The controller utilizes Neural Networks to control a nonlinear dynamic system by tracking a given reference signal. The main goal is to minimize the error between the system output and the desired reference trajectory.
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Reference Model:
- The reference model is defined by the transfer function:
$$G_m(s) = \frac{K}{\frac{1}{\omega_n^2}s^2 + \frac{2\xi}{\omega_n}s + 1}$$ - Generates the desired reference signal.
- Uses the reference input which is given by:
$$r(k) = \sin\left(\frac{2\pi k}{25}\right) + \sin\left(\frac{2\pi k}{10}\right)$$
- The reference model is defined by the transfer function:
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Dynamic System:
- The nonlinear dynamic system is represented by:
$$y(k+1) = \frac{y(k) y(k-1) u(k) + u^3(k) + 0.5 y(k-1)}{1 + y^2(k) + y^2(k-1)}$$
- The nonlinear dynamic system is represented by:
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NN Controller:
- Adjusts the control input to minimize the tracking error.
- Utilizes gradients and parameters of the RBF NN model to update the control signal.
[1] Slema, S., Errachdi, A., & Benrejeb, M. (2018, March). A radial basis function neural network model reference adaptive controller for nonlinear systems. In 2018 15th International Multi-Conference on Systems, Signals & Devices (SSD) (pp. 958-964). IEEE.
