JPH03245201A - Shortest time controller - Google Patents

Abstract

PURPOSE:To minimize the control time by selecting the control gain of the shortest time in order to eliminate the deviation caused between a controlled variable and the target value within an input limit range in sampling and then generating an input to be applied a control subject. CONSTITUTION:When the initial value of a state variable of the position, the velocity, etc., is given to a control subject 11 having the limitation of input, an arithmetic means 12 calculates (m) pieces of control gain Fc in order to set the state value at '0' in (m) hours from the present point. Then a controller 13 selects one of these gains Fc so as to set the deviation et caused between a controlled variable Xt calculated by an adder 14 within an input limit range and the target value Xd at '0' the shortest time. An input Ut is obtained from the gain Fc and the deviation et and inputted to the subject 11. Thus it is possible to obtain a controller that can produce an input coincident with the value Xd in the shortest time.

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention provides a control device that matches a controlled variable with a target value in the shortest possible time when there is a limit to input in a motion mechanical system such as a robot or other controlled object. Regarding.

[Prior Art] For example, motion mechanical systems such as robots (mainly robot arms) used in various industrial fields are controlled by controllers that generate position commands. In such a control system, it is desired that the position match the target value in the shortest possible time, but the position command from the conventional control device cannot reach the target value in the shortest time. On the other hand, as a method for controlling in the shortest time, the motor output is accelerated with the maximum positive (negative) torque, and then decelerated with the maximum negative (positive) torque.
"bang-bang" control is known.

[Problems to be Solved by the Invention] However, the conventional °'bang-bang' control has a problem in that it is difficult to determine the switching point from acceleration to deceleration.

In addition, in actual controlled objects such as robots, there are limits to the input such as voltage applied to the motor, and there is no known method for effective shortest time control within the limited input range3. The maximum output torque of the corresponding motor is not necessarily constant with respect to speed, and there is a limit to that speed, so it is extremely difficult to control the speed etc. for the shortest possible time so that the state is within a limited range. The problem was that it was difficult.

SUMMARY OF THE INVENTION An object of the present invention is to provide a control device that can generate an input that causes a controlled variable to match a target value in the shortest possible time for a controlled object with limited human power.

Another object of the present invention is to solve cases where the input limit depends on the state so that the maximum output torque is not constant with respect to the speed in a motion mechanical system such as a robot, or where there is a limit on a state variable such as speed. An object of the present invention is to provide a control device capable of generating an input that matches a target value in the shortest possible time even in some cases.

[Means for Solving the Problems] The present invention provides a calculation means for calculating a control gain determined by a parameter representing a controlled object whose input is limited and a time from the current moment until the state variable of the controlled object is set to O. Then, among the control gains calculated by the calculation means, select a control gain that makes the deviation between the control amount and the target value 0 in the shortest time within the limited range of input to the controlled object, and select that control gain. and a controller that generates an input to a controlled object from the deviation and the deviation.

Specifically, when the initial values of state variables such as position and velocity are given to a controlled object with limited input, the process (=τ1
τ2. ..., τyo) time to set the state variable to O, the current feedback input side is U(t) = Fc + t
+ ・x(tl fi
m (the more, the better) control gain FC images are determined as l.

In addition, making the controlled variable match the target value in the shortest possible time is
Deviation e between the control amount x ftl and the target value xd (constant)
Since it is equivalent to reducing (t) to 0 in the shortest time, use the above F c 17+ to find out how much time i can make the deviation from the current time i within the input limit range,
From among them, select the FcIT that makes the deviation 0 in the shortest time and generate the input U (t)6. To explain in more detail, the n-th controlled object (continuous system) with limited input is -
Numerically, it is expressed by the following state equation.

LJ (t) l≦U, n,,
+2-21 Here, A and B are parameters representing the controlled object, A is a matrix of nXn, and B is a matrix of nXl6
f2−]) The solution to the equation is x (tl = expfAt) ·X fO) (3). In the case of controllability, when the initial value x(0) is given, the minimum energy input that makes the state variable O in time is U ft) = -B ” exp I -A ”t,
)・x(0) (T indicates a transposed matrix) (4) Here, the minimum energy human power is the input that minimizes the evaluation function J expressed by the following equation.

If 1=0 in equation (4), then U to) = F c fil ・X (ol6-
1) F e (τ=13T (6-21) This Fc1T is τ=τ+, Ez, ”',
T- respectively, calculate m F e lT'll
I F c (τff1l, “”..., FC,
Find τ1.

Here, if the target value is X a (constant), the deviation is e
(tl = x(t) - Xd(71), and e(tl = Ae(tl +BU(tl (8
1, so the deviation e (t
), and when there is a deviation from the target value, by selecting F C + τ) which takes the input limit value ±U□8,
An input U (t) that reduces the deviation to O in the shortest time is found. Therefore.

Llftl=FC++・eft)
+9).

FIG. 1 shows the control device of the present invention when the controlled object is a continuous system as described above.

In the figure, 1) is the controlled object expressed by [2-1) and (2-21 formula), and 12 is m F according to +6-21 formula.
A calculation means 13 calculates cft1, and a calculation means 13 calculates the deviation e (
The controller 14 selects F c (τ) that makes t) O in the shortest time, and generates the input U ftl to the controlled object 1) from the F c 171 and the deviation e (tl) using equation (9). This is an adder that generates the control amount x (tl and the deviation e ft from the target value Xa).

Furthermore, when performing digital control by calculating inputs to a controlled object overnight, the present invention expresses the controlled object as a model that is discretized at a predetermined sampling time,
The calculation means is configured to calculate the control gain based on the number of samplings from the current time until the state variable is set to O.

Specifically, when the initial value of the discretized state variable of the controlled object is given, the number of samplings K (=
The state feedback input law that makes the state 0 at +, kg, ..., kpl is U m = F a no ・X k (as 101,
p control gains F a I (the more the better)
Calculate YI.

As mentioned above, matching the target value in the shortest time is
Since this is equivalent to bringing the deviation em between the control amount x5 and the target value is determined using the above F d (Ml), and F a +ii+ which makes the deviation ek 0 in the shortest time is selected from among them to generate the input Uk.

More specifically, when expressions (2-1) and +2-21 representing the control object described above are expressed as a discrete model sampled at predetermined time intervals, × = ΦXk-+ 1 r Uk-1 (1)-1 )IU5
1≦U, , (1, 1-21 where Φ is a matrix of nXn and ``is a matrix of nXl.

fil-1) when the state of the equation is k (=1)i,, k2.・
..., L) The minimum energy input that becomes O after sampling is expressed as . Here, the minimum energy input is the human power that minimizes the evaluation function J expressed by the following equation.

0O J=Σ　U−”Ub (13) The input at k=o is (J　o　=　F　a　tM+　’　X.

(14-1) 14-21 xo: Becomes the initial value of the state. Therefore, i=r+, kg,..., F a + in ip! + that is, p Fa+rn, F
dlrzl −..., Fd+i+p+ is calculated.

On the other hand, if the target value is X a (constant), the deviation is e
w = X i + X a (
151, and further 5=Φe++-+ + r U, l-+
f16), so the deviation e in xo of f14-1) equation
Using k, when there is a deviation from the target value, for example, by selecting F1a) which takes the limit value U, . Therefore, 1 U k= F +++'i'+ He 1)
control is performed by setting f17).

FIG. 2 shows a control device of the present invention in which the controlled object is represented by a discrete model as described above.

In the figure, 21 is the controlled object expressed by formulas fil-1) and (1)-21, and 22 is p according to formula f14-21.
Calculating means 23 calculates (1 of the p F d+T;+ calculated by the calculating means 22
)-2) Select FalW+ to make the deviation ek between the controlled variable x and the target value x 6 O in the shortest time within the range of the formula, and
6rf+ and the deviation e3 by equation (17), the controller generates the input Uk to the controlled object 21, and 24 is an adder that generates the deviation ek from the control amount xk and the target value x6.

Furthermore, when the controlled object is a motion control system such as a robot, the output torque decreases as the speed increases. In this way, when the limit on the input to the controlled object depends on the state variable of the controlled object, 1. The control device of the present invention is equipped with a means for changing the input limit range according to the state variable, A control gain that makes the above deviation 0 in the shortest time within the specified limit range is selected, and if the control time using that control gain is not the minimum, the original input limit value is configured to be input to the controlled object. be done.

Specifically, the maximum output torque for the current state variable (for example, speed) is determined, the input value tJ waxs determined from that value is set as the new input limit, and the aforementioned control gain FC peak or F a is set within that range. +Y+ is selected, and when the control time or page by the control gain is the minimum, the selected FCLτ or F a (generates input to the controlled object from the cotton deviation as described above,
If k or k is not minimum, the original input limit value ±U, 18
is the input to the controlled object.

FIG. 3 shows a configuration in which this control device is applied to the discrete control system shown in FIG. 2. In the figure, 25 indicates the input limit according to the state variable (for example, velocity) of the controlled object 21.
This is input limit changing means for changing to max*.

Furthermore, when a motion mechanical system is to be controlled, restrictions are placed on the state variables of the controlled object. For example, limits are placed on speed when detecting position. In such a case, in order to ensure that the state variable is within the specified range, the control device of the present invention determines whether or not the value of the state variable is within the specified range, and the control device determines whether the value of the state variable is within the specified range. When the range is exceeded,
Means may be provided for generating the original limited input limit value as an input to the controlled object.

The configuration when this control device is applied to a discrete control system is shown in the fourth section.
As shown in the figure. In the figure, 26 is a determination means for determining whether the value of the state variable (for example, velocity) of the controlled object 21 is within a specified range V, and if it is within the range, the controller 23 If it is not within the range, the original input limit value ±Uy is generated as an input to the controlled object 21.

[Operation] In the control device shown in FIG. 1, the calculation means 12 (6-2
m F c1r+ are calculated according to Equation 1 and their values are held. In the controller 13, as shown in the flowchart of FIG.
6, and select F c (Tl) to make the deviation e 0 in the shortest time within the limited input range.

Then, from the selected F e ITI and the deviation e, a human power utt+ is generated that makes the control amount match the target value in the shortest possible time.

Similarly, in the control device shown in FIG. 2, the calculation means 22 (
p F6 increments are calculated according to formula 14-21 and their values are held. The controller 23 takes in the deviation ek between the state X and the target value x 6 from the adder 24 as shown in the flowchart of FIG. Select a, T;l. Then, the selected F a +'Q'l and the deviation e
, an input U that makes the controlled variable match the target value in the shortest possible time.
Generate k.

In the control device of FIG. 3, as shown in the flowchart of FIG. 7, the current state variable (for example, speed; c)
is input into the input limit changing means 25, and the input limit is changed to 5 U waxs according to the loaded state variable. The controller 23 takes in the deviation eh between the state X3 and the target value x6 from the adder 24, and selects F a n+ that makes the deviation ek 0 in the shortest time within the changed input range U + naxs. and,
Determine whether R of the selected F1a) is the minimum, and
es'', as mentioned above, p6.i and the deviation e8
If k is not the minimum, the input U8 to the controlled object is generated by adding the signs F and σ1·ek to the original human power limit value U-8.

Furthermore, in the control device of FIG. 4, as shown in the flowchart of FIG. 8, the current state variable (for example, speed) is imported into the determining means 26, and the value of the imported state variable is determined within a specified range. V8. Determine whether it is within the range. If the value exceeds the specified range, the input Uk to the controlled object is generated by attaching the opposite sign to the original input limit value [1wax and e].6 Also, if the value of the state variable is specified If it is within the range V r i m, a command is sent to the controller 23, and the controller 23 takes in the deviation Qk between the state 6 x and the target value x 6 from the adder 24, and calculates the deviation within the limited input range. (F61 to turn ?b to O in the shortest time
Select M+. Then, from the selected F a 1f+ and the deviation e, an input U is generated that makes the control amount match the target value in the shortest possible time.

[Example] Hereinafter, an example in which the present invention is applied to a motion mechanical system will be described.

First, a motion mechanical system represented by a robot is a continuous system expressed by a second-order differential equation, and if the output torque of the motor used in this system is τ, and the input voltage to the motor is U, then
The relationship between the two is expressed by the following equation.

τ= K U f18
1 However, IUI≦U, . . . is a torque constant.

As shown in Fig. 9, the moment of inertia J,
The controlled object that drives the mechanical system 2 with the viscous friction coefficient D1 is expressed by the following equation.

I U it) l≦U wax
[19-2) (day 1, J = J + + J
2, D = D + +D! J2: Moment of inertia of the rotor of the above 2: D2: Coefficient of viscous friction of the rotor of the motor
(20-1) However, (20-3) (20-4) Next, the state of this controlled object is K (=h+, k2.
..., ili''p) Set to O after sampling, the current input is U o = F a fil Hx.

(21-1) F dl';il =-F"lΦ-1)0(ΣΦ-"F
``0(Φ-'l''l-'(21-2) ×.= is the initial value of the state, so as mentioned above, = r,, W2...
, F a n1l− i.e. Falr++ at Vl,
Fa+ru −..., F a (Wp+ is determined in advance.

Here, the deviation ek between the control amount xk and the target value x6 is F 6 jWl. Here, an example will be given to explain how to select F 6 jWl.

For example, if the above Zumbling number k (=,, k2゜...-bp) is 8 (i.e. p=8), then k
= to,, k2. --, F a fi for k,
ll + F a n2), F□ma. 1 is determined in advance. At this time, for example, + = 5. k2=IO,
k,=1.5. k,=20. k, = 25° k6 = 3
0. k7=35. k+<L, such as k,=40
＜・・・・・・＜ It is assumed that Ito's Koyuki formula holds true.

According to the control device of FIG. 2, the controller 23
It operates according to the procedure shown in Figure 0.

Considering this deviation as the initial value of equation (21-1), and using F a +ir+ determined in advance, the deviation ei+ can be reduced to 0 in the shortest time within the limited input range ±TJ am. F a lfl is selected by the above-mentioned controller to obtain U. This U. Let it be an input U that makes the controlled variable match the target value by sampling. From then on, (17
) is controlled according to the formula.

9, assuming p=8, Ll m =
The calculation F a +ba+'e k is performed. Then, it is determined whether Uk is within the limit range ±U + max, and if l UkI<U
(Uk is generated by 231. Note that sg
n ((J J indicates the sign (+ or -) of U3.

If IUbl<TJms++, then F with p as p-1.
d+Wy+, Fana+ + “”’ + Fa
Calculate Uk=Fa, ma, ·ek in the order of lmB, and determine whether U≦U□8 for each Uk. and,
Select one rIii F a +Tpin from Fdnp+ where l ut, l>U, □ holds for the first time. For example, I ut, l=l F d+T71−ekl≦U w
axu+tl= l Fa+hs+ ・eJ≦U ea
a'xU k1= I F d(Tsl Heml>
If TJeaax, select F□ma,).

Using F d+7941) selected in this way, U m =
F a + h p”ll e k (calculate 241,
U according to the above formula (23). generate.

Also, even if p=l, that is, Fdnn, l Ukl>U
□If one does not hold, choose F□W'B and U
Generate k=F dtr++ ・e m.

By the way, in equation (18) representing the motor output torque of the exercise machine system shown in Fig. 9, U III a N is considered to be constant, but as shown in Fig. 1), the maximum output torque T
, wax decreases as the speed increases. In such a case, the control device shown in FIG.
The following calculations are performed when finding the

First, the maximum output torque (approximated by a straight line (first-order) according to the speed range as shown in Figure 1) is determined by the complete speed at the current moment, and from this value, U of equation (18) is calculated. The value of is calculated. As shown in FIG. 7, using the value of U as the input limit U m+aX#, the controller 23 selects F6r;
+T+, the output U3 becomes TJ 1) = sgn(
F6tma) eu) Umax (calculated as 251. At this time, if the minimum value of F, +T++ is selected from among the F d+;+ calculated in advance, use formula (25). Instead, Uk is generated using equation (17).

Furthermore, when a motion mechanical system as described in -h is to be controlled, a restriction is placed on the speed of -M when detecting the position. At this time, if the target value is large, the speed limit of the above-mentioned controlled object will be exceeded. In such a case, the speed of the state variable is the specified value (V, .

: A value smaller than the upper speed limit), an input Uk that falls within the specified range is required.

Therefore, using the control device shown in FIG. 4, as shown in FIG. 8, when 1-cross 1>Vz, U t+ = sgn (e 1) ) Untax
By inputting f261, the specified VI
, when U8 is exceeded, the state variable is changed to v9.1 with maximum human power U8.
Let it go inside.

Finally, the results of motor control using the control device of the present invention will be shown. This controls a direct drive motor called a 6-inch Megatorque Motor (registered trademark) manufactured by NSK Ltd. That is, the controlled object is a moving mechanical system in which input is limited, maximum output torque is not constant with respect to speed, and speed is also limited. In order to control this, calculations were performed by a computer according to the control algorithms shown in FIGS. 7 and 8, and three control inputs were generated.

The input amplitude limit is ±10 volts, the moment of inertia of the controlled object is 0.2 kgm2, and when the speed limit is not applied (Figure 7), the change in input voltage when the target position is set to 0.50 rad. is shown in FIG. in this case,
FdLf is length=1. kg,...8 Fa(FB, Fa(rzl + °゛°
°゛Fd(val) was determined in advance, and when the deviation between the control amount and the target value was taken in by zumbling every 2.0m5ec, it was selected as shown in Fig. 14 within the limited input range. .The position of the controlled object is 0.00rad
to 0.50 rad, as shown in FIG.

In addition, the speed limit (V in Figure 8) is set to 12.0ra.
FIG. 16 shows the change in speed when it is set to d/sec.

When the target value is 2.00 rad, the position of the controlled object is from 0.00 rad to 2.00 rad, from the 15th
Changes occurred as shown in the figure.

From the above experimental results, even if there is a limit to the input and the maximum output torque decreases in the high speed range as shown in Figure 1), even if the input limit depends on the state, the target can be achieved in the shortest possible time. It has been demonstrated that it can be controlled to match the value.

Although the embodiments have been described above, the present invention is not limited thereto. For example, although the apparatus of the present invention can be constructed in blocks as shown in FIGS. 1 to 4, the calculations of each part can be executed by one computer. Furthermore, the format of the signal representing the configuration and state within each block can be determined as appropriate depending on the structure and function of the controlled object.

[Effects of the Invention] As described above, according to the present invention, it is possible to perform control to match the target value in the shortest time that was conventionally possible, and this can be achieved even when there are restrictions on the state variables. The target value is easily given in steps.

In addition, when controlling a motion control system, even when the input limit changes depending on the state, such as maximum torque decreasing as the speed increases, that is, changes over time, the control amount can be brought to the target value in the shortest possible time. Can be matched.

Furthermore, even when restrictions are placed on the state of the controlled object (for example, speed), it is possible to match the target value within the specified limits in the shortest possible time.

[Brief explanation of drawings]

Fig. 1 is a block diagram showing the control device of the present invention when the controlled object is a continuous system, Fig. 2 is a block diagram showing the control device of the present invention when the controlled object is a discrete system, and Fig. 3 is a block diagram showing the control device of the present invention when the controlled object is a discrete system. FIG. 4 is a block diagram showing the control device of the present invention when the limit of human power of the controlled object is not constant with respect to the state variable. FIG. 4 shows the configuration of the control device of the present invention when there is a limit to the state variable of the controlled object. The block diagram, FIGS. 5 to 8 are flowcharts showing the control algorithms in the control devices shown in FIGS. 1 to 4, respectively, FIG. 9 is an explanatory diagram of the motion mechanical system, and FIG. 1) is a graph showing the speed-torque characteristics at maximum input in a motion mechanical system; 12, 13 and 14 are flowcharts showing an example of a procedure for selecting and generating an input; Figures 15 and 16 are diagrams showing the position output, input voltage, and selected control gain with respect to the target value when the speed limit is not applied, as experimental results using the control device of the present invention. It is a figure which shows the position output and speed with respect to a target value in the case of a restriction|limiting. 1). 21...Controlled object, 12.22...Calculating means, 13.23...Controller, 14.24...Adder, 25...Input limit changing means, 26...Judging means.

Claims (4)

[Claims] (1) a calculation means for calculating a control gain determined by a parameter representing a controlled object whose input is limited and a time from the current time until the state variable of the controlled object is set to 0; Among the control gains, a control gain that makes the deviation between the controlled amount and the target value 0 in the shortest time within a limited range of input to the controlled object is selected, and from the control gain and the deviation, the controlled object A shortest time control device comprising: a controller that generates an input to the controller; (2) The controlled object is represented by a model that is discretized at a predetermined sampling time, and the calculation means calculates the control gain based on the number of samplings from the current time until the state variable is set to 0. The shortest time control device according to claim (1). (3) If the restriction of the input to the controlled object depends on the state of the controlled object, the controller includes means for changing the input restriction range according to the state variable, and the controller includes:
Select a control gain that makes the deviation 0 in the shortest time within the changed limit range, and if the control time by that control gain is not the minimum, use the original input limit value as the input to the controlled object. Claim (1)
) or the shortest time control device described in (2). (4) If the state variable to be controlled has a limit, determine whether the value of the state variable is within a prespecified range;
The shortest method according to claim 1 or 2, further comprising means for generating an original limited input limit value as an input to the controlled object when the value exceeds a specified range. Time control device.