JPH04348402A - Optimum integration type regulator and image scanner using this regulator - Google Patents

Abstract

PURPOSE:To attain the exact control of a controlled system by changing the feedback gain in accordance with the change of each coefficient matrix of a state equation. CONSTITUTION:The deviation (e) between the target value R and the detection output (y) is calculated at an arithmetic part 13 in a speed control mode of a motor 2. Then the deviation (e) is given to a gain deciding part 34 where the optimum feedback gains K0 and K1 are calculated from the coil resistance value obtained at that time and inputted to the multipliers 35 and 33. The difference between the outputs of both multipliers 35 and 33 is calculated at an arithmetic part 18, and a control input (u) is calculated and inputted to the motor 2. That is, both gains KO and K1 are obtained when a state equation is solved after a coefficient (coil resistance value) is grasped in the control sampling cycle. Therefore the exact speed control is attained despite the change of the coil resistance value.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an integral type optimal regulator and an image scanner using the same.

0002

BACKGROUND OF THE INVENTION Conventionally, this type of integral type optimal regulator has been used, for example, to control the speed of a motor, and a method for determining the weight of an evaluation function when determining a solution is described in Japanese Patent Application Laid-Open No. 1-240.
There is one shown in Publication No. 903. In selecting the weight of the evaluation function when determining the solution, the weight of the evaluation function is selected after the approximate weight is selected to be the same as the solution obtained by PI control without calculating the response of the state variable after the solution is derived. It is designed to determine. This provides a criterion for selecting the weight of the evaluation function when determining the optimal regulator solution, and it is possible to shorten the time required to determine the weight of the evaluation function.

Motor speed control using such an integral type optimal regulator will be explained with reference to FIGS. 7 to 10. First, FIG. 7 shows a speed control block diagram for a motor 2 for driving a traveling body (carriage) 1 in an image scanner. Basically, microprocessor 3
, ROM4, and RAM5. A command generation circuit 8 and interface circuits 9 and 10 are connected to the microcomputer 6 via a bus 7. The command generation circuit 8 generates a state command signal (speed command signal, etc.) that commands the state of the motor 2.
It is for outputting . Interface circuit 9
is for driving, and is for converting the digital value of the calculation result of the microcomputer 6 into a pulse-like signal (control signal) for operating a power semiconductor, such as a power transistor, forming the driving circuit 11. The drive circuit 11 operates based on this pulsed signal and controls the voltage applied to the motor 2. This causes the motor 2 to rotate at a desired speed. On the other hand, the motor 2 is provided with an incremental encoder 12 for detecting its rotational speed. This incremental encoder 12
The output is input to the interface circuit 10, converted into a digital value, the number of output pulses is counted by a built-in counter, the rotational speed is detected, and is fed back to the microcomputer 6 through the bus 7.

The illustrated circuit example is a discrete type microcomputer 6, but the command generation circuit 8,
The same applies to a microcomputer in which the interface circuits 9 and 10 are integrated into one chip.

[0005] Next, a calculation method for an integral type optimal regulator in which the output does not deviate from the target value calculated by the microcomputer 6 will be explained. Generally, the self-inductance L of a DC motor is small and can be ignored, so the state equation becomes as shown in equation (1). however,
ω: Motor angular velocity, outer 1: Motor angular acceleration, KT
: torque constant of the motor, J: inertia between the motor and load, u: input voltage of the motor, Ra: armature resistance.

[0006]

[Outside 1]

[0007]

[Math 1]

The output equation is (2) where c is a constant.
It becomes like the expression.

[0009]

[Math 2]

Further, the state equation of the discrete system and its output equation are as shown in equations (3) and (4), respectively. however,
Let p and q be constants determined by the sampling time.

[0011]

[Math 3]

FIG. 8 shows a block diagram of the integral type optimal regulator control system. First, R(k) is a command speed given from the command generation circuit 8 to rotate the motor 2 at a target speed, and is input to the calculation section 13. Also, motor 2
The angular velocity ω(k) (detected by the incremental encoder 12) is multiplied by a constant c by the multiplier 15 via the feedback loop 14 to produce an output y(k) (detected velocity of the motor 2 converted into a digital value by the interface circuit 10). It is fed back to the arithmetic unit 13 as . The calculation result e(k) by the calculation unit 13 is integrated by the integration block 16, then multiplied by a feedback gain K0 by the multiplier 17, and output to the calculation unit 18. On the other hand, the angular velocity ω(k) of the motor 2 is fed back to the arithmetic unit 18 through a feedback loop 19, and during this feedback, it is multiplied by a feedback gain K1 in a multiplier 20. The arithmetic unit 18 calculates the difference between the two inputs and uses this as a control input u(k) to control the motor 2 and rotate it at a desired angular velocity. Here, K0
, K1 are optimal gain vectors determined by solving the Riccati equation.

[0013] Such an optimal gain vector is obtained as follows. First, a state equation like equation (5) is created from equations (3) and (4). However, s(k)=ω(k)
−ω(k−1), d(k)=u(k)−u(k−1).

[0014]

[Math 4]

The matrices included in equation (5) are expressed as (6) and (7)
Place it like the formula,

[0016]

[Math 5]

As an evaluation function when controlling the motor 2, (
8) Use the formula.

[0018]

[Math 6]

Control input d(
Find k). Note that W is a non-negative weighting coefficient.

On the other hand, the Riccati equation is given by equation (9), where Wx is a weight matrix.

[0021]

[Math 7]

Now, if the steady solution of equation (9) is H, the optimal gain vector G=(K0, K1) is expressed as (10)
It is determined by the formula. In these equations, P1' and Q1' represent the transposed matrices of P1 and Q1, respectively, and the negative first power represents the inverse matrix.

[0023]

[Math. 8]

Next, the incremental encoder 12
A processing method of the interface circuit 10 that performs output processing and detects speed will be described. This interface circuit 10 connects the output of the incremental encoder 12 to an interrupt of the microprocessor 3, and
It is equipped with a counter that counts the reference clock CLK. Now, in FIG. 9, incremental encoder 1
The description will start from the state immediately before the edge E1 of output OB No. 2 arrives. The built-in counter measures the pulse period of the output OB,
A count number given based on the clock CLK (for example,
Decrement count from 0FFFFH). When edge E1 reaches the interrupt of microprocessor 3,
The interrupt routine shown in FIG. 10 is executed. Then, the decremented count value of the counter is latched in the storage register built into the interface circuit 10 (counter latching). Then, the latched decrement count value is stored in the RAM 5. Then, the count initial value (0FFFF
H), starts decrement counting again, and ends the interrupt processing. When edge E2 reaches the interrupt again, the above-described process is repeated in the same way.

At this time, the speed ω(k) is obtained from equation (11). However, TCLK: CLK period, NE
: Incremental encoder division number, n: CLK count number = OFFFFH - decrement count number, K:
Let it be the unit conversion constant for angular velocity.

[0026]

[Math. 9]

[0027]

[Problems to be Solved by the Invention] In the speed control system of the motor 2 using such an integral type optimal regulator, if the weighting coefficient W is determined, the optimal gain set (K0, K1) becomes (9
) is uniformly determined by solving the Riccati equation shown in the formula, and is not changed during motor operation. However, when the motor 2 operates, the coil temperature increases due to Joule heat, and the resistance value Ra of the coil changes. Then, each coefficient (-K
The values of T2/Ra·J and KT/Ra·J also change. Along with this, each coefficient of the Riccati equation also changes, so the optimal gain (K0, K1
) will also change. Therefore, if the gain value set before the motor is in operation is used as in the conventional method described above, accurate control cannot be achieved.

Incidentally, according to the present applicant, the resistance value of the coil is determined while the motor is operating, and the input voltage to the motor is corrected using the ratio of that value and the initial coil resistance value at room temperature as a correction coefficient. Accordingly, a motor has been proposed in which accurate control can be performed even when the coil temperature rises and the coil resistance value fluctuates during motor operation. However, even this proposed method lacks control accuracy because it does not take into account changes in the optimal gain based on changes in the internal state due to changes in coil resistance.

[0029]

[Means for solving the problem] The state value of the controlled object is fed back and compared with the target value, and after integrating the result of this calculation, the value obtained by multiplying by the feedback gain,
2. The integral type optimal regulator according to claim 1, wherein a difference between a state value of the controlled object multiplied by another feedback gain and a value fed back is calculated and used as a control input for the controlled object to solve a state equation. In invention,
detection means for detecting changes in each coefficient matrix of the state equation;
Gain changing means is provided for changing the feedback gain according to changes in each coefficient matrix.

In the invention as claimed in claim 2, the gain changing means includes integral type optimal regulator solution determining means for determining an optimal feedback gain according to changes in each coefficient matrix, and the determined optimal feedback gain is changed to a new feedback gain. It was decided that

In the invention as set forth in claim 3, a storage means is provided for storing an optimal feedback gain determined in advance for changes in each coefficient matrix of a plurality of state equations, and a gain changing means is provided for storing an optimal feedback gain determined in advance for changes in each coefficient matrix of a plurality of state equations. Accordingly, the present invention includes an extraction means for extracting the optimal feedback gain from the storage means, and the extracted optimal feedback gain is used as a new feedback gain.

Furthermore, in the invention as set forth in claim 4, the integral type optimum regulator as set forth in claim 1, 2, or 3 is provided for controlling the speed of the image scanner as the object to be controlled is a motor for driving a traveling body.

[0033]

According to the invention as claimed in claim 1, since the feedback gain is changed by the gain changing means in accordance with changes in each coefficient matrix of the state equation, each of the state equations is Even if the coefficient matrix changes, the control takes into account changes in the feedback gain, and the controlled object is accurately controlled.

According to the invention as set forth in claim 2, the gain changing means is an integral type optimal regulator solution determining means for determining the optimal feedback gain in accordance with changes in each coefficient matrix, and Since the gain is changed after determining the optimal feedback gain, the optimal feedback gain can be accurately determined for any change in each coefficient matrix of the state equation during control, making it possible to perform more accurate control.

Further, according to the third aspect of the invention, the optimal feedback gain is determined in advance for changes in each coefficient matrix of a plurality of state equations and stored in the storage means, and the gain changing means The optimum feedback gain is extracted from the storage means by the extraction means in response to a change in and is used as a new feedback gain, so it is possible to immediately obtain the optimum feedback gain when each coefficient matrix of the state equation changes during control. This allows for more accurate control.

Furthermore, according to the invention as set forth in claim 4, since the speed of the image scanner traveling body driving motor is controlled using these integral type optimal regulators, accurate speed control is achieved and highly accurate reading can be performed. can be set.

[0037]

[Embodiment] An embodiment of the invention according to claims 1 and 4 is shown in FIG.
This will be explained based on FIG. Components that are the same as those shown in FIGS. 7 to 10 are indicated using the same reference numerals. In this embodiment, an integral type optimal regulator is applied to speed control of a motor 2 for driving a traveling body of an image scanner. First, FIG. 2 shows a block diagram of the entire control system. Basically, it is the same as that shown in FIG. 7, but a temperature sensor (for example, a thermistor) 21 is added to measure the coil temperature of the motor 2 and serve as a detection means. This temperature sensor 21
The coil temperature is measured based on a command from the microcomputer 6, and the measurement results are taken into the microcomputer 6 via the bus 7. The other parts are the same as those shown in FIG. 7, and this embodiment may also have a one-chip microcomputer configuration.

Next, the configuration of the image scanner 22 will be explained with reference to FIG. First, a document table 24 is provided on which a document 23 to be read is placed. This manuscript table 2
4, an illumination lamp 25, reflective mirrors 26, 27
, an equal-magnification photoelectric conversion unit consisting of an equal-magnification imaging lens 28 and a CCD line sensor 29 is movably provided as the traveling body 1, and is configured to sub-scan the surface of the document. This traveling body 1 is driven by a motor 2 in the sub-scanning direction. That is, a wire 32 is stretched between a drive pulley 30 and a driven pulley 31 which are rotationally driven by the motor 2, and a part of this wire 32 is connected to the traveling body 1, so that the rotation of the motor 2 The traveling body 1 accordingly reciprocates. Note that the present invention is not limited to such a same-magnification image scanner, but can be similarly applied to an image scanner having a reduction optical system.

FIG. 1 shows a block diagram of the integral type optimal regulator control system of this embodiment. In the figure, 2 is a motor to be controlled, but unlike in the case of FIG. 8, in this example it represents the change in the coefficients of ω(k) and u(k) for each sampling period, so ω(k+1)= p(k)・ω(k
)+q(k)・u(k). Angular velocity ω(k) detected by incremental encoder 12
is multiplied by a constant c by a multiplier 15 via a feedback loop 14, and is given to the arithmetic unit 13 as an output y(k). On the other hand, the angular velocity ω(k) passes through another feedback loop 19, is multiplied by a feedback gain K1(k) by a multiplier 33, and is provided to the calculation unit 18. The calculation unit 13 calculates the deviation e(k) between the target value R(k) and the detected output y(k), which is integrated by the integration block 16 and x
0(k), the gain determining unit 3 serves as a gain changing means.
given to 4. The gain determining unit 34 determines the optimum feedback gains K0(k), K1 from the coil resistance value at that time.
(k) is calculated and each value is input to multipliers 35 and 33. After that, the integral value x0(k) of the deviation is multiplied by a multiplier 35.
The resultant signal is multiplied by the feedback gain K0(k) and provided to the arithmetic unit 18. In the calculation unit 18, multipliers 35, 3
3 and calculate the control input u(k). This control input u(k) is input to the motor 2 and controlled to rotate at a desired angular velocity.

As described above, when the integral value x0(k) of the deviation is given to the gain determining section 34 from the integration block 16, the optimum feedback gains K0(k) and K1(k) based on the coil resistance value at that time are determined. The feedback gains K0(k) and K1(k) are calculated and output to the multipliers 35 and 33, respectively, but the feedback gains K0(k) and K1(k) at this time are determined by accurately understanding the parameters (resistance value of the coil) in the sampling period of the control. This is the value obtained by solving the Riccati equation. Therefore, by using such changed feedback gains K0(k) and K1(k), it is possible to provide optimal feedback for each sampling period of the control, and accurate speed control can be achieved even when the coil resistance value changes. becomes possible. In particular, by using it to control the motor 2 for driving the traveling body 1 of the image scanner 22 as in this embodiment, highly accurate reading can be performed.

Next, an embodiment of the invention according to claims 2 and 4 will be explained with reference to FIG. FIG. 4 shows the feedback gain determination method of this embodiment, which is executed by the gain determination unit 34 shown in FIG. First, when the integral value x0(k) of the deviation is sent from the integration block 16 to the gain determining section 34, the temperature of the coil is measured. This is executed by inputting the output of the temperature sensor 21, that is, the temperature of the coil, into the microcomputer 6. Next, the resistance value of the coil is determined from the measured temperature. This process is performed as follows. First, when current flows through the coil, the coil temperature rises due to Joule heat and the coil resistance value changes. For example, assuming that the electrical copper wire most commonly used as a coil conductor has a resistance value of Rt at a temperature of t°C and a resistance value of R0 at 0°C, then in the range of +150°C to -200°C, Rt = R0 ( 1+0.0043t). If we pay attention to the fact that the temperature t and the resistance value Rt are in a 1:1 relationship, the coil resistance value at that time is calculated from the formula for calculating Rt mentioned above and the coil temperature measured by the temperature sensor 21. It turns out you can easily ask for it.

After determining the coil resistance value at a certain sampling period k during motor operation in this way, by substituting this resistance value into the state equation (1), (1
) The coefficients of ω(k) and u(k) in the equation are recalculated.

After this, as in the case of the conventional method, a steady-state solution to the Riccati equation is found, and the optimum feedback gain (K0, K1) is found from the found steady-state solution. Next, the values of the optimal feedback gains (K0, K1) obtained are assigned to each multiplier 35, 33, and the integral value of the deviation x0(
k) is output to the multiplier 35. The optimal feedback gains (K0, K1) obtained in this way take into account changes in coil resistance due to changes in coil temperature during motor operation. This allows for very accurate control. Therefore, by applying it to the image scanner 22,
More accurate speed control can be performed and more accurate readings can be performed.

Further, an embodiment of the invention according to claims 3 and 4 will be explained with reference to FIGS. 5 and 6. FIG. 5 shows the feedback gain determination method of this embodiment, which is executed by the gain determination section 34 shown in FIG. First, when the integral value x0(k) of the deviation is sent from the integration block 16 to the gain determining section 34, the temperature of the coil is measured. This is executed by inputting the output of the temperature sensor 21, that is, the temperature of the coil, into the microcomputer 6, as in the case of FIG. Thereafter, a feedback gain suitable for the coil temperature at that time, that is, the coil resistance value, is extracted and determined from a table 36 in the memory 4 that stores in advance the relationship between the coil temperature and the optimum feedback gain as shown in FIG. The values of the extracted optimal feedback gains (K0, K1) are substituted into the respective multipliers 35 and 33, and the integral value x0(k) of the deviation is outputted to the multiplier 35. The optimal feedback gain (K0, K1) obtained in this way is obtained by converting the coil temperature into a coil resistance value, determining the optimal feedback gain (K0, K1) at that resistance value, and storing it in the memory 4 as a table. Once the coil resistance value has been stored and measured every control sampling period, the gain can be immediately selected using this table. In addition, the coil temperatures in this table are arranged in descending order of absolute value, so even if there is no temperature value that matches the measured value in the table, the value closest to the measured temperature value is found and the corresponding action is taken. All you have to do is select the gain that you want, and you can respond flexibly. In any case, by using the table, the optimum feedback gain can be selected immediately when the coil temperature is detected. Therefore, by applying the present invention to the image scanner 22, more accurate speed control can be performed and more accurate reading can be performed.

[0045]

Effects of the Invention Since the present invention is configured as described above, according to the invention as claimed in claim 1, the feedback gain is changed by the gain changing means according to the change in each coefficient matrix of the state equation, so that the operation Even if each coefficient matrix of the state equation changes during the control of the controlled object, this control takes into account changes in the feedback gain, and can accurately control the controlled object. Further, according to the invention as claimed in claim 2, since the gain changing means is an integral type optimal regulator solution determining means for determining the optimal feedback gain according to changes in each coefficient matrix, each coefficient matrix of the state equation under control is changed. Since the optimal feedback gain can be accurately determined for every change, more accurate control can be achieved. On the other hand, according to the invention described in claim 3,
Optimal feedback gains are determined in advance for changes in each coefficient matrix of a plurality of state equations and stored in a storage means, and the gain changing means extracts the optimal feedback gains from the storage means by an extraction means in accordance with changes in each coefficient matrix. Since this is extracted and used as a new feedback gain, when each coefficient matrix of the state equation changes during control, the optimum feedback gain can be immediately determined, making it possible to perform more accurate control.

Furthermore, according to the invention as set forth in claim 4, since the speed of the motor for driving the image scanner traveling body is controlled using these integral type optimal regulators, accurate speed control is possible and highly accurate reading is possible. can be made to do so.

[Brief explanation of the drawing]

FIG. 1 is a block diagram of an integral optimal regulator control system showing an embodiment of the invention as claimed in claims 1 and 4;

FIG. 2 is a block diagram showing the entire control system.

FIG. 3 is a schematic configuration diagram of an image scanner.

FIG. 4 is a flowchart showing an integral optimal regulator solution determination process according to an embodiment of the invention according to claims 2 and 4;

FIG. 5 is a flowchart showing an integral optimal regulator solution determination process according to an embodiment of the invention according to claims 3 and 4;

FIG. 6 is an explanatory diagram showing a storage means.

FIG. 7 is a block diagram showing the entire control system of a conventional example.

FIG. 8 is a block diagram of the integral type optimal regulator control system.

FIG. 9 is a timing chart showing a speed detection method.

FIG. 10 is a flowchart showing the processing.

[Explanation of symbols]

2 Traveling body drive motor = controlled object 21
Detection means 34 Gain change means 36 Storage means

Claims (4)

[Claims] 1. The state value of the controlled object is fed back and compared with a target value, and the result of this calculation is integrated, and then a value obtained by multiplying the state value of the controlled object by a feedback gain and another feedback gain are applied to the state value of the controlled object. In the integral type optimal regulator, the difference between the multiplied and fed-back value is calculated and used as the control input for the controlled object to solve the state equation, and a detecting means for detecting a change in each coefficient matrix of the state equation; An integral type optimal regulator, comprising: gain changing means for changing the feedback gain in accordance with changes in a coefficient matrix. 2. The state value of the controlled object is fed back and compared with a target value, and the result of this calculation is integrated, and then a value obtained by multiplying the state value of the controlled object by a feedback gain and another feedback gain are applied to the state value of the controlled object. In the integral type optimal regulator, the difference between the multiplied and fed-back value is calculated and used as the control input for the controlled object to solve the state equation, and a detecting means for detecting a change in each coefficient matrix of the state equation; An integral type optimum regulator comprising: an integral type optimum regulator solution determining means for determining an optimum feedback gain according to a change in a coefficient matrix; and gain changing means for setting the obtained optimum feedback gain as a new feedback gain. regulator. 3. The state value of the controlled object is fed back and compared with the target value, and the result of this calculation is integrated, and then a value obtained by multiplying the state value of the controlled object by a feedback gain and another feedback gain are applied to the state value of the controlled object. In the integral type optimal regulator, the difference between the multiplied and fed-back value is calculated and used as the control input for the controlled object to solve the state equation, and a plurality of detecting means for detecting changes in each coefficient matrix of the state equation; storage means for storing an optimal feedback gain determined in advance for a change in each coefficient matrix of the state equation; and an extraction means for extracting the optimal feedback gain from the storage means according to a change in each coefficient matrix. What is claimed is: 1. An integral type optimal regulator comprising: gain changing means for setting the extracted optimal feedback gain as a new feedback gain. 4. An image scanner comprising the integral type optimum regulator according to claim 1, which controls the speed of a motor for driving a traveling body as a controlled object.