You need to work in case study simulation project of non-linear mechatronics system either Multi-Input Multi-Output (MIMO) system or Single-Input Single-Output (SISO) system. Each group (up to three students) needs to find a nonlinear system (systems related to actual and practical engineering applications are encouraged). You may choose any nonlinear dynamical system from any reference (textbook, research article, etc.). Please make sure that you have all the parameters of the selected system form reliable source of information (make sure to cite your references). Once you have selected one dynamical system, the modeling and simulation of the system can be achieved by completing the following steps: 1) Derive a set of governing equations that describes the dynamics of the system. 2) Determine the equilibrium points of the system and derive the linearized models of the system around the equilibrium points. 3) Represent the linearized model in state-space form: 4) Obtain the transfer functions associated with state-space model (find the transfer function associated with each input-output pair). 4) obtain analogous system representation in mechanical and electrical format. 5) Simulate and plot the open-loop state variables in response to different initial conditions and external inputs. (solution of state and output equations using Matlab software). 6) Simulate and plot the closed-loop state variables in response to different feedback Gain K Vector (you may use Matlab software) 7) Study the effect of fluctuation in system parameters (parameters of your mathematical model) on the stability of the system. (you may use MATLAB software