The block diagram for this project is seen to consist of two loops. The system to be
controlled and its actuator represent the plant, which is given by G_{p}(s). All other blocks
shown in the diagram are part of the compensator. The blocks G_{c1} and
G_{c2} are already determined.
The rest of the compensator values have to be determined, using the structure shown in the diagram. Values for the
parameters {M_{e}, T_{1}, T_{2}} are different for each student. The value of
M_{e} ranges from 1.1E+06 to 1.7E+06 pounds mass; the
value of T_{1} ranges from 1 to 3 seconds; and the value of T_{2} also ranges from 1 to 3 seconds.

The output C(s) represents position, and R(s) is the desired position. U(s) is the control signal being applied to
the plant. The outer loop (unity feedback from C(s) to the summing junction) is referred to as the position loop. The
loop that passes through Gc2(s) is referred to as the rate loop. Specifications are imposed on both the rate loop and
the position loop. When considering the rate loop, the position loop is assumed to be open, and the block
G_{c0}(s) is
assumed to be unity. The output of the rate loop is the derivative of the output position. When considering the position
loop, the complete block diagram is used.

**Rate Loop:**

- The phase margin must be at least 30 degrees, and at least 7 seconds of pure time delay must be tolerated by the rate loop without loss of stability;
- The settling time for the unit step response must be less than 200 seconds; and
- The overshoot for the unit step response must be less than 5%.

**Position Loop:**

- The settling time for the unit step response must be less than 500 seconds;
- The overshoot for the unit step response must be less than 10%; and
- The value of the control signal u(t) must fall within the range [-7, +10] at all times when the input is a unit step.

- Design the compensator that will satisfy all specifications;
- Document your design in a written report that describes your design procedure. Include the plots necessary to verify that your design is satisfactory, and include your computer code.

MATLAB is the preferred software to use for this project. Some useful functions are: conv (multiplies polynomials), bode (generates magnitude and phase vs. frequency), logspace (create a logarithmically spaced frequency array), semilogx (makes Bode plots on semilog scale), log10 (common logarithm), step (generates the step response), roots (computes the roots of polynomials), series (combines blocks in series), feedback (combines blocks in feedback configuration), cloop (produces closed-loop transfer function when unity feedback is used), rlocus (makes root locus plots), polyval (evaluates a polynomial at a specified location).

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*Lastest revision on
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