HW13_09 - command response the final value theorem fails...

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AE361 Stability and Control Homework 13 Work with the code you developed for Problem 12. Extend the MATLAB code to do the following: a) Form the transfer function E(s)/ (s) c θ . c E(s) (s) (s) = θ - θ is the error in the usual sense, but also here is the error at the summing junction. It is what is driving the PID controller and from there the elevator servo. b) Form the transfer function for elevator command deflection c e c (s)/ (s) δ θ . This is the output of the PID controller and drives the elevator servo. c) Use these transfer functions to examine error response and servo command response to a unit step input in c θ . Assume the input command for c θ has an amplitude of 5 degrees. There are at least three ways to examine steady state response. It can be done using the final value theorem in the case of the steady state error. For the steady state elevator
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Unformatted text preview: command response the final value theorem fails because the order of the numerator in the transfer function is higher than the order of the denominator. Annotation on the step response graph also fails for the same reason. It can be done by using the transfer functions and the MATLAB function dcgain . This works for both the error response and the elevator command response. The fail safe method is to extend the time span of the step response and look at the graph at large time. Since this might be hard to read due to scaling of the axes, also print out the points the graph is made from and look at what it approaches at large time. Get the result for elevator command respose at least two ways for verification....
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