1. Write the SS equations for the plant in controller canonical form. 2. Determine if the plant is controllable. 3. Sketch the simulation diagram for the plant and controller showing the state feedback loops. 4. Determine the characteristic equation of the plant with full state feedback. Note: This equation will be a function of the feedback gains ki. 5. Determine the desired characteristic equation the system to meet the transient response specifications. Hint: (i) Determine the desired , and n . (ii) Then place the third pole ten times further from the imaginary axis. 6. Determine the necessary feedback gains K = [k1, k2, k3]. 7. Using Matlab, plot the response of the plant with full state feedback to a unit step input and indicate on the plot the actual % overshoot and settling time.

In part one of the project a proportional controller was designed for an antenna positioning system. Part two of this project requires the design a State Feedback Controller for the same antenna positioning system. Setting the pre-amplifier gain to 200, provides the plant closed loop transfer function shown below. U(s) = 0;() Y(S) = 0.(S) 1326 G(s)=- s+101.7s? +171s +1326 Problem: Using the simplified block diagram of the plant for the antenna system shown above, design a full state feedback controller to yield a 10% overshoot, and a 2% setting time of 1 second. Place the third pole of the system 10 times further from the imaginary axis than the second order dominant pole. In part one of the project a proportional controller was designed for an antenna positioning system. Part two of this project requires the design a State Feedback Controller for the same antenna positioning system. Setting the pre-amplifier gain to 200, provides the plant closed loop transfer function shown below. U(s) = 0;() Y(S) = 0.(S) 1326 G(s)=- s+101.7s? +171s +1326 Problem: Using the simplified block diagram of the plant for the antenna system shown above, design a full state feedback controller to yield a 10% overshoot, and a 2% setting time of 1 second. Place the third pole of the system 10 times further from the imaginary axis than the second order dominant pole