Control of an LTO-3 drive

Transcription

1 Control of an LTO-3 drive I.D. Maassen van den Brink (52234) DCT Traineeship report Coach(es): Supervisor: Prof. Dr. Ir. R.A. de Callafon Prof. Dr. Ir. M. Steinbuch Technische Universiteit Eindhoven Department Mechanical Engineering Dynamics and Control Technology Group Eindhoven, August, 29

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3 Contents 1 Introduction 1 2 LTO-3 tape drive Linear Tape Open technology Operating principle of an LTO drive LTO-3 tape drive System Identification Experimental setup Sensitivity function Process Sensitivity function Actuator Fit LS Model Controller design PID Controller Control design using loop shaping Simulation results Control design using H loop shaping H loop shaping design procedure Reduction of the high order controller Simulation results Real-time implementation of the external controllers Setup Results PID and H controller Conclusions and recommendations 23 References

4 4 CONTENTS

5 Chapter 1 Introduction Motivation The most effective way of storing digital data is data storage on tapes. However, due to the fast increase of capacity and transfer rates of other storage techniques, such as hard disc data storage, improvements have to be made with respect to the performance of tape storage technology. One way of improving this technology is by increasing the capacity of the tapes. Another desired improvement of tape drive technology is the increase of transfer rates of tape drives via high track density recording. Objective The transfer rates of tape drives are proportional to the Lateral Tape Motion (LTM) of the tape drive, which is the main source of disturbances in the writing and reading process. Therefore, accurate control of the disturbance on the tape caused by the Lateral Tape Motion is necessary to improve the performance of the tape drive. The objective of this traineeship research is the design of advanced controllers for the high precision actuator to improve the error correction in LTO-3 drives. The controllers are designed using MATLAB and implemented on an LTO tape drive with the MATLAB Simulink Real-Time Windows Target and a National Instruments data acquisition board. The system identification of the tape drive is realized by MATLAB and Labview. Outline In the first chapter the operating principle of an LTO drive is explained, according to the first generation LTO-1 and the third generation LTO-3 tape drive, followed by the identification of the system in Chapter 3. In Chapter 4 and Chapter 5 two controllers are designed and experimentally tested on the LTO-3 tape drive. The last chapter contains the conclusions and recommendations resulting from this research. 1

6 2 CHAPTER 1. INTRODUCTION

7 Chapter 2 LTO-3 tape drive In this chapter the basics of Linear Tape Open technology and the operating principle of LTO drives is described. 2.1 Linear Tape Open technology Magnetic data storage technology, like tape drives, is a widely used data storage technique in backup systems. Linear Tape-Open (LTO) technology was developed by HP, IBM and Quantum, at which the "open format" technology means that users will have multiple sources of products and media. Figure 2.1 pictures an LTO-3 drive. Figure 2.1: Picture of an LTO-3 drive. 2.2 Operating principle of an LTO drive An LTO tape is divided into four data bands, with in between five servo bands, and two edge guard bands. The tape head fills each data band sequentially by writing data on the 11 data wraps. Two servo bands, on the top and bottom of a data band, provide location information to the head as it 3

8 4 CHAPTER 2. LTO-3 TAPE DRIVE writes and verifies data tracks within that band. With a dual source of servo information a more accurate positioning of the head can be obtained and it also provides tolerance for media defects in the servo area. The servo tracks contain a zigzag pattern, at which the ratio between a and b is a measure for the head position. The head position is converted into a Position Error Signal (PES). The first generation LTO tape contains six servo tracks within each servo band, see figure 2.2. Figure 2.2: Configuration of a LTO-1 tape with head The head of the LTO-1 tape drive contains eight read and write elements, which may be in a stacked, staggered, or arranged in separate modules. Therefore, data can be written on 48 tracks within one data band or on 24 tracks in total. The aligned of the read/write head with the data bands on the tape is done by two actuators, a lead screw for the rough positioning and a voice coil for the suppression of the high frequent disturbances. When an error occurs while writing data on the tape this will immediately be notified by the read element of the head and the block of data is rewritten farther down the tape. The task of the edge guard bands is to protect the data on the outermost bands. 2.3 LTO-3 tape drive The LTO-3 drive is the third generation Linear Tape Open drive. The working principle of this drive is exactly the same as for the LTO-1 drive, but the configuration is different. A tape head containing 16 instead of 8 write and read elements increases the capacity and transfer rates of the tape drive. A LTO-3 tape drive can write data on 74 data tracks in total, at which a single reel of the cartridge can contain up to 4 [Gb].

9 Chapter 3 System Identification The dynamics of a system can be derived from measured Frequency Response Functions with different inputs and outputs. In this chapter, first a simplified model of the tape drive is presented in Section 3.1. In the following two sections the Sensitivity and Process Sensitivity functions are experimentally determined, followed by the derivation of the plant in Section 3.4. Finally a model of the plant is presented in Section Experimental setup The experimental setup of the tape drive can be explained according to the simplified model displayed in the blockdiagram in Figure 3.1. The tape drive is indicated by the plant P (s). The internal digital controller of the plant is modeled as a separate part of the drive, indicated by C i (q), with adjustable loop gain K loop to able and disable the controller. Furthermore, the internal controller consists of a DA converter and a current amplifier β. The digital analogue converters in the system use zero order hold algorithms, resulting in half a sample time step time delay. The external controller C e (q) possesses a AD and DA converter and an unknown gain difference of the external control signal α. The analogue digital converter is assumed to have no time delay. Four signals can be identified in the blockdiagram. The injected reference signal REF, the Position Error Signal (PES), the input current of the voice coils I sense and the disturbance signal caused by the lateral tape motion (LTM). The delay block represents a delay τ d due to the sum- Figure 3.1: Blockdiagram of the experimental setup 5

10 6 CHAPTER 3. SYSTEM IDENTIFICATION mation of REF and the control signal. Lastly, the adjustable gain of the DA converter of the plant for the conversion from voltage to micro meters is indicated by µ. 3.2 Sensitivity function The dynamics of the plant can be derived from measured Frequency Response Functions (FRF s) of the system. Two different FRF s can be determined from the reference input signal (REF) and two output signals, I sense and PES. The first FRF function is the Sensitivity Function of a system, which represents the ratio between the input and the feedback error. The smaller the amplitude of the Sensitivity, the more the disturbances are attenuated at the corresponding frequencies. The amplitude of the Sensitivity can only be made small over a limited frequency, the bandwidth, in order to maintain a stable system. The Sensitivity function can be determined by the transfer function between the input signal REF and the output signal I sense. This transfer Function can easily be derived from the blockdiagram in Figure 3.1 according to: S(s) = αβγe sτ de s T /2 1 + βk loop e s T /2 P (s)c i (e s T ). (3.1) As already mentioned before, the AD converter has no time delay, while the DA converter has half a sample time step time delay due to the ZOH algorithm. The value of the α, β and γ gain is determined in earlier experiments [2]. There is an additional delay due to the summation, which can be determined from the phase shift of the Sensitivity Function and corresponds to one sample time step time delay. The actual frequency response function of the Sensitivity Function can be measured via spectral analysis. Hereto, chirp signals are applied to the tape drive with a small frequency range to obtain a high frequency resolution. The obtained results are shown in Figure 3.2. The amplitude of the Sensitivity function shows a bad noise attenuation between 3 and 15 [Hz].

11 3.3. PROCESS SENSITIVITY FUNCTION 7 Magnitude [db] Frequency [Hz] (a) Amplitude response 25 2 Phase [deg] Frequency [Hz] (b) Phase responsel Figure 3.2: Bode plot of the Sensitivity. 3.3 Process Sensitivity function The Process Sensitivity function can be determined from the reference input signal and the PES output signal according to: P S(s) = αβµe sτ de s T P (s) 1 + βk loop e s T /2 P (s)c i (e s T ). (3.2) Figure 3.2 shows the Process Sensitivity function of the system, obtained by spectral analysis.

12 8 CHAPTER 3. SYSTEM IDENTIFICATION 2 Magnitude [db] Frequency [Hz] (a) Amplitude response 2 Phase [deg] Actuator Frequency [Hz] (b) Phase responsel Figure 3.3: Bode plot of the Process Sensitivity. The dynamics of the plant can be derived from the ratio between the Sensitivity Function and Process Sensitivity Function according to: P (s) = P S S γ µ e e s T /2. (3.3) For control purposes one is interested in the mapping from REF to PES with the DA and AD converter of the data acquisition board included, which results in a plant for experiments P e defined by: P e (s) = αβµ c e sτ d e s T P (s) = P S S αβγ µ c µ e e sτ d e s T /2 (3.4) 3.5 Fit LS Model A model of the through experiments obtained plant FRF is designed with the MATLAB toolbox FREQID, designed by Prof. R.A. de Callafon. This toolbox uses a least square optimization and curve fitting of the complex frequency data to obtain a state space model. The model that fitted the actual data the best is a 5 th order model. The actual calculated plant transfer function data and the model are shown in Figure 3.4.

13 3.5. FIT LS MODEL 9 Magnitude [db] Plant Model Frequency [Hz] (a) Amplitude response 4 2 Phase [deg] Frequency [Hz] (b) Phase responsel Figure 3.4: Bode plot of the original signal and the model.

14 1 CHAPTER 3. SYSTEM IDENTIFICATION

15 Chapter 4 Controller design In this chapter two controllers are designed for the attenuation of the disturbances in the LTO-3 tape drive model obtained in the previous chapter. The first controller is designed using loop shaping techniques and the second controller by loop shaping design with H synthesis. 4.1 PID Controller First, a PID controller is designed using loop shaping design in Subsection 4.1.1, after which the simulation results are presented in Subsection Control design using loop shaping The designed controller should satisfy some predefined robustness margins. For example, the modulus margin in the Sensisitvity function is limited at a maximum of 6 [db] and the phase lead at the cross-over frequency should at least be 4 [ o ], in order to prevent the controlled system from becoming unstable. Furthermore, a as high as possible bandwidth is desired. A logical first step in designing a controller using loop shaping techniques, is by applying a lead filter in order to add phase lead to the open loop transfer function. To satisfy the robustness margins, the zero and pole of the filter are placed as high as possible. Secondly, an integrator is added tot he controller to suppress the low-frequent disturbances. The integrator can not be a pure integrator to prevent drifting of the control signal, when implementing the controller realtime. Next, the gain of the controller is adjusted to obtain a satisfying bandwidth. A peak in the plant model at about 155 [Hz] prevents the controller from obtaining a satisfying bandwidth, without the system becoming unstable. A notch filter is added to the controller to filter away this peak. Finally, after a process of trial and error to obtain a as high as possible bandwidth, while satisfying the required robustness margins a PID controller is obtained with the following specifications: Bandwidth 426 [Hz] Gain margin 6.4 [db] Phase margin 42.5 [ o ] Modulus margin 6. [db] 11

16 12 CHAPTER 4. CONTROLLER DESIGN Simulation results The open-loop transfer function is displayed in Figure 4.1. Figure 4.2 shows the Sensitivity function of the PID controller plant and the plant controlled by the internal controller. 4 Magnitude [db] Frequency [Hz] (a) Amplitude response 55 5 Phase [deg] Frequency [Hz] (b) Phase responsel Figure 4.1: Bode plot of the open-loop transfer function. As can be seen, the Sensitivity function of the PID controlled plant shows some improvement with respect to the Sensitivity function of the plant controlled by the internal controller, but not a lot. This is due to that the original internal controller is probably also designed using loop shaping techniques.

17 4.2. CONTROL DESIGN USING H LOOP SHAPING 13 Magnitude [db] Frequency [Hz] (a) Amplitude response Phase [deg] Internal controller PID controller Frequency [Hz] (b) Phase responsel Figure 4.2: Bode plot of the Sensitivity of the internal and PID controller. In the next subsection another technique is used for the design of a controller. 4.2 Control design using H loop shaping In this section a controller is designed using the H Loop Shaping Design Procedure in Subsection 4.2.1, after which, the order of the designed controller is reduced to a lower order controller in Subsection The simulation results are presented in Subsection H loop shaping design procedure The loop shaping design procedure for the design of an H controller can be divided into three steps: 1. Loop shaping The original open-loop shape of the plant is improved to get a desired open-loop shape. This is done by shaping the singular values of the nominal plant, using pre- and postcompensators W1(s) and W2(s) [1]. These compensators are combined with the plant to form the weighted plant P w (s), where: P w (s) = W 2 (s)p (s)w 1 (s). (4.1)

18 14 CHAPTER 4. CONTROLLER DESIGN Figure 4.3: Weighted plant The weighting functions W 1 (s) and W 2 (s) contain the desired properties of the feedback controller (integrator, bandwidth, high frequency roll-off, etc.), with an optimal trade-off between performance and robust stability. In this project we are dealing with a SISO system, so there is only one weighting function W (s). To obtain the weighted plant, the nominal plant is multiplied with weighting W (s): P w (s) = W (s)p (s). (4.2) The desired properties of the feedback controller is a bandwidth of at least 4 [Hz] and the controlled system should satisfy the robustness margins stated in the previous section. By using the loop shaping procedure, a weighting function W (s) is designed which consists of a 1 st order low-pass filter, an integrator and a notch. The 1 st order low-pass filter causes a high frequency roll-off which prevents that the controller will have too much gain in the less reliable high-frequent region. Adding an integrator ensures us that the controller does not have a feedthrough term that may be a problem when implementing the controller. The notch filters away the peak at 155 [Hz]in the plant model and thereby, increases the gain margin of the open loop transfer function. 2. Robust Stabilization The next step in designing a controller using H loop shaping, is minimizing the H norm of closed loop equation [1]. [ ɛ 1 = min I C (s) ] (I P w (s)c (s)) 1 M 1 w. (4.3) M w and Ñw define the normalized coprime factors of the weighted plant such that: P w (s) = M 1 w Ñw. (4.4) Post multiplying this equation by: [ Mw Ñ w ], (4.5) leads to: [ ] ɛ 1 = min I (I P C (s) w (s)c (s)) 1 [ I P w (s) ]. (4.6)

19 4.2. CONTROL DESIGN USING H LOOP SHAPING 15 Figure 4.4: Weighted controller In case of a single-input single-output system, this equation can be rewritten as a fourblock problem with the four common closed-loop transfer function objectives: Sensitivity, Process Sensitivity, Control Sensitivity and Complementary Sensitivity. [ ] ɛ 1 = min 1 P w (s) 1 C (s) P w (s)c (s) (1 P wc (s)) (4.7) [ = min S(s) C (s)s(s) ] P w (s)s(s). (4.8) P w (s)c (s)s(s) 3. Constructing controller The final feedback controller can be constructed by combining the H controller C with the weighting functions W 1 and W 2, such that [1]: C(s) = W 2 (s)c (s)w 1 (s). (4.9) Or in the SISO problem: C(s) = W (s)c (s). (4.1) The designed H controller obtained a bandwidth of 4 [Hz], while satisfying the required robustness margins Reduction of the high order controller The order of the designed high order controller of the previous subsection can be reduced by using the MATLAB LTset toolbox. The reduction tool of this toolbox reduces the 19 th order controller to a 11 th order model, without changing the bandwidth or robustness margins of the controller.

20 16 CHAPTER 4. CONTROLLER DESIGN Simulation results Figure 4.5 and 4.6 show the bode plots of the open-loop transfer function and Sensitivity function of the H controlled plant model respectively. Magnitude [db] Frequency [Hz] (a) Amplitude response 6 55 Phase [deg] Frequency [Hz] (b) Phase responsel Figure 4.5: Bode plot of the open-loop transfer function. The Sensitivity in Figure 4.6 shows that the H controller has a lower modulus margin between 3 and 7 [Hz] than the internal controller, but the Sensitivity profile in this frequency range is not as flat as the Sensitivity of the PID controller. For frequencies above 7 [Hz] the Sensitivity of the H controller shows better results than the internal and PID controller, but for low frequencies these two controllers show better results.

21 4.2. CONTROL DESIGN USING H LOOP SHAPING 17 Magnitude [db] Frequency [Hz] (a) Amplitude response Phase [deg] Internal controller PID controller H infinity controller Frequency [Hz] (b) Phase responsel Figure 4.6: Bode plot of the Sensitivity of the internal and PID controller.

22 18 CHAPTER 4. CONTROLLER DESIGN

23 Chapter 5 Real-time implementation of the external controllers In this chapter the designed PID and H controllers are implemented on the LTO-3 tape drive via MATLAB Simulink. In Section 5.1 the setup of the external control implementation is discussed, followed by the results of the implementation of both controllers in Section Setup For the real-time implementation of the PID and H controllers the real-time windows target of MATLAB Simulink is used. Figure 5.1 shows a graphical representation of the setup of the experiment. The adjustable DA converter gain and the external control gain α are indicated by the gain block. Furthermore, an offset of 1.25 [V] of the PES signal is subtracted from the signal and indicated by the constant block. This constant also includes an offset of the AD converter. The saturation block in the Simulink model is necessary for... Figure 5.1: Simulink model. The data acquisition is done by a National Instruments I/O board. The LTO-3 tape drive samples the PES signal with a sample frequency of f s = 2 [khz]. Therefor the system is also sampled at this frequency by Simulink. 19

24 2CHAPTER 5. REAL-TIME IMPLEMENTATION OF THE EXTERNAL CONTROLLERS 5.2 Results PID and H controller Figure 5.2 represents the PES error signals of the plant by implementation of the internal controller, and the external PID and H controller. These PES signals are measured with the tape drive moving in forward direction. Error [V] Time [s] (a) Internal controller Error [V] Time [s] (b) PID controller Error [V] Time [s] (c) Hinf controller Figure 5.2: PES error signals by application of the internal controller or the external PID controller, with the tape moving in forward direction. As can be seen, both the PID and the H controller obtain a reduced PES signal, compared to the internal controller. For the tape drive moving in backward direction the result of the PID controller is approximately similar, but the H controller performs unsatisfying, compared to the internal controller, see Figure 5.3.

25 5.2. RESULTS PID AND H CONTROLLER 21 Error [V] Time [s] (a) Internal controller Error [V] Time [s] (b) PID controller Error [V] Time [s] (c) Hinf controller Figure 5.3: PES error signals by application of the internal controller or the external PID controller, with the tape moving in backward direction. The amount of error can be described by the variance of the PES signal, which is for the three controllers listed in Table 5.1. A low variance indicates a low average PES signal. The values for the variance correspond to the results shown in the previous two figures. Forward Backward Internal controller PID controller Hinf controller Table 5.1: Variances of the PES signals for the internal and PID controller, with the tape moving in forward or backward direction. Especially the PID controller shows some good results with respect an improved error correction of the LTO-3 drive, despite of the delays involved with the feedthrough term.

26 22CHAPTER 5. REAL-TIME IMPLEMENTATION OF THE EXTERNAL CONTROLLERS

27 Chapter 6 Conclusions and recommendations Accurate control of the disturbance on the tape caused by the Lateral Tape Motion is necessary to improve the performance of the tape drive. In this thesis a PID controller was successfully implemented on the LTO-3 tape drive with a decrease in the variance of the error signal in forward direction and backward direction of the writing and reading by the tape drive. this reduced error signal corresponds to the flattened Sensitivity function of the PID controller for higher frequencies, compared to the Sensitivity function of the internal controller. The results obtained with the H controller are good for tape motion in forward direction, but less satisfying for backward tape drive motion. These bad results correspond to the limited flattening of the Sensitivity at higher frequencies and presumably, the motion in backward direction is more dominated by noise resulting from the LTM, than motion in forward direction. By modeling the LTM disturbance and incorporate the obtained model in the loop shaping procedure for the design of controllers will give significantly better results, since then the disturbances can be suppressed at the frequencies at which they occur. Low-frequent disturbations will now longer be suppressed at the cost of the high-frequent disturbance amplification. Figure 6.1 shows the first results of the obtained PES of an applied H controller to the plant model, with an model of the LTM disturbance included during the design procedure of the controller. Figure 6.1: PES of H controller with model of LTM disturbance. 23

28 24 CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS

29 Bibliography [1] Duncan MacFarlane and Keith Glover. A loop shaping design procedure using h-infinity synthesis. IEEE Transactions on Automatic Control, 37(6): , June [2] T. ten Dam. External control of a linear tape open drive. traineeship report, Technische Universiteit Eindhoven,