around 617 seconds.
Peak time (tp) and Overshoot (OS)
The first peak occurs within the first 25 to 30 seconds. So, we will zoom into that duration (0 to 30 seconds). Peak time is the time by when the output reaches the maximum output for a given input and will trace back to the steady state value. Overshoot is the amount by which the peak differs from the steady-state value.
We will measure the time at which the output reaches the peak and the output after 1000 seconds. The difference between the outputs at these times gives the overshoot. From the below figure we can see that the peak occurs at a peak time of 15.808 seconds and the peak overshoots the steady-state value by 6.379radians
Open Loop Analysis For Aircraft Pitch Control With Pitch angle input of 0.15 radians Open Loop...
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