A typical hard disk drive actuator can be modeled quite accurately as a double integrator:
where y is the displacement of the read/write head in micrometer and u is actuator input voltage in volts. The sampling rate used in a typical hard disk drive servo system is about 1kHz, which is equivalent to a sampling period T=1/1000=0.001seconds. It is required to design an appropriate controller such that the resulting closed loop system has an overshoot less than 20% and a settling time of less than 6 milliseconds due to a step reference of 1 micrometer.
Your tasks are to:
1. Design either a digital PD or PI controller that meets the above design specifications using model matching method with:
a) first approach: design a continuous-time controller that meets the design specifications and then discretize it using a bilinear transformation or other discretization technique to obtain digital controller.
b) discretize the continuous- time plant first or directly work on discrete-time plant to design a digital controller using the well known PID framework.
2. Design either a digital PD or PI controller that meets the design specifications using the second approach using root locus method.
3. Show all the detailed design procedures in (1) and (2) and show the simulation results using Matlab/Simulink. (Note: Put attention to the units of measurement when you show simulation results).
4. Use MATLAB commands such as: c2d (to discretize continuous system; with option ‘zoh’ for conventional discretization or ‘tustin’ for bilinear transformation) and other commands.
