Design Case Studies

Deriving the Model

Using Newton's law, a simple model for the read/write head is the differential equation

where is the inertia of the head assembly, is the viscous damping coefficient of the bearings, is the return spring constant, is the motor torque constant, is the angular position of the head, and is the input current.

Taking the Laplace transform, the transfer function from to is

Using the values kg , Nm/(rad/sec), Nm/rad, and Nm/rad, form the transfer function description of this system. At the MATLAB prompt, type

• J = .01; C = 0.004; K = 10; Ki = .05;
  num = Ki;
  den = [J C K];
  H = tf(num,den)
  

MATLAB responds with

• Transfer function:
           0.05
  -----------------------
  0.01 s^2 + 0.004 s + 10
  

Hard-Disk Read/Write Head Controller

Model Discretization