DE4240788A1 - Fuzzy logic based servo controller - has loop input error values received by fuzzy logic circuit to determine corrective action based upon linguistic rules - Google Patents

Abstract

An alternative to conventional PID (linear) control of a process is provided by system employing fuzzy logic rules to determine the values to be applied for correction to a non-linear control system . The inputs generated (36,38,52) are received by a fuzzy logic circuit (58) to convert them into linguistic based rule values i.e. very big, big, small, very small etc. A memory (54) stores the defined membership functions for the different ranges of value and a second memory (92) stores the rules. The membership grade values are combined (62,64) and a control output is produced (66). USE/ADVANTAGE - For non-linear process control systems, robots etc. Provides insensitivity to parameter changes.

Description

The invention relates to a controller on the input variable are switched on and an output variable as a manipulated variable delivers.

Regulators of the aforementioned type are usually PID controllers that are designed on the basis of linear control theory. Such controllers pose problems if the Control systems are non-linear. Your behavior is strong too depending on the parameters of the controlled system. Changes this Parameters easily cause the control to become unstable.

There are also known "optimal" controllers which are called Kalman filters Use condition monitors. Such controllers are also based a linear theory. The application of such Kalman Filter is too complex for many applications.

The invention has for its object a controller build that he with comparatively low technical Effort to master non-linear controlled systems permitted and insensitive to the prior art against parameter changes.

According to the invention, this object is achieved with a controller solved at the outset by

• a) an unset logic circuit for converting the input Variables in linguistic values accordingly overlapping value ranges of the input variables,
• b) first storage means for determining membership Functions, each in the individual value ranges are defined and a degree of belonging to one corresponding to the relevant value range specify linguistic value
• c) second storage means for defining and storing Rules for linking linguistic input values to form a liguistic starting value,
• d) means for determining the linguistic values that the Input variables are to be assigned, and the associated one Degrees of membership,
• e) a correlation logic circuit for correlating the Degrees of membership according to the rules of association for the linguistic input values to form a Degree of affiliation for the linguistic initial Value,
• f) means for changing the membership function of the initial linguistic value according to the the correlation of the degree of membership of this Output value and
• g) Means for forming an actuator means output variables of the controller to be activated from the so changed membership functions of the addressed initial linguistic values.

There are thus value ranges for the different Input variables fixed. These ranges of values overlap yourself. The value ranges are "linguistic values"  assigned. These are values that are not through numbers but through fuzzy terms such as "large", "medium" or "small" are expressed. Even "zero" can be blurred in such a way Logic a finite range of values around the actual value mean zero of the input quantity around. The different Value ranges are assigned to "membership functions". These membership functions give a "membership Degree "with which a considered input value for a certain range of values and linguistic value. In the has non-overlapping parts of the value ranges Membership function expediently the value "1". In the overlapping parts of the value ranges have the Membership functions then values less than one. A The input value considered can then be two neighboring ones Belong to values and z. B. with a membership Grade 0.2 "large" and with a membership grade 0.8 "medium" his.

This is now processed first linguistic values based on certain knowledge-based Regulate. This results in a - again linguistic - Initial value. This linguistic output value is given by the correlation logic circuit again a "membership Degree ", which results from the degrees of membership of the gives linguistic input values. A membership The function of this linguistic output value is based on In accordance with this degree of membership changed. There for one considered combination of input values, possibly several of the knowledge-based rules may apply if one or several of the input variables in overlapping parts of the Ranges of values, several such can change Membership functions result. The output variable must again an analog quantity or a defined numerical value be made up of the possibly changed membership Functions are formed by an appropriate operation.  

This procedure with the "detour" over linguistic values that but then again in analog signals or numerical values needs to be implemented seems complicated. But it offers decisive advantages in many cases:

The saved, knowledge-based rules depend on that the respective range of input variables. These rules can therefore be different for different areas his. This can be empirically determined or theoretical recognized, possibly non-linear behavior of the controlled system Be taken into account.

Changes to parameters of the controlled system occur because of the Subdivision of the measuring ranges of the input variables into Value ranges not immediately apparent. The regulation this makes it less sensitive to such parameter changes. This can be shown by a simulation. Through simulation can also be shown that the control with fuzzy logic leads to usable control accuracies.

Embodiments of the invention are the subject of the dependent Claims.

Embodiments of the invention are below Reference to the accompanying drawings explained in more detail.

. The control with fuzzy logic (fuzzy logic), and knowledge-based rules using the control of a tracking for a target - Figure 1 shows as a - simple.

Fig. 2 illustrates the coordinate systems used therein.

Fig. 3 is a block diagram and illustrates the basic structure of the control loop.

Fig. 4 is a block diagram illustrating the construction of the controller.

Fig. 5 shows for two input variables the course of the membership functions.

FIG. 6 is a schematic illustration and shows a geometrical illustration of a rule memory for defining and storing the rules.

Figure 7 is a block diagram illustrating the processing of input linguistic values and degrees of membership to an output linguistic value and a membership function applicable to it.

Fig. 8 illustrates the formation of an output variable of the regulator, through which an actuator is controlled.

Fig. 9 shows the controller described as another application of a robot having six degrees of freedom, with its system for one axis of the robot using a controller of the present type.

FIG. 10 shows the structure of the control loop for the axis of the robot from FIG. 10 in a representation similar to that in FIG. 3.

In Fig. 1, an optical instrument, for example a telescope, is designated by 10 . The instrument 10 is intended to pursue a moving target. For this purpose, the instrument 10 can be pivoted in a frame 12 about an axis Y ^T. The pivoting takes place by means of an elevation servomotor 14 .

The pivot angle about the axis Y ^{T can} be tapped as an elevation angle by means of an elevation tap 16 . An axis X ^T is the line of sight to the target. An axis Z ^T is perpendicular to the other two axes of this coordinate system.

The frame 12 is rotatably supported about a vertical axis. The frame 12 is adjusted about the vertical axis by an azimuth servomotor 18 . The azimuth position of the frame 12 is tapped by an azimuth tap 20 .

Azimuth and elevation are based on an earth-fixed coordinate system X ^R , Y ^R and Z ^R. X ^{R is,} for example, the north direction, Z ^R the vertical and the plane spanned by the directions X ^R and Y ^R the horizontal plane. The elevation angle is labeled EL. The azimuth angle is designated AZ ( Fig. 2).

The elevation angle EL of the instrument 10 is applied from the elevation tap 16 to a controller 22 . This is represented by a line 24 . The azimuth angle AZ of the instrument 10 is also applied to the controller 22 by the azimuth tap 20 . This is represented by a line 26 . The controller 22 also receives a measured value for the elevation of the target via an elevation input 28 and a measured value for the azimuth of the target via an azimuth input 30 . Control deviations for elevation and azimuth are determined by forming the difference.

Fig. 3 shows a block diagram of the control loop for tracking in azimuth: The controller 22 is fed the control deviation in the clock interval k, the time derivative of the control deviation in the clock interval k and - as a feedback - the output variable of the controller 22 in the clock interval k-1. The output variable here is the angular velocity ω of the frame 12 around the Z ^R axis.

The control deviation ε is formed in a summing point 32 . The azimuth angle of the azimuth tap 20 is applied to the summing point 23 once with a negative sign. This is represented by a line 34 . On the other hand, the azimuth angle of a target to be tracked is applied via a azimuth input 30 by a measuring device, not shown.

The control deviation ε _k is applied to a first input 36 . The time derivative _k - of the control deviation is applied to a second input 38 . This time derivative is formed from the system deviation by delaying the system deviation ε _k in a branch 40 by a delay element 42 by a clock interval T. The difference between the control deviation ε _k in the clock interval k and and the control deviation ε _k-1 in the clock interval k-1 is formed in a summing point 44 . This difference, as represented by block 46 , is divided by the length T of the clock interval. That provides _k .

The output variable ω _{k of} the controller 22 is delayed in a feedback loop 48 by a delay element 50 by a clock interval T. The delayed output variable, namely the angular velocity ω _{k-1 of} the frame 12 , is applied to an input 52 of the controller 22 .

Fig. 4 schematically shows the structure of the regulator 22.

The controller 22 contains a memory 54 for defining and storing "membership functions". The memory 54 is connected via a connection 56 to a device 58 for determining "degrees of membership". The input variables of the controller 22 are connected to the device 58 via the inputs 36 , 38 and 52 . The device 58 forms membership degrees from this, which reflect the degree of affiliation of the input variables to various linguistic values "large", "small" etc.

The degrees of membership are connected to a database and inference device 62 via connections 60 . The database and inference device 62 contains a memory in which knowledge-based rules are stored in “if-then” form, according to which linguistic input values are also converted into linguistic output values. Membership functions are formed from the linguistic input values and the degrees of membership assigned to them, the sum of which, represented by a summing point 64 using an output generator, is used to generate an output variable ω _{k of} the controller 22 .

Fig. 5 shows the conversion of the input variables of the controller illustrated in "linguistic values" and belongingness degrees. The measuring range of the input variables, i.e. ε, and ω, is divided into overlapping value ranges. Linguistic values are assigned to these value ranges. In the present case these are the linguistic values: "negative large" = NL, "negative medium" = NM, "negative small" = NS, "zero" = ZE, "positive small" = PS, "positive medium" = PM and "positive large" = PL. This is shown in the first line of FIG. 5 for the feedback variable (ω _k-1 ). The second line shows this for the control deviation ε and its time derivative. Membership functions are assigned to the various overlapping value ranges. An input variable that lies in an overlap area of the value areas can be assigned to two different linguistic values. For example, the value 30 ° / sec of the input variables ω is both "positive small" and "positive medium". It lies in the overlap area of these two value areas. The membership functions then indicate the degree to which the value of the input variable is assigned to one and the degree to which it is assigned to the other linguistic value.

As can be seen from FIG. 5, these membership functions have a trapezoidal course in the exemplary embodiment described here: in the part of each value range in which there is no overlap with an adjacent value range, the value of the membership function is "1.0" . The assigned membership function is "0" outside the value range. Within the overlap areas, a linear increase in membership function from 0 to 1.0 is assumed. The membership functions can possibly also have a course other than trapezoidal. The membership functions are shown in FIG. 5 above the relevant value ranges. The membership function for the value range of the linguistic value "positive medium" is designated by 68 , for example. The value ranges for the linguistic values positive or negative "large" are unlimited on one side.

FIG. 7 shows how, for a specific combination of input variables ε _k = 1.8, _k = 5 and ω _k-1 = -9, the degrees of membership and a linguistic output value as well as the membership value belonging to this output value Function can be determined.

This is done using the membership functions shown in FIG. 5. For ε _k = 1.8, the membership function 70 results in a degree of membership of m _ZE (ε _k ) = 0.2 for the linguistic value “zero” (ZE). For _k = 5, the membership function 72 for the linguistic value "positive small" (PS) results in a degree of membership of m _PS (- _k ) = 0.4. For ω _k-1 = -9 a membership degree m _NS (ω _k-1 ) = 0.3 results from the membership function 74 for the linguistic value "negative small" (NS). The determination of the linguistic values ZE, PS and NS and the degrees of membership assigned to them is symbolized in FIG. 7 by blocks 76 , 78 and 80 .

According to a knowledge-based rule stored in the memory, a linguistic output value is determined from the linguistic input values. This memory is represented by a block 82 in FIG. 7. An example of a knowledge-based rule is given in block 82 :

IF ε _k = ZE AND _k = PS AND ω _k-1 = NS THEN ω _k = ZE.

If the control deviation cumulatively has the linguistic value "zero", the time derivative of the control deviation has the linguistic value "positive small" and the returned angular velocity has the linguistic value "negatively small", then the angular velocity acting as the output variable of the controller 22 has the linguistic value "zero". The linguistic value zero is a finite range of values surrounding the numerical value zero with an assigned membership function 84 . According to the specified rule, the values of the input variables would result in this linguistic output value ZE.

The rules contain three input variables ε _k , _k and ω _k-1 . This can be represented geometrically in the manner shown in FIG. 6 by three coordinates. Value ranges NL, NM, NS, ZE, PS, PM and PL define sections on the coordinate axis. Each of the rules can be defined by a cube in this coordinate system with certain assigned linguistic values e.g. B. PL, NM, NS are shown as "coordinates" in which this rule is "filed". In FIG. 6, "ε = PL" for example is shown plane. In FIG. 6, 92 denotes the memory organized in this way, in which in each case three “linguistic” input values are assigned a linguistic output value that results according to a rule. Fig. 6 also shows another example of such a stored rule.

A correlation logic circuit 86 converts the degrees of membership of the various input variables, in the present case 0.2; 0.4 and 0.3, a degree of membership determines which of the output variables ω _{k is} assigned. Since the various input variables are linked by AND in the rule used here, the degree of affiliation of the output variables is equal to the smallest of the degrees of affiliation of the input variables. In a way, that's their intersection. The degree of membership of the output variables is thus m _ZE (ω _k ) = 0.2. The membership function 84 for the linguistic value "zero" (ZE) of the angular velocity is multiplied by this membership degree 0.2. This gives the function 88 in FIG. 7. The formation of this changed membership function 88 is represented in FIG. 7 by a block 90 .

If the rule contains an OR link, it becomes analog to a union the highest of each assigned degrees of membership as the degree of membership of the Output variables selected.

Since the values of the input variables U. in at the same time different of the overlapping value ranges and with different linguistic values at the same time corresponding degrees of affiliation are to be assigned u. U. at the same time several of the aforementioned rules addressed. These rules can be different so that also account for non-linear and coupled controlled systems can be worn. Each of these rules leads to one linguistic output variable with an associated, after In accordance with the degree of membership changed membership Function.

This is indicated in Fig. 8. The rule specified in block 82 of FIG. 7 leads, with the specified values of the input variables, to the membership function of the linguistic value "zero" (ZE) which has been changed by a factor of 0.2. This is represented in FIG. 8 by block 90 (corresponding to FIG. 7). The same values of the input variables ε _k , _k and ω _k-1 lead to different linguistic input values with different degrees of membership, possibly to the applicability of another one of the stored rules and finally to another linguistic output value PM with one Membership function 68 and a membership function 94 changed by a factor of 0.15. This is indicated in FIG. 8 by a block 96 .

The changed membership functions 88 and 94 obtained are output and superimposed on outputs F ₁ and F ₂ . This is indicated by a "summing point" 96 . The result is a superimposed membership function m _u (ω), which is represented by curve 96 in FIG. 8. The output variable ω _{k of} the controller 22 is obtained from this superimposed membership function m _u (ω) by weighted averaging. It is formed with the function m _u (ω):

This variable ω _k forms the output variable of the controller 22 . The device for performing these operations is generally represented by a block 98 in FIG. 8.

FIGS. 9 and 10, a further application illustrate a regulator of the present type. In Fig. 9 and 10, a six-axis robot is controlled. Fig. 9, the control shows a pitch axis.

According to the prior art, a linear PID controller is provided for each of the axes with certain activation values for the P, D and I component. The controller controls a servomotor 100 ( FIG. 9). An angle encoder 102 attached to the axis to be controlled is used to feed back the actual value. Each controller works independently of the control processes of the other axes. There are various problems with this: It is difficult to set the activation values of the controllers on the various axes so that the robot as a whole under all conditions, e.g. B. disturbances, shows satisfactory static and dynamic behavior in the entire work area. The behavior of the controller can be very different from parameter fluctuations or changes. The behavior of the robot is influenced by the forces acting on the end effector, e.g. B. caused by loads.

A controller of the present type, with fuzzy logic and knowledge-based rules can become one lead more favorable control behavior.

In Fig. 9, 104 is a six-axis robot. Only the regulation of an axis with the servomotor 100 and the angle encoder 102 is considered. This regulation takes place by means of a controller 106 . An angular position setpoint is supplied to controller 106 via an input 108 . The desired angular position value is compared with an actual angular position value, which is supplied by the angle sensor 104 via a feedback loop 110 . The controller 106 supplies a control signal to the servomotor 100 via a line 112 .

A control deviation ε _{k is} formed by forming the difference between the commanded angular position setpoint at the input 108 and an actual angular position value from the angle transmitter 102 in a summing point 114 . The control deviation ε _k is connected to an input 116 of the controller 106 . The time derivative _k - the control deviation - is located at an input 118 of the controller 106 . Finally, at an input 120 - similar to FIG. 3 - the output variable ω _{k-1 of} the controller 106 delayed by a clock period T is present as feedback. The delayed output variable is fed back from the output 122 of the controller 106 to the input 120 via a feedback loop 124 . The feedback loop 124 contains a delay element which delays the output of the controller 106 by one clock period. The time derivative _{k of} the control deviation is formed from the control deviation by means of a delay element 128 . The difference between ε _k and ε _{k-1 is} formed at a summing point 130 . This difference, as represented by block 132 , is divided by the length T of the clock interval. That provides _k . The output 122 of the controller 106 delivers a rotational speed ω _{k of} the servomotor 100 . For this purpose, the output 122 of the controller 106 is connected to the servomotor 100 .

The structure of the controller 106 itself essentially corresponds to that of the controller 22 in the exemplary embodiment from FIGS. 1 to 9. The predetermined rules are of course adapted to the special conditions of the robot 104 .

Claims (7)

1. Controller to which input variables are connected and which supplies an output variable as a manipulated variable, characterized by :

• a) an unset logic circuit ( 58 ) for converting the input variables into linguistic values corresponding to overlapping value ranges of the input variables,
• b) first storage means ( 54 ) for defining membership functions, which are each defined in the individual value ranges and indicate a degree of membership in a linguistic value corresponding to the relevant value range,
• c) second storage means ( 92 ) for defining and storing rules for linking linguistic input values to form a liguistic output value,
• d) means ( 76 , 78 , 80 ) for determining the degrees of membership with which the input variables belong to the linguistic value ranges of the premise parts of the linking rules.
• e) a correlation logic circuit ( 86 ) for correlating the degrees of membership in accordance with the linking rules for the linguistic input values in order to form a level of membership for the linguistic output value,
• f) means ( 90 ) for changing the membership function of the linguistic output value in accordance with the degree of membership of this output value resulting from the correlation and
• g) means ( 98 ) for forming a controller output signal to be connected to the actuator means from the membership functions of the linguistic output values mentioned which have been changed in this way.

2. Controller according to claim 1, characterized in that the membership defined in the first storage means Functions are represented by a trapezoidal shape Functional representation with linear increase or decrease in the overlap areas of the neighboring value areas. 3. Controller according to claim 1 or 2, characterized in that in the second storage means rules in the form "If.., then. . "are saved, with the" if "part of the rule a combination of linguistic input values and the "then" part contains the initial linguistic value. 4. Controller according to claim 3, characterized in that the correlation logic circuit ( 86 ) takes into account the smallest of the degrees of membership of the linguistic input values when the linguistic input values are ANDed as the degree of membership of the linguistic output value. 5. Controller according to claim 3 or 4, characterized in that the correlation logic circuit ( 86 ) with an OR operation of the linguistic input values as the degree of membership of the linguistic output value the largest of the membership degrees of the linguistic input values considered. 6. Controller according to one of claims 1 to 5, characterized characterized that the means to change the Affiliation function of the mean output value contain this membership function for multiplication with the degree of affiliation of the initial value. 7. Controller according to one of claims 1 to 6, characterized in that the means ( 98 ) for forming a controller output signal to be connected to the actuator means generate as a controller output signal a weighted mean value of the output variables with the changed membership functions.