188 6 Track Following of a Single-stage Actuator experimental performance. The above discrete-time PID controller is obtained from a continuous-time counterpart using the ZOH method with a sampling frequency of 20 kHz. Once again, we note that the above PID controller is tuned to meet the requirements on the gain and phase margins, and the design specifications on the sensitivity and complementary sensitivity functions. Although the PID control has the simplest structure, its dynamical order, which is 3, is higher than that of the RPT and CNF controllers. As expected, the complete control input is given by (6.29) 6.4 Simulation and Implementation Results In this section we present the simulation and actual implementation results of our de- signs and their comparison. The following tests are presented: i) the track-following test of the closed-loop systems, ii) the frequency-domain test including the Bode and Nyquist plots as well as the plots of the resulting sensitivity and complemen- tary sensitivity functions, iii) the runout disturbance test, and lastly iv) the PES test. Our controller was implemented on an open HDD with a sampling rate of 20 kHz. Closed-loop actuation tests were performed using an LDV to measure the R/W head position. The resolution used for LDV was 2 l um/V. This displacement output is then fed into the DSP, which would then generate the necessary control signal to the VCM actuator. The actual implementation setup is as depicted in Figure 1.7. 6.4.1 Track-following Test The simulation result and actual implementation result of the closed-loop responses for the control systems are, respectively, shown in Figures 6.6 and 6.7. It is noted that the PID control generates large overshoots in both simulation and implementation, while the systems with the RPT and CNF control have very little overshoot. We sum- marize the resulting 5% settling time, which is commonly used in the HDD research community, in Table 6.1. Clearly, the CNF control gives the best performance in the time domain compared to those of the other two systems. Table 6.1. Performances of the track-following controllers Settling time (ms) PID control RPT control CNF control Simulation 3.10 0.95 0.80 Implementation 2.65 1.05 0.85 Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark. 6.4 Simulation and Implementation Results 189 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 Time (ms) Displacement (μm) PID (overshoot 41%) RPT CNF (a) Output responses 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −0.05 0 0.05 0.1 Time (ms) Input signal to VCM (V) PID RPT CNF (b) Control signals Figure 6.6. Simulation result: step responses with PID, RPT and CNF control Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark. 190 6 Track Following of a Single-stage Actuator 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (ms) Displacement (μm) PID (overshoot 31%) RPT CNF (a) Output responses 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −0.05 0 0.05 0.1 Time (ms) Input signal to VCM (V) PID RPT CNF (b) Control signals Figure 6.7. Implementation result: step responses with PID, RPT and CNF control Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark. 6.4 Simulation and Implementation Results 191 We believe that the shortcoming of the PID control is mainly due to its structure, i.e. it only feeds in the error signal, , instead of feeding in both and inde- pendently. We trust that the same problem might be present in other control methods if the only signal fed is . The PID control structure might well be as simple as most researchers and engineers have claimed. However, the RPT controller is even simpler, but it and the CNF controller have fully utilized all available information associated with the actual system. Unfortunately, we could not compare our results with those in the literature. Most of the references we found in the open literature contained only simulation results in this regard. Some of the implementation results we found were, however, very different in nature. For example, Hanselmann and Engelke [18] reported an imple- mentation result of a disk drive control system design using the LQG approach with a sampling frequency of 34 kHz. The overall step response in [18] with a higher-order LQG controller and higher sampling frequency is worse than that of ours. 6.4.2 Frequency-domain Test For practical consideration, it is important and necessary to examine the frequency- domain properties of control system design, which include the results of gain and phase margins and the plots of sensitivity and complementary sensitivity functions. Traditionally, gain and phase margins can be obtained through the Bode plot of the open-loop transfer function comprising the given plant and the controller. However, for the HDD system considered in our design, which has additional high-frequency resonance modes, the corresponding Bode plots might have more than one gain and/or phase crossover frequencies. Thus, it is important to verify the stability mar- gins obtained from the associated Nyquist plots. Figures 6.8 to 6.13, respectively, show the Bode plot, the Nyquist plot, and the sensitivity and complementary sen- sitivity functions, as well as the closed-loop transfer functions (from the reference input to the controlled output ) of the resulting control systems. For the CNF design, which is a nonlinear controller, its frequency-domain functions are cal- culated at the steady-state situation for which the nonlinear gain function has approached its final constant value. The results show that all these designs meet the frequency-domain specifications and have about the same closed-loop bandwidth. 6.4.3 Runout Disturbance Test Although we do not consider the effects of runout disturbances in our problem for- mulation, it turns out that our controllers are capable of rejecting the repeatable runout disturbances, which are mainly due to the imperfectness of the data tracks and the spindle motor speeds, and commonly have frequencies at the multiples of the spindle speed, which is about Hz. We simulate these runout effects by inject- ing a sinusoidal signal into the measurement output, i.e. the new measurement output is the sum of the actuator output and the runout disturbance. Figure 6.14 shows the implementation result of the output responses of the overall control system compris- ing the tenth-order model of the VCM actuator model and the controllers together Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark. 192 6 Track Following of a Single-stage Actuator 10 0 10 1 10 2 10 3 10 4 10 5 −200 −150 −100 −50 0 50 100 Frequency (Hz) Magnitude (dB) 10 0 10 1 10 2 10 3 10 4 10 5 −700 −600 −500 −400 −300 −200 −100 Frequency (Hz) Phase (deg) GM = 16.4 dB PM = 46.5 ° (a) Bode plot −1 −0.8 −0.6 −0.4 −0.2 0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 0 dB −20 dB −10 dB −6 dB −4 dB −2 dB 20 dB 10 dB 6 dB 4 dB 2 dB Real axis Imaginary axis (b) Nyquist plot Figure 6.8. Bode and Nyquist plots of the PID control system Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark. 6.4 Simulation and Implementation Results 193 10 0 10 1 10 2 10 3 10 4 10 5 −200 −150 −100 −50 0 50 100 Frequency (Hz) Magnitude (dB) 10 0 10 1 10 2 10 3 10 4 10 5 −600 −500 −400 −300 −200 −100 Frequency (Hz) Phase (deg) GM = 11.7 dB PM = 35.5 ° (a) Bode plot −1 −0.8 −0.6 −0.4 −0.2 0 0.2 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 0 dB −20 dB −10 dB −6 dB −4 dB−2 dB 20 dB 10 dB 6 dB 4 dB 2 dB Real axis Imaginary axis (b) Nyquist plot Figure 6.9. Bode and Nyquist plots of the RPT control system Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark. 194 6 Track Following of a Single-stage Actuator 10 0 10 1 10 2 10 3 10 4 10 5 −200 −150 −100 −50 0 50 100 Frequency (Hz) Magnitude (dB) 10 0 10 1 10 2 10 3 10 4 10 5 −600 −500 −400 −300 −200 −100 Frequency (Hz) Phase (deg) GM = 8.6 dB PM = 40 ° (a) Bode plot −1 −0.8 −0.6 −0.4 −0.2 0 0.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 0 dB −20 dB −10 dB −6 dB −4 dB −2 dB 20 dB 10 dB 6 dB 4 dB 2 dB Real axis Imaginary axis (b) Nyquist plot Figure 6.10. Bode and Nyquist plots of the CNF control system Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark. 6.4 Simulation and Implementation Results 195 10 0 10 1 10 2 10 3 10 4 10 5 −120 −100 −80 −60 −40 −20 0 Frequency (Hz) Magnitude (dB) T function (max. 3.1 dB) S function (max. 3.1 dB) (a) Sensitivity and complementary sensitivity functions 10 0 10 1 10 2 10 3 10 4 10 5 −200 −150 −100 −50 0 Frequency (Hz) Magnitude (dB) 10 0 10 1 10 2 10 3 10 4 10 5 −800 −600 −400 −200 0 Frequency (Hz) Phase (deg) BW = 514 Hz (b) Closed-loop response Figure 6.11. Sensitivity functions and closed-loop transfer function of the PID control system Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark. 196 6 Track Following of a Single-stage Actuator 10 0 10 1 10 2 10 3 10 4 10 5 −120 −100 −80 −60 −40 −20 0 Frequency (Hz) Magnitude (dB) T function (max. 4.7 dB) S function (max. 5.2 dB) (a) Sensitivity and complementary sensitivity functions 10 0 10 1 10 2 10 3 10 4 10 5 −200 −150 −100 −50 0 Frequency (Hz) Magnitude (dB) 10 0 10 1 10 2 10 3 10 4 10 5 −600 −500 −400 −300 −200 −100 0 Frequency (Hz) Phase (deg) BW = 553 Hz (b) Closed-loop response Figure 6.12. Sensitivity functions and closed-loop transfer function of the RPT control system Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark. 6.4 Simulation and Implementation Results 197 10 0 10 1 10 2 10 3 10 4 10 5 −120 −100 −80 −60 −40 −20 0 Frequency (Hz) Magnitude (dB) T function (max. 3.6 dB) S function (max. 4.9 dB) (a) Sensitivity and complementary sensitivity functions 10 0 10 1 10 2 10 3 10 4 10 5 −200 −150 −100 −50 0 Frequency (Hz) Magnitude (dB) 10 0 10 1 10 2 10 3 10 4 10 5 −600 −500 −400 −300 −200 −100 0 Frequency (Hz) Phase (deg) BW = 576 Hz (b) Closed-loop response Figure 6.13. Sensitivity functions and closed-loop transfer function of the CNF control system Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark. [...]... system 8 Dual-stage Actuated Servo Systems 8.1 Introduction The present demand for large-capacity disk drives is leading to an increase in areal density at a rate of 100% per year This requires a positioning accuracy of the order of a few nanometers The servo bandwidth of the current disk drive actuators makes it very hard to achieve this The VCM actuator used in conventional disk drives has hundreds of... the presence of runouts For actual drives, prewritten PES data might be estimated at high sampling rates using servo sector measurements (see, for example, [141]) In disk drive applications, the variation in the position of the R/W head from the center of the track during track following, which can be directly read off as the PES, is very important Trackfollowing servo systems have to ensure that the... PID controller We note that the results can be further improved if we used a better VCM actuator and arm assembly (such as those used in minidrives and microdrives) with a higher resonance frequency We will carry out a detailed study on the servo system of a microdrive later in Chapter 9 200 6 Track Following of a Single-stage Actuator 4000 3500 4000 PID 3500 4000 CNF RPT 3500 3000 3000 2500 Points... off as the PES, is very important Trackfollowing servo systems have to ensure that the PES is kept to a minimum Having deviations that are above the tolerance of the disk drive would result in too many read or write errors, making the disk drive unusable A suitable measure is the standard A useful guideline is to make the value less deviation of the readings, than of the track pitch, which is about um... Mechanical disturbances include spindle motor variations, disk flutter and slider vibrations Electrical noises include quantization errors, media noise, servo demodulator noise and power amplifier noise NRROs are usually random and unpredictable by nature, unlike repeatable runouts They are also of a lower magnitude (see, e.g., [1]) A perfect servo system for HDDs has to reject both the RROs and NRROs... have simplified the system somewhat by removing many sources of disturbances, especially that of the spinning magnetic disk Therefore, we actually have to add the runouts and other disturbances into the system manually Based on previous experiments, we know that the runouts in real disk drives are composed mainly of RROs, which are basically sinusoidal with a frequency of about 55 Hz, equivalent to the... 8.3 that the actual responses and those of the identified models are matched very well at the frequencies of interest 8.3 Dual-stage Servo System Design We now carry out the design of servo systems for the HDD with a dual-stage actuator Similarly, we would like to design our servo systems to the following constraints and requirements V, whereas the con1 The control input to the VCM actuator does not exceed... less than 0.05 um, l i.e 5% of one track pitch As pointed out earlier, the R/W head of the HDD servo system can start writing data onto the disk when it is within 5% of one track pitch of the target 4 the gain margin and phase margin of the overall design are respectively greater than 6 dB and ; 8.3 Dual-stage Servo System Design 221 5 the maximum peaks of the sensitivity and complementary sensitivity... sampling frequency of 20 kHz Implementations are carried out at a sampling frequency of 20 kHz The results of the dual-stage actuated HDD servo systems will then be compared with those of the servo systems with a single-stage actuator The latter are done on the same drive by keeping the microactuator inactive throughout the whole implementation process The controller parameters for the single-stage actuated... reinforce the integration action Again, the simulation um and implementation results of the servo system with the CNF control law will be presented in the next section for an easy comparison 7.5 Simulation and Implementation Results Now, we are ready to present the simulation and implementation results for all three servo systems discussed in the previous sections and do a full-scale comparison on the performances . actual drives, prewritten PES data might be estimated at high sampling rates using servo sector measurements (see, for example, [141]). In disk drive applications,. used in minidrives and microdrives) with a higher reso- nance frequency. We will carry out a detailed study on the servo system of a micro- drive later