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For a design project in a Control course, my classmates and I must create a Controller that steers an unknown system to a given trajectory within certain constraints. The system is given to us in Matlab, and we use Simulink to observe the output of the system when given an input of our choice. As we can only observe the input-output behaviour of our nonlinear, time-variant system, we have come up with a Transfer Function that heuristically models our system behaviour (by creating a Bode plot). A snapshot of our Simulink model can be seen here.

Currently, we are investigating a closed-loop feedback approach, and we have found that our system is tending towards zero whenever given a constant input. The function we wish to mirror is a simple step function, with a step size of 1. However, we find that our system error always tends toward one instead of zero, and it does not follow the input trajectory at all.

We have considered pole-cancelling and PID controllers, and have been unsuccessful so far. Does anyone have an idea of an approach to use that would stop our system from tending towards zero?

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With this controller

$$ C=\frac{0.001(s+100)}{s(s+1)(s+0.001)} $$

you get very close to the bandwidth limit imposed by the right-hand-planes zeros of your plant.

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