networks () and some other random optimization methods incorporated
with statistical techniques (, ) are employed for their well known ro-
bustness property to the error of objective function and ability of global search.
Simplex method () and Sequential Quadratic Programming (SQP) ()
have been used to find the optimal controller within a convex sub-region of
One advantage of numerical search method is that the cost function C can
be of any type, such as ITAE, the Integral of the Time multiplied by the
Absolute value of the Error, or a combination of probability of the stability,
phase margin, time responses, etc, and is not limited to the quadratic cost
functions or desired pole locations which yield closed-form solutions. When the
field of search is suﬃciently wide, non-gradient based method do not get stuck,
but a gradient algorithm may, for complex cost functions with a multitude of
local minima. For the case of RNS algorithm it also has the advantage of being
very simple to implement. Its main steps are given below:
1. The designer initiates the random search by defining the limits of the
search space D.
2. A random number generator selects points d k within D,wherek =
1, 2, ···,N s , is the number of search points.
3. The value of J(d k ) is tested for each k, and the point giving the lowest
value is taken to be the estimate of the global minimizer, d ∗ .
However, non-gradient based methods are typically slow and need many
iterations to find the optimal or near optimal solution even in a relatively small
region. A practical approach is to search in a wider space and successively zoom
in to a smaller space which contains the optimal point.
If the performance surface is convex within the allowable region of controller
parameters, response surface method  or gradient based method  can
be used to find an optimal solution. Other application examples include FIR
filter optimization using LMS method, iterative learning control for runout
compensation, see   ,  and the references therein. There
has been some study on whether the controller should adapt to the controlled
output (which could be the true PES containing RRO and NRRO, or NRRO
only), or measured output which is the measured PES that contains both RRO
and NRRO and sensing noise .
The next few sections of this chapter provide an insight of the control
problem for HDD servomechanism with the help of a few different design ap-
proaches. A simple PID type controller is first designed and its limitations to
meet the requirements for high bandwidth are explained. Different methods
are suggested to deal with the actuator resonances so that the bandwidth can
be extended to meet design specifications. Given this basic control design, we
then discuss the factors that limit the performance of the HDD servo system.