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An inverted pendulum has the following TF 60 G(S) = s2 + 36 1. Design a state observer in discrete time. You can use either pole placement or the linear quadratic estimator solutions from MATLAB to get a reasonable speed of response and a stable error system. Show a simulation of the observer performance using SIMULINK and add some noise to the output of G(s). 2. Assume a plant transfer function of as + b (S) Simulate the pendulum model in Simulink with noisy output and a suitable input sequence, to identify the system parameters a,b,c using the batch least-squares method. = s to Compare the values you obtain with the actual in G(s). An inverted pendulum has the following TF 60 G(S) = s2 + 36 1. Design a state observer in discrete time. You can use either pole placement or the linear quadratic estimator solutions from MATLAB to get a reasonable speed of response and a stable error system. Show a simulation of the observer performance using SIMULINK and add some noise to the output of G(s). 2. Assume a plant transfer function of as + b (S) Simulate the pendulum model in Simulink with noisy output and a suitable input sequence, to identify the system parameters a,b,c using the batch least-squares method. = s to Compare the values you obtain with the actual in G(s)