Ref/Def CW2 – Control of Non-linear Systems

Answer the following question using the worksheet provided. Scan both your answers including the worksheet and upload to Studynet in the usual way.

a) Assuming a linear model, the theoretical open loop frequency response data for a thrust vector controlled projectile is given in the Table 1.

Table 1 – Open loop frequency response data

Plot this data on the Nyquist plot on Worksheet attached. Explain what terms gain margin and phase margin mean. Hence determine the gain and phase margins and state whether the closed loop will be stable.

b) The actuator that controls the direction of the thrust is non-linear. What assumptions must be made if a describing function is to be used to model this type of actuator?

Hence, if a non-linear bang-bang method of guidance is used such that the actuator that changes the direction can either give +4 degrees or -4 degrees for the thrust vector angle relative to the projectile body, draw an appropriate input vs output curve to describe the non-linearity.

c) The describing function for the actuator is:

Plot the -1/N curve on the Nyquist plot on Worksheet for a range of input amplitudes 1 < X < 5.

d) Explain how Nyquist Stability Criterion for linear systems has to be modified for nonlinear systems. What is a limit cycle? Hence determine the magnitude and frequency of the limit cycle.

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