JP2002055701A - Lqc/ltr robust controller based on disturbance observer for focusing servo of optical disk drive - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a disk drive focusing servo controller capable of simultaneously and efficiently removing model uncertainty, system parameter fluctuation, or disturbance by adopting a disturbance observer, and mounting an external servo controller on an external loop. SOLUTION: This method for controlling a disk drive focusing servo to be used for a disk drive focus plant comprise a step for constructing a nominal design plant by adding a disturbance observer to be operated in the same way as the focus plant, a step for constructing a corrected design plant in the nominal design plant by a white noise into consideration, a step for forming a target filter loop fulfilling prescribed performance, stability and a robust condition based on the corrected design plant for acquiring a filter gain matrix, and a step for restoring the transmission function matrix of the target filter loop from the loop transmission function matrix of the corrected design plant for acquiring a control gain matrix.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a controller used for a disk drive focusing servo, and more particularly, to a model uncertainty and a system parameter variation by using a disturbance observer and mounting an external servo controller in an external loop. And a disk drive focusing servo controller capable of efficiently removing disturbance simultaneously.

[0002]

2. Description of the Related Art There is a demand for an information storage device capable of recording at a high speed, a large capacity, a small size and at a low cost due to social demands for an ultra-high speed information age. DVD (Digital Ve
The rsatile disk) -RAM (random access memory) has proved its usefulness as a peripheral storage device of a personal computer, and the 4.7 GB class is currently being used. In the future, a 15GB class device that can store high-resolution moving images for more than 2 hours will be released. For the early release of such a device, technological development in various fields should be made, one of which is focusing of a disc.

There are five types of servo systems in an optical disk system capable of high-density recording.

A focusing servo for controlling a focus driver in a direction perpendicular to the disk surface so that an optical focus can be accurately focused on a recording layer of the disk. The track center can be accurately positioned despite various disturbances. A tracking servo that controls the tracking driver in the disk radial direction so that the optical focus follows,
A sled servo that moves the optical focus to a specific track of the disk quickly to obtain the required information, various factors such as the higher the density, the smaller the optical focus, the thinner the disk A tilt (tilt) servo that compensates for the disk surface and the objective lens surface not being parallel but oblique, and a spindle (spind) that maintains the disk rotation speed at a constant linear speed along the recording / reproducing position
le) Servo and so on.

The basic purpose of the focusing servo is to
The purpose is to enable a light beam to be accurately scanned at a desired position on the disk surface. If focusing fails, a position error or runout occurs. This error is mainly caused by mechanical and electrical disturbances,
This error includes a periodic error and an aperiodic error.

A periodic run-out (repeatable run-ou)
t: RRO) is defined as a periodic component that coincides with the disk rotation period during the disturbance applied to the driver, and is mainly induced by factors such as disk eccentricity and vibration of the pickup assembly due to disk rotational vibration. . A portion that occurs independently of an integral multiple of the number of revolutions is called a non-repeatable run-out (NRRO). RRO is almost entirely caused by mechanical disturbance, and NRRO is generated by combining mechanical and electric disturbances.

[0007] Among them, research for solving a periodic error by iterative control has been continued, but it has a disadvantage of amplifying an aperiodic error. In addition, various methods have been proposed to solve the problem of amplifying aperiodic errors.However, since the frequency band of interest is limited by the frequency component of the aperiodic errors, it is not general. Does not work efficiently when there is a control instruction. Furthermore, in the case of an optical disk drive, a constant linear velocity (CL) in which the disk rotation speed changes according to the position of the head
Since it has the structure of V) and has the property of changing the frequency of disturbance, it is difficult to apply iterative control. Under these circumstances, the specifications of the focusing controller for 4.7 GB-class DVD-RAMs that are now commonly used require a bandwidth of 2 kHz, a phase margin of 40 degrees or more, and a residual allowable position error of 0.23 μm or less. ing.

Recently, as optical disk devices have been developed to high speeds and large capacities, the need for a controller having high accuracy and robustness has increased, and various methods for designing such controllers have been studied. . Of course, robust control is a field that has been studied for a long time, and various forms of methods have already been proposed. There is LQ control that has a very robust structure in terms of stability, and sliding mode control (Sliding M
There is ode control (SMC), and there is time delay control (TDC) which shows good performance by directly predicting and removing a function expressing disturbance using time delay.

A control method using a difference between an actual system and a model based on a model includes a model reference adaptive control (M) in an adaptive control field.
RAC) and a similar model reference robust control (Model
Reference Robust Control (MRRC). In the field of robust control, many methods based on models have been proposed. These include the Disturbance Observe
r: DOB), Internal Model Controlle
r: IMC), Adaptive Robust Controller
l: ARC).

A control method based on a disturbance observer proposed by Ohnishi and used widely recently has a simple structure and shows good performance for disturbance control. A conventional system based on a disturbance observer is shown in FIG. Figure 2 shows a closed-loop system based on the nominal model.
Is shown in In FIG. 2, the nominal disturbance model is applied to a system including an observer.

[0011] However, if the overall system does not meet the given residual tolerance, it must be widened to meet this. This involves various constraints, which results in increased costs when implementing the system.

Although a controller based on a disturbance observer is generally efficient, employing a disturbance observer alone is not enough to eliminate the residual tolerance. In order to solve such a problem, it is necessary to increase the bandwidth of the entire system. However, increasing the bandwidth has many technical limitations.

[0013]

SUMMARY OF THE INVENTION The present invention has been made in view of such a problem, and an object thereof is to provide a disturbance observer with an LQG / LTR (Linear Quadratic Gau).
ssian Control with Loop Transfer Recovery) to provide a new control system that satisfies the given residual tolerance.

[0014]

According to the present invention, there is provided a method for controlling a disk drive focusing servo used in a disk drive focus plant. Constructing a nominal design plant by adding a disturbance observer to the disk drive focusing plant to operate similarly to the disk drive focus plant, and modifying the nominal design plant to account for white noise Constructing a modified design plant and forming a target filter loop satisfying predetermined performance, stability and robustness conditions based on the modified design plant to obtain a filter gain matrix. And the control gain Disk drive focusing control method characterized by the loop transfer function matrix of modified design plant for obtaining a helix and a step of recovering a transfer function matrix of the target filter loop is provided.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will be described below in detail with reference to the accompanying drawings.

LQG / LTR (Linear Quadratic Gaussian Cont)
(rol with Loop Transfer Recovery) For the controller design, a disturbance observer was added to the optical disk driver focus plant model in (Equation 28), and the added plant model was selected as the nominal design plant. . A plant model equation with a disturbance observer is represented by a state equation as follows.

[0017]

(Equation 7)

[0018]

(Equation 8)

Where x _n (t) ∈R ⁿ is the state vector of the nominal plant, u (t) ∈R ⁿ is the input vector of the nominal plant, y
(t) ∈R ^m is the output vector of the nominal plant.

In (Equation 1) and (Equation 2), y (t) is an output variable,
This represents the focus error e (t) of the optical disk drive.

The LQG / LTR method has an advantage that a control gain matrix G and a filter gain matrix H, which are design parameters of a model reference compensator, can be separately designed. The filter gain matrix H is selected when designing the TFL, and the control gain matrix G is selected when performing the LTR procedure. Also, if only TELs that meet the required design specifications are designed, the performance of the feedback system using MBC using the LTR method
Robustness has the advantage that it can be restored as designed by TFL.

FIG. 3 is a block diagram showing the structure of the TEL. If the loop is cut at the plant output, or similarly at the error signal, the TFL loop TFM G _F (s) is:

[0023]

(Equation 9)

Here,

[0025]

(Equation 10)

H is a filter gain matrix.
The sensitivity TFM of TFL, S _F (s), and the closed-loop TFM, C
_F (s) is as follows.

[0027]

[Equation 11]

[0028]

(Equation 12)

The TFL design problem is to select a filter gain matrix H that satisfies the following performance-robustness.

Performance conditions:

[0031]

(Equation 13)

Stability—robustness condition:

[0033]

[Equation 14]

[0034] Here, ρ _m (ω) is a function representing the maximum allowable performance in the frequency domain, E _m (ω) represents the maximum multiplicative modeling error in the frequency domain.

Since the TFL has exactly the same structure as the Kalman filter, the nominal stability of the TFL is automatically satisfied if the system [A _n , C _n ] can be detected.

A method of designing a TFL under such characteristics will be described. First, a state space model formula of a design plant modified in consideration of virtual white noise for a process and a sensor is created as shown in (Formula 9) and (Formula 10).

[0037]

(Equation 15)

[0038]

(Equation 16)

Here, ξ (t) is virtual process white noise, and θ (t) is virtual sensor white noise. That is,

[0040]

[Equation 17]

[0041]

(Equation 18)

The matrix L and the scalar are used as design parameters. Then, in order to select the filter gain matrix H with the modified design plant dynamics, it is necessary to design a Kalman filter for virtual sensor noise. That is, the filter gain matrix H is

[0043]

[Equation 19]

Here, the matrix P is a filter logarithmic recursion (Ricc
ati)

[0045]

(Equation 20)

In order to select the design parameters and L, the frequency domain equivalent result of the Kalman filter is used.

[0047]

(Equation 21)

L is selected so as to form a suitable loop,
Is selected to satisfy the required bandwidth or crossover frequency. The method of selecting the matrix L is briefly summarized.

First, when matching singular values at low frequencies,

[0050]

(Equation 22)

Alternatively,

[0052]

(Equation 23)

Second, when matching singular values at high frequency,

[0054]

(Equation 24)

Third, when the singular values are simultaneously made coincident at the high frequency and the low frequency,

[0056]

(Equation 25)

With this method, the LTR stage is performed after the TFL design, which is the first stage of the LQG / LTR design method, is completed.
In the LTR stage, a control gain matrix G, which is another design parameter of the LQG / LTR compensator, is selected.

The loop transfer recovery (LTR) method is one of the very powerful and useful methods used in multivariable feedback control system design. The LTR stage is a stage of restoring the compensated plant loop TFM G _n (s) K (s) to TFL of the TFL, G _F (s).

In order to try the LTR, the low-cost LQR problem is generally used. In order to select not only LTR but also the control gain matrix G which is a design parameter of LQG / LTR compensator,
A solution must be found for the control logarithmic Rekati equation with the weighting matrix Q = C _n ^T C _n and the control weighting parameter ρ → 0.

[0060]

(Equation 26)

At this time, the control gain matrix G is selected using (Equation 21).

[0062]

[Equation 27]

In order to derive the basic concept of the LTR, when the control weighting parameter ρ approaches 0, the limit behavior of CARE (limiti
ng behavior). System [A _n , B _n ]
Is stable, [A _n , C _n ] is detectable, and ρ → under the assumption that the design plant is the minimum phase plant.
When 0, the ultimate behavior of CARE is as follows.

[0064]

[Equation 28]

By combining (Equation 21) and (Equation 22),

[0066]

(Equation 29)

Then, when ρ approaches 0, the limiting behavior of the control gain matrix G is as follows.

[0068]

[Equation 30]

[0069] Here, U is a unitary matrix is U ^T U = 1 (u
nitary matrix). This extreme behavior is an important property used in the LTR method.

When the control system is stable and (Equation 24) is satisfied, it is an important result of the LTR that the TFM, K (s) of the model reference compensator (MBC) behaves in an extreme manner as follows. is there.

[0071]

[Equation 31]

Using the LTR result equation of (Equation 25), the ultimate behavior of the loop TFM T (s) cut on the plant output side is as follows.

[0073]

(Equation 32)

From (Equation 26), it can be seen that the LQG / LTR compensator can make the reciprocal of the nominal plant TFM, G _n (s), a new loop TFM, G _F (s), when ρ approaches 0. I understand.

FIG. 4 is a diagram showing a disturbance observer according to the present invention.
TFLs designed for nominal plants and restored routes
The loop shape of the TFM is shown. According to Figure 4, is recovered
The singular value shape of the loop TFM is at least
The outlier shape is well recovered. So, following command and outside
System performance, such as rejection, is as designed in TFL
It will converge within the tolerance of the system. Also,
At high frequencies, TFL of TFL and G_FThe singular value of (jω) is -20dB / dec
While rolling off, recovered loop TFM and G _n(jω)
The singular value of K (jω) decays to -40 dB / dec. Therefore, LQG / L
The TR loop has a higher modeling error due to high frequency dynamics than TFL.
More robust to differences and sensor noise.

In conclusion, after forming a loop that satisfies the design specifications with TFL, an LQG / LTR compensator having satisfactory performance and stability-robustness is obtained by trying an LTR using the low-cost control LQR problem. Can be designed.

Simulated Experiment In the simulated experiment, first, a change in the frequency response characteristic of the driver due to a change in the parameter of the driver is shown, and an LQG / LTR robust controller for a model as shown in (Equation 27) is designed. This is
Using atlab, the performance of the controller due to the change of the driver's parameter is evaluated relative to the case of applying the conventional general linear controller, and the problems that appear here are solved using the method proposed in the present invention Indicates that

Focusing Driver Modeling of DVDR The model of the wire spring type two-axis driver can be classified and modeled into two types. This is a mechanical system and an electronic machine in the form of a spring-mass-damper.
As shown in the tertiary system. However, the poles of the electronic machine are so far apart in the servo band that they are not considered here. Therefore, the transfer function can be simplified as shown in (Equation 28).

[0079]

[Equation 33]

[0080]

[Equation 34]

The transfer function can be obtained based on the specifications of the optical pickup for DVD / CD practically used in Table 1.

[0082]

【table 1】

The nominal model for controller design disturbance observer design is (Equation 28)
And the design parameter value is G ₀ = 3.5 mm /
v, f ₀ = 20 Hz, Q = 15 dB. This is as shown in FIG.

The Q-filter is composed of a third-order filter as shown in (Equation 29). At this time, τ ₁ = 10 ^-13 , τ ₂ = 3 × 10 ^-9 , τ
₃ = 3 × 10 ^-4 , designed to have a cutoff frequency at about 8 kHz.

[0085]

(Equation 35)

As described above, the LQG / LTR robust controller based on the nominal model using the property of the disturbance observer is
-Designed to have 2kHz bandwidth and low frequency gain of about 70dB in the region. The LQG / LTR controller designed in S-domain was converted to Z-domain for realization using digital signal processor. At this time, when the sampling frequency, the f _s to 88.2kHz, the compensator transfer function is as follows.

[0087]

[Equation 36]

Here, the parameter values are a ₁ = 0.1119 and a ₂ = 0.
0185, b ₁ = 14541 and b ₂ = -11965. When the control input u _{LQG / LTR} (k) is obtained by (Equation 30), it is as follows.

[0089]

(37)

The controller thus determined and Q (s), G
_n (s) was converted by a controller in the discrete time domain using the Bilinear conversion method and applied.

C (z) (= K
_{LQG / LTR} (z)), Q (z), and G _n (z) were used to construct a system as shown in FIG. 2, and a simulation experiment was performed using matlab. At this time, (expression
A torque disturbance such as 32) and an output disturbance such as (Equation 33) were applied. This is shown in FIGS. 6 and 7. In the case of output disturbance, a maximum of 300 μm was applied, and as a torque disturbance, a maximum of 1.3 mV was applied.

[0092]

(38)

[0093]

[Equation 39]

Simulation Experiment Results FIG. 8 shows a Bode diagram of the focusing driver according to the design specifications in Table 2. Such a large change in the characteristics is represented by model uncertainty. FIG. 9 shows the disturbance rejection performance when a conventional general linear controller is applied to three types of drivers having the specifications shown in Table 2. As can be seen in FIG.
It shows a large difference of up to 20μm in disturbance rejection performance due to design specification fluctuations. Looking at the tracking error when the control command is 0, the error of a general linear controller appears at about ± 25 μm as shown in FIG. Table 2 shows the controllers proposed in the present invention.
FIG. 10 shows that the difference in performance is as small as 0.03 μm at maximum when applied to a driver having the design specification of FIG. 11 and 12 show the error between the excessive response and the normal state in two parts with different display units. The tracking error of the proposed controller represents ± 25 μm, as in FIG.
This is an error corresponding to 0.1% of the tracking error of a general linear controller, and is included in the allowable error range mentioned above. Also, the transient response of the proposed system is not as clean as when only a general linear controller is applied,
It turns out that it converges quickly. In order to grasp the characteristics of the system, the output for each input in the continuous time domain is shown in a Bode diagram as shown in FIGS. 13, 14, 15, and 16. FIG.
Is the output characteristic for the control command.The characteristics of the proposed controller are almost the same in the servo band as in the case of the linear controller, but the attenuation characteristics (att
enuation characteristics). And it turns out that it shows the bandwidth of 2 kHz mentioned above. The characteristics of the output with respect to the torque disturbance and the output disturbance show effective removal performance with respect to the disturbance as shown in FIGS.

[0095]

[Table 2]

Since the frequency band of the disturbance applied in the previous simulation experiment is approximately 1.3-1.8 Krad / sec, it can be considered that a better disturbance rejection performance is exhibited for disturbances below that. However, as shown in FIG. 16, when only the LQG / LTR robust controller applied in the present invention is used for the compensator, the attenuation characteristic in the noise band is clear as expected from the main body when the LQG / LTR robust controller applied in the present invention is used. I understand.

While the preferred embodiment of the present invention has been described above, those skilled in the art will be able to make various modifications without departing from the scope of the present invention.

[0098]

Thus, the control system constructed according to the present invention is designed on the basis of a nominal model based on a disturbance observer and does not require a difficult design method. It has already been verified that the proposed controller performs well for model imperfections and disturbance rejection. Further, when the controller according to the present invention is applied, in the disk drive servo control, the output characteristic with respect to a control command does not fluctuate, and the output characteristic with respect to disturbance is greatly improved.

[Brief description of the drawings]

FIG. 1 is a system to which a disturbance observer according to a conventional technique is applied.

FIG. 2 is a control system based on a disturbance observer according to the prior art.

FIG. 3 is a structure of a target filter loop according to the present invention.

FIG. 4 shows a target filter loop and a recovered loop.
This is a TFM loop shape.

FIG. 5 is a Bode diagram of a focusing driver model.

FIG. 6 is a characteristic diagram of an output disturbance.

FIG. 7 is a characteristic diagram of torque disturbance.

FIG. 8 is a Bode diagram due to a change in the specification of a driver.

FIG. 9 is a diagram illustrating a change in position error of a general linear controller.

FIG. 10 is a diagram showing a change in position error of the proposed controller.

FIG. 11 is a diagram illustrating a position error of a general linear controller.

FIG. 12 is a diagram showing a position error of a proposed controller.

FIG. 13 is a Bode diagram of control commands versus outputs.

FIG. 14 is a Bode diagram of torque disturbance versus output.

FIG. 15 is a Bode diagram of output disturbance versus output.

FIG. 16 is a Bode plot of measurement noise versus output.

Claims (4)

[Claims] 1. A method of controlling a disk drive focusing servo used in a disk drive focus plant, the method comprising: adding a disturbance observer to the disk drive focus plant so as to operate in the same manner as the disk drive focus plant. Constructing a design plant; constructing a modified design plant in the nominal design plant in consideration of white noise; and determining predetermined performance, stability and robustness based on the modified design plant to obtain a filter gain matrix. Forming a target filter loop that satisfies the condition; and recovering the target filter loop transfer function matrix from the modified design plant loop transfer function matrix to determine a control gain matrix. Disk drive focusing control method characterized by including and. 2. The nominal design plant is given by the following equation: (Equation 2) Where x _n (t) ∈R ⁿ is the state vector of the nominal design plant, u (t) ∈R ⁿ is the input vector of the nominal design plant, and y (t) ∈R ^m is the nominal design plant. 2. The disk drive focusing control method according to claim 1, wherein the output vector is a plant output vector. 3. The modified design plant according to the following equation: (Equation 4) Where x _n (t) ∈R ⁿ is the state vector of the modified design plant, u (t) ∈R ⁿ is the input vector of the modified design plant, and y (t) ∈R ^m is the modified design 2. The disk drive focusing control method according to claim 1, wherein an output vector of the plant, ξ (t) is virtual process white noise, and θ (t) is virtual sensor white noise. 4. The predetermined performance, stability and robustness condition is a performance condition: Stability-robustness condition: Where ρ _m (ω) is a function representing the maximum permissible performance in the frequency domain, and E _m (ω) represents a maximum multiply-type modeling error in the frequency domain. The disk drive focusing control method according to claim 1, wherein: