controller with a sampling frequency of 4 kHz is used for the feedforward and feedback controllers, which is in the form of 

$$K_{{}_{p}}=K_{{}_{f}}\Bigg{(}\frac{z+f\!\!\!/_{1}}{z+f\!\!\!/_{2}}\Bigg{)}\hskip56.905512ptK_{{}_{s}}=K_{{}_{b}}\Bigg{(}\frac{z+f\!\!\!/_{1}}{z+f\!\!\!/_{2}}\Bigg{)}\tag{17}$$

respectively. The control objective during the tracking in HDD is to follow the destination track with a minimum tracking error. Note that only time domain performance specifications are considered in this paper, and the design task is to search for a set of optimal controller parameters 
{Kf, Kb, ff1, ff2, fb1, fb2**} such that the HDD servo system meets all design requirements. These** 
requirements are that overshoots and undershoots of the step response should be kept less than 5% 
since the head can only read or write within r**5% of the target; the 5% settling time in the step** 
response should be less than 2 milliseconds and settle to the steady-state as quickly as possible (Goh et al. 2001). Besides these performance specifications, the system is also subject to the hard constraint of actuator saturation, i.e., the control input should not exceed r**2 volts due to the** 
physical constraint on the VCM actuator. 

![0_image_0.png](0_image_0.png)

The multi-objective evolutionary algorithm (MOEA) proposed in this paper has been embedded into a powerful GUI-based MOEA toolbox (Tan et al. 2001b) for ease-of-use and for straightforward application to practical problems. The toolbox is developed under the Matlab (The Math Works, 1998) programming environment, which allows users to make use of the versatile Matlab functions and other useful toolboxes such as Simulink (The Math Works, 1999). It allows any trade-off scenario for MO design optimization to be examined effectively, aiding decision-making for a global solution that best meets all design specifications. In addition, the toolbox is equipped with a powerful graphical user interface (GUI) and is ready for immediate use without much knowledge of evolutionary computing or programming in Matlab. A file handling capability for saving all simulation results and model files in a Mat-file format for Matlab or text-file format for software packages like Microsoft Excel is also available in the toolbox. Through the GUI window of MOEA toolbox, the time domain design specifications can be conveniently set as depicted in Figure 25, where Tr, OS, Ts, SSE, u and ue **represents the rise time, overshoot,** settling time, steady-state error, control input and change in control input, respectively. 