JPH0628005A - Control method using sliding mode control system - Google Patents

Abstract

PURPOSE:To control a controlled system by the convergence characteristic of an error appropriate to the control status of the controlled system. CONSTITUTION:A control output nu to a motor system 2 in a servo control system is switched and outputted by a sliding mode control system 3 so that the control status of the motor system 2 is converged upon a control sliding face for approaching errors e, e' or the like to '0' in accordance with a determination constant lambda for determining the convergence characteristics of the errors e, e' or the like in the control variable theta, theta' of the system 2. A switching variable S(= e'+lambdae) is used for the switching operation of the control output nu. After converging the switching variable S upon '0' (S=0), the constant lambda is variably set up at least based upon the error (e) and the primary time differential value e' of the error (e) (lambda=-e'/e). Thereby the determination constant lambdacapable of determining the convergence characteristic of a current appropriate error can be set up.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a sliding system for performing robust control by introducing a switching operation into an output to a controlled object including a nonlinear element such as a motor for driving each axis of a robot which has a large parameter variation. The present invention relates to a mode control system, and more particularly to a control method using a sliding mode control system capable of suppressing a steady-state error caused by control chattering.

[0002]

2. Description of the Related Art For example, when a robot or the like is driven, the load inertia applied to the motor and the nonlinear term vary greatly, so that highly accurate control cannot be performed by PID control. Therefore, the sliding mode control system as described above is applied. Servo control systems 21, 21 _a and 21 _b using the general sliding mode control system 23 as described above are shown in FIGS. 10, 11 and 12. A general sliding mode control system usually controls a secondary system, and here the motor system 2 represented by the following equation is set as a control target. J θ ″ + C = τ + D (1) where J: inertia (varies depending on the posture in the case of a robot etc.) θ: rotation angle of the motor τ: torque C: non-linearity of friction, viscosity, centrifugal force, Coriolis, gravity term, etc. Term D: Disturbance term In the following description, ′ attached to the right shoulder of each symbol is the first-order time derivative of the symbol, ″ is the second-order time derivative, and ^
Represents the estimated value. Each of the above servo control systems 21 to 2
In 1 _b , the rotation angle θ and the rotation angular velocity θ ′ as the controlled variables
Error e, e ′ for each target value θ _d , θ _d ′ of
The sliding mode control system 23 switches and outputs a calculation value for calculating the torque τ, which is a control command value to the motor system 2, so that the value becomes closer to zero. The servo control system 21 compensates the control command value from the sliding mode control system 23 by the estimated output calculated by the non-linear compensation system 6 to further improve the control accuracy. In addition, the servo control system 2
The motor system 2 to 1 _a, for example, to estimate the control state using the model 4 was expressed by the transfer function or the like, the torque τ of the estimated output J ^ θ "+ C ^ and motor system 2 from the model 4 Is calculated as a disturbance value δ by a subtractor 7. The disturbance value δ is compensated by a filter 5 as a disturbance estimation observer to calculate a disturbance estimated value δ ^, and the disturbance estimated value δ ^ is calculated. The control command value from the sliding mode control system 23 to the motor system 2 is compensated.

The servo control system 21 _b controls the motor system 2 by combining the nonlinear compensation system 6, model 4, subtractor 7, and filter 5 in each of the servo control systems 21 and 21 _a described above. The accuracy is further improved. The sliding mode control system 23 is a control system that can suppress the fluctuations of the nonlinear term C and the disturbance term D even if the nonlinear term C and the disturbance term D change suddenly and keep the errors e and e ′ at zero. Here, the error system for the motor system 2 can be expressed as Je ″ = τ−Jθ _d ″ −C + D (2). Now, when the torque τ is divided into the control input ν from the sliding mode control system 23 and the control input ξ from other control systems (for example, the non-linear system compensation system 6 and the filter 5), τ = ν + ξ (3 ). Thereby, the error system of the equation (2) is described as Je ″ = ν + E (4) E = ξ−Jθ _d ″ −C + D (5). Here, the control input ξ is (−Jθ _d ″
Considering the compensation input for −C + D), E in Eq. (5)
Can be considered as a compensation error that could not be compensated by the control input ξ. Further, the compensation error E can be separated into terms E _D e, E _V e ′ relating to the errors e and e ′ and a term E _C irrelevant to them, as in the following equation. E = E _C + E _D e + E _V e ′ (6) Here, E _C , E _D , and E _V are compensation error coefficients corresponding to the above-mentioned respective terms. By substituting equation (6) to (4), can be expressed as _{Je "= ν + E C +} E D e + E V e '... (7). The equation (7) the error system is stabilized asymptotically Thus, the control input ν of the sliding mode control system 23 is determined, where the switching variable S for switching the control input to the motor system 2 is selected.
Is expressed by the following equation: S = e ′ + λe (8) where λ is defined as a decision constant (positive number) for determining the convergence characteristic of the error e. And the sliding mode control system 2
The control input ν from 3 is obtained by the following equation. ν = − (K _C + K _D | e | + K _v | e ′ |) · sgn (S) (9) where sgn (x) returns a value of 1 if x ≧ 0, and x
If <0, it is a sign function that returns a value of -1.

Further, K _C , K _D and K _V are control gains which are set corresponding to the compensation error coefficients E _C , E _D and E _V , respectively. Therefore, the function V with a candidate Lyapunov function is set by the following equation, V = S ^2/2 ... (10). Furthermore, 1 time derivative value V of the function V 'is, V' = SS '= S (e "+ λe') = S (Je" + λJe ') / J = S (ν + E C + E D e + E V e' + λJe ′) / J = S (− (K _C + K _D | e | + K _V | e ′ |) · sgn (S) + E _C + E _D e + E _V e ′ + λJe ′) / J ≦ | S | (-(K _C + K _D | e | + K _V | e ′ |) + | E _C | + | E _D | × | e | + | E _V + λJ | × | e ′ |) / J = | S | ((| E _C | _{-K C) + (| E D} | -K D) | e | + (| E V + λJ | -K V) | e '|) / J ... a (11). Therefore, the control gains K _C , K _D , and K _V are _expressed as K _C ≧ | E _C | ... (12 _a ) K _D ≧ | E _D | (12 _b ) K _V ≧ | E _V + λ × (J ^ + ΔJ) | (12 _c ), and if these conditional expressions are satisfied, the first-order time differential value V ′ of the function V of the expression (11) is V ′ ≦ | S | ((| E _C | −K _C ) + (| E _D | −K _D ) | e | + (| E _V + λJ | −K _V ) e ′ |) / J ≦ 0 (13) Therefore, it can be seen that the function V is a well-known Lyapunov function for executing appropriate sliding mode control.

The Lyapunov function V is always positive and has a minimum value of 0. If V'≤0, the Lyapunov function V converges to the minimum value (= 0). In addition, the switching variable S
(Control slip surface) always converges, and the control response is S = 0.
Is determined by the constant response function of. That is, according to Lyapunov's theorem, the switching variable S is asymptotically stable, and if S → 0 (t → ∞) (14) is compensated and the switching variable S becomes 0, then e ′ = − λe (15) ) Holds from equation (8). As a result, the error e also becomes asymptotically stable, and the error e also converges to zero. In this case, it is important whether or not the control gain that satisfies the conditional expression (( _12a ) to ( _12c )) can be selected. Therefore, if the range of the error e is limited, it is possible to estimate the upper and lower limits of the compensation input ξ, the rotation angle θ, and the nonlinear term C. Therefore, the upper and lower limits of the compensation error E can also be determined. Furthermore, each compensation error coefficient E _C , E _D ,
The upper and lower limits of E _V can also be estimated. Therefore, it suffices to set the control gains K _C , K _D and K _V that are sufficiently larger than the estimated values of the upper and lower limits of each compensation error coefficient.

[0006]

SUMMARY OF THE INVENTION As described above, the slurry
According to the idling mode control system 23, theoretically the disturbance
Completely cancel the effects of fluctuations in term D, nonlinear term C, and inertia J
Therefore, optimum control can be performed. But
However, when performing actual control, the sign of the switching variable S
Therefore, it is necessary to switch the controller (not shown),
Can not be realized by analog control structure
Yes. Therefore, it is necessary to use a computer (CPU)
It is realized by the Tal control structure. Therefore,
Sampling cycle (switching output cycle)
Done. Thus, the above sliding mode control
According to the system 23, the control variable ν is disconnected by the switching variable S.
Every sampling cycle ΔT in order to change and change
Micro vibration called chattering occurs in the control of
However, this causes a steady error. As mentioned above
Sliding mode control, which is theoretically superior, is common
Chattering as described above is not widely used.
This is due to the phenomenon and the above steady-state error. In the example below,
The steady error will be described. The above steady error is the above control
The amount of change in the input ν that changed discontinuously and the sampling period Δ
It depends on T. Now, the above errors e and e'are minute.
Then, according to the control law of equation (9), the torque τ which is the control command value
The discontinuous change in the above can be calculated from Eqs. (9) and (3) above.
In K_CBecomes Therefore, the steady-state error e_fIs the function
Staff ｜ e_f│ ≦ △ T × ｜ K_C-E_C| / Λ / J (16) Therefore, the above sliding mode control system
Steady error e_fIn order to reduce the
Shortening cycle ΔT, or the term of the above control gain
K_C-E_COr decrease the above decision constant λ.
It can be realized by But Naga
, The sampling period ΔT depends on the calculation speed of the CPU, etc.
Due to this, there is a limit to shortening. In addition, the above control
Gain K_CIs a conditional expression ((12_a) Expression)
In order to satisfy this conditional expression, the control gay
N K _CIs the compensation error coefficient E_CSet to a fairly large value
It is fixed. This is the conditional expression ((12_a) ~ (1
Two_c) Each compensation error coefficient E in Eq._c, E_D, E_VThe value of
I am uncertain and I can only get a rough value.
Therefore, these upper and lower limits are also set as rough values.
It Therefore, each control gain corresponding to these is compensated
Unless it is set to a value much larger than the error coefficient,
Because it may not be possible to satisfy the above conditional expression.
It For this reason, the control gain term K_C-E_C
There is also a limit to the extremely small value of.

On the other hand, the convergence characteristic of the error e by the sliding mode control system 23 is determined depending on the value of the determination constant λ. However, in the prior art, the above-mentioned determination constant λ, once set, remains a fixed value and is generally not changed during control. And
The convergence characteristic of the error e is uniquely determined by the set decision constant λ. However, as the convergence characteristic of the error e, there may be another preferable convergence characteristic from the viewpoint of sliding mode control. However, in the prior art, since the convergence characteristic of the error e is constant, the error e is not always converged by the preferable convergence characteristic as described above. On the other hand, in the sliding mode control system 23, as shown in the equation (14), first, the switching variable S is calculated so as to converge to 0, and when the switching variable S converges to 0, the equation (15) is established. Error e
The convergence property of becomes clear. However, the error e between the current control amount and the target amount may be extremely large, such as when the control is in the initial state or when the target angle θ _d is suddenly and largely changed. In such a case, the control state of the motor system 2 is in a state where it is far from the control slip surface, that is, the switching variable S is far from 0. In such a state, it is not clear what convergence characteristic the error e behaves. There is also a problem that the convergence characteristic of the error e becomes unclear for a relatively long time until the switching variable S converges to zero. Therefore, an object of the present invention is to provide a sliding mode control system capable of controlling the controlled object by controlling the controlled object using the sliding mode control system by the convergence property of the error suitable for the control state of the controlled object. It is to provide the control method used.

[0008]

In order to achieve the above-mentioned object, the main means adopted by the present invention is the gist of the present invention. However, in order to bring the error of the control amount close to 0 In a control method using a sliding mode control system for switching and outputting a control command value to the controlled object so that the state converges in accordance with a preset constant for determining the convergence characteristic of the error , The above-mentioned decision constant is at least the above error and one of the errors
It is configured as a control method using a sliding mode control system, which is set so as to be changeable based on the next time differential value. As the above-mentioned decision constant, it is also possible to adopt a configuration in which the above-mentioned decision constant is largely changed as the above-mentioned error decreases. Further, within the range in which the above-mentioned determination constant satisfies the following conditional expression λ <0.5 / ΔT (where λ: the above-mentioned determination constant), which shows the relationship between the control command value and the switching output cycle ΔT, The configuration may be changed so that Then, when the maximum acceleration of the controlled object is set in advance, the decision constant is calculated using a conditional expression for obtaining a first-order time differential value of the decision constant using the maximum acceleration. It is also possible to adopt a configuration in which the setting is changed based on the primary time differential value of. Further, it is also possible to adopt a configuration in which the above-mentioned error and the first-order time differential value of this error are forcibly set when the above-mentioned error is extremely large.

[0009]

In the control method using the sliding mode control system according to the present invention, the decision constant for determining the convergence characteristic of the error in the sliding mode control system is not a constant value during the control. , Is set to be changeable based on at least the error and the first-order time differential value of the error. Therefore, the control state can be converged with an arbitrary convergence characteristic by the decision constant set to be changeable as described above. Therefore, for example, it is possible to change the setting of the determination constant so that the convergence characteristic of the error is preferable for the control state at that time.
It should be noted that if the above-mentioned decision constant is changed so that it becomes larger as the above-mentioned error decreases, it is possible to prevent chattering of the control state that should be converged on the above-mentioned control slip surface, and the steady state caused by this The error can be made extremely small. Further, when the above-mentioned decision constant is increased within a range satisfying the conditional expression showing the relation between the control command value and the switching output cycle ΔT, the decision constant is controlled without being changed more than necessary. The efficiency above can be increased. When the maximum acceleration of the controlled object is preset, the decision constant is 1 of the decision constant.
When the setting is changed based on the next time differential value, the decision constant for converging the error in the shortest time can be set. On the other hand, when the error is extremely large, for example, in the initial state of control, the error and the first-order time differential value of the error are calculated so that the control state converges on the control slip surface. By forcibly setting the switching variable to 0, the decision constant is forcibly set by the error and the first-order time differential value of the error. Therefore,
The inconvenience that the switching variable does not converge for a relatively long period of time, the setting of the decision constant cannot be changed during that period, and the convergence characteristics of the error cannot be predicted can be solved. It

[0010]

Embodiments of the present invention will be described with reference to the accompanying drawings.
Examples will be described to provide an understanding of the present invention. In addition,
The following example is an example embodying the present invention.
It does not limit the technical scope of Ming. here
FIG. 1 shows a sliding mode according to an embodiment of the present invention.
Block diagram showing a servo control system equipped with a drive control system, Fig. 2
Indicates a servo control system with a disturbance estimation observer.
Fig. 3 shows a nonlinear compensation system added to the servo control system of Fig. 2.
FIG. 4 is a block diagram showing the configuration of the obtained servo control system.
Error Convergence Characteristic of Servo Control System Using Transfer Function
The sliding mode control system expressed as
Rotation angle θ when simulating the stem
Fig. 4 is a graph showing the step response results for
Decision decision corresponding to the step response result of the indicated rotation angle θ
Fig. 6 is a graph showing the change of several λ over time.
At constant angular acceleration (maximum acceleration) set in
If the time response with the shortest difference convergence time is simulated,
Fig. 7 is a graph showing the result of step response in the case of
Represents the change over time of the decision constant λ corresponding to the step response result
The graph and Fig. 8 are under different conditions from those shown in Fig. 4.
Rotation angle obtained by simulation of secondary system
FIG. 9 is a graph showing the step response result of the degree θ, and FIG.
The change over time of the decision constant λ corresponding to the step response result is displayed.
It is a graph figure. However, as shown in FIGS.
Conventional servo control system 21, 21_a, 21 _bIn common with
The same symbols are used for the elements, and detailed explanations are given.
The description is omitted. The servo control system 1 according to this embodiment is shown in FIG.
As shown in, the motor system 2 (rotation from the controlled object
Angle θ, rotation angular velocity θ ′ (control amount)
Corresponding target value θ_d, Θ_dBased on the error e, e '
Sliding mode control system 3 calculates
The force ν (equation (3)) is calculated and output. And the above service
The non-linear compensation system 6 of the control system 1 uses the current rotation angle θ ′.
And rotational angular velocity θ ″, etc. and target values corresponding to these
θ_d′, Θ_d″ Etc.
Estimated output J ^ θ_d”+ C ^ is calculated. This estimated output
The control input from the sliding mode control system
The torque τ (control command value) that compensates for the force ν is calculated.
Output to the data system 2.

By the way, the servo control system 1 of the present embodiment is
The basic configuration of the conventional servo control system 21 shown in FIG.
Almost the same, but different from the above conventional servo control system 21
Is at least the rotation as a state quantity of the motor system 2.
Angle θ, rotational angular velocity θ ′ and target values corresponding to these
θ_d, Θ_d’, And the corresponding error e,
e ′ is calculated, and this error e and the first-order time differential value of the error e
For sliding mode control system 3 based on
The decision constant λ can be set to be changeable
That is, the λ adjuster 8 is provided. The above λ adjustment
If the decision constant λ is changed by the instrument 8 as described above,
In this case, the above equations (11) to (13) are used as they are.
Can't do it. Therefore, change the above decision constant λ.
(11) is transformed into the following equation.
It V ′ = SS ′ = S (e ″ + λe ′ + λ′e) = S (Je ″ + λJe ′ + λ′Je) / J = S (ν + E_C+ E_De + E_Ve ′ + λJe ′ + λ′Je) / J = S (-(K_C+ K_D│e│ + K_V│e'│) ・ sgn (S) + E_C + E_De + E_Ve ′ + λJe ′ + λ′Je) / J ≦ | S | (-(K_C+ K_D│e│ + K_V| E '|) + | E_C｜ ＋ ｜ E_D+ Λ'J | × | e | + | E_V+ ΛJ ′ | × | e ′ |) / J = | S | ((| E_C｜ -K_C) + (| E_D+ Λ'J | -K_D) | E | + (| E_V+ ΛJ | -K_V) | E '|) / J (17) On the other hand, (12_a) Expression ~ (12_c) Control gay corresponding to the expression
N K_C, K_D, K_VAre transformed as
To be done. K_C≧ | E_C｜… (18_a) K_D≧ | E_D+ Λ '+ (J ^ + ΔJ) | ... (18_b) K_V≧ | E_V+ Λ × (J ^ + ΔJ) |… (18_c) The control gain is (18_a) Expression ~ (18_c) Like the formula
If transformed, the first-order time derivative of the function V shown in equation (17)
The value V ′ is a negative value, similar to the equation (13), and
It can be said that the number V is a Lyapunov function. By the way, (18_b)
In the second term on the right side of the equation, the compensation error coefficient E_DShould meet
As a condition, there is a term of the first-order time differential value of the above decision constant λ.
Existence Consider the first-order time derivative λ'of the above decision constant
Then, the conditional expression (18_a) ~ (18 _c)formula
Within the range of the control gain determined to satisfy
The decision constant λ can be varied.

Modes for changing the setting of the determination constant λ based on at least the error e and the first-order time differential value e ′ of the error will be described below for each mode. Steady state error e _f in sliding mode control system 3
Modification for reducing the above-mentioned steady-state error e _f depends on the above-mentioned determination constant λ in addition to the sampling period ΔT and control gain K _C , as is apparent from the equation (16). I understand. Therefore, in order to reduce the steady-state error e _f , (1
Within a range satisfying the 8 _a) formula ~ (18 _c) type, it may be as large as possible setting the decision constant lambda. Changing mode for setting and changing the decision constant λ while preventing overshoot of the control state on the control slip surface By the way, when the error e is relatively large, the decision constant λ
If the value is made extremely large, the change speed of the error e becomes larger than the speed at which the switching variable S converges to 0, which causes the control state of the motor system 2 to overshoot the control slip surface. Therefore, the above decision constant cannot be unnecessarily increased. More specifically, if the decision constant λ is increased, the error e reacts sensitively, so that the error e quickly approaches zero before the switching variable S converges to zero. However, since the first differential value e'of the error is too large, the control state of the error e largely overshoots from the control slip surface. That is, until the switching variable S gradually converges to 0, the error e repeats overshooting and causes a large amplitude chattering phenomenon that vibrates largely in the vicinity of 0. Then, as the switching variable S converges to 0, the amplitude of the error e also decreases.

Therefore, as shown in, the decision constant λ cannot be unnecessarily increased only to reduce the steady-state error e _f , and as the error e decreases, that is, the error e becomes sufficiently small. with the, by the decision constant λ is increased, it is possible to achieve any of the effect of preventing the overshoot of the possible and the error e to reduce the steady-state error e _f. For example, the determination constant λ and the error e
For some constants Λ, e _min , and e _{max related} to, the decision constant λ can be defined as: When e ≧ e _min λ = Λ / e _min ( _19a ) When e _min > e ≧ e _max λ = Λ / e ( _19b ) When e _max > e λ = Λ / e _max (( _19a ) 19 _c ) Here, Λ / e _min is set as the lower limit value of the decision constant λ, and is for preventing the decision constant λ from being set too small. Also, Λ / e _max is the decision constant λ
Is set as the upper limit value of. Therefore, by arbitrarily setting the determination constant λ between the upper limit value and the lower limit value, it is possible to control the motor system 2 with a preferable error convergence characteristic suitable for the control state of the control target. .

Changing Mode of Decision Constant λ Due to Control Function of Servo Control System 1 As described in the above section, the reason why the upper limit value for setting the decision constant λ as small as possible is set will be described below. When the controller switching control of the sliding mode control system 3 is performed every certain sampling period ΔT, between the sampling period ΔT and the determination constant λ that also represents the response speed of the motor system 2 as a control target. , The following equation holds as the basis of the digital control method. λ <0.5 / ΔT (20) Therefore, even if the above-mentioned determination constant λ is set to be larger than 0.5 / ΔT, it is useless for the control response and may result in a bad response result. This is to avoid Modification of the above-mentioned determination constant λ when the error convergence characteristic by the sliding mode control system 3 is given by using a transfer function. For example, when the error convergence characteristic is given by the transfer function G,
The following equation is set as the transfer function G. G = ω ² / (s ² + 2ζωs + ω ² ) (21) Then, from this equation (21) and the equation (15) (e ′ = − λe) when the switching variable S = 0, the following equation is established. To do. ^{e "= - 2ζωe'-ω 2} e = -λe'-λ'e ... (22) and first-order time differential value of the decision constant λ of this time λ '
Can be given as λ ′ = {(2ζω−λ) e ′ + ω ² e} / e = − (2ζω−λ) λ + ω ² = λ ² −2ζωλ + ω ² (23) However, when the control input ζ from the nonlinear compensation system 6 is 1 or less, the decision constant λ may become infinite, and the decision constant λ needs to be set sufficiently larger than the value of 1. . Then, if λ >> 1, the following equation is solved using the reciprocal σ (= 1 / λ) of the above-mentioned determination constant λ. [sigma] '=-1 + ^{2 [} zeta] [omega] [lambda]-[omega] ^{2 [} lambda] ² (24) The determination constant [lambda] may be determined by solving this equation (24) to obtain [sigma].

FIG. 4 shows the result of the step response regarding the rotation angle θ when the decision constant λ is changed so as to simulate the response of the servo control system 1 as the response of the secondary system by using the transfer function G as described above. Shown in. Further, FIG. 5 shows changes in the decision constant λ corresponding to the response curve C1 in FIG. That is, by changing the determination constant λ during the control of the motor system 2 as shown in FIG. 5, it is possible to obtain the response characteristic as shown by the curve C1. Therefore, it is possible to arbitrarily change the determination constant λ, and it is possible to obtain a suitable error convergence characteristic according to the control state of the motor system 2. When the maximum angular acceleration a is given to the motor system 2 and the decision constant λ is changed to minimize the convergence time of the error In this case, the first-order time differential value λ ′ of the decision constant λ is Calculate from the formula. λ ′ = (a · e · sgn (e−e ′ ² / 2a) −e ′ ² ) / e ² (25) The first-order time differential value λ ′ of the above decision constant is the maximum angular acceleration a and the error e. , The first-order time differential value e ′ of the error is calculated, and the determination constant λ may be changed according to the first-order time differential value λ ′ of the calculated determination constant. However,
According to the equation (25), when the error e becomes 0, the first-order differential value λ ′ of the decision constant also becomes 0. Therefore, in order to avoid this, a small amount Δe of the error e is considered in the equation (25). Then (2
Equation (5) may be transformed into the following equation. λ ′ = (a · e · sgn (e−e ′ ² / 2a) −e ′ ² ) / (e ² + Δe) (26) The determination determined by the above formula (25) or formula (26) If the constant λ is used, the maximum angular acceleration a is given to the motor system 2, whereby the error convergence characteristic in the shortest convergence time can be obtained when the angular acceleration θ ′ is limited. As described above, the maximum angular acceleration a (= 2000
rotation angle θ when the determination constant λ is changed so that the convergence time is the shortest when rad / sec ² ) is provided.
The simulation result of the step response with respect to is shown by the curve C2 in FIG. Further, FIG. 7 shows the result of changing the decision constant λ whose setting has been changed at this time. Therefore, according to the modification shown by, even if the control regulation condition for the control of the motor system 2 is given, the determination constant λ can be arbitrarily changed within the range satisfying the regulation condition. Further, the setting of the decision constant λ can be changed so that the above-mentioned control state becomes the best. Change mode of the decision constant λ when the current control state is away from the target state, for example, when the error e is extremely large. Now, when the control state of the servo control system 1 is in the initial state, for example, the target value of the rotation angle It is assumed that the switching variable S is not 0 as in the case where the setting of θ _d is suddenly changed. In the case of the change modes in the above, the case where e = 1, e ′ = 0 is considered as the initial state, and since the initial value of the decision constant λ is set to 0, the switching variable S becomes 0, Good responses as shown in FIGS. 4 and 6 could be obtained. On the other hand, in the initial state of, if e = 1, e ′ ≠ 0, λ = 0, S ≠ 0, and a good response as shown in FIGS. 4 and 6 cannot be obtained.

Therefore, in the present embodiment, as in the initial state or when the target value θ _d is suddenly changed, the S
When ≠ 0, that is, when the following equation holds for a small value S _{min of the} switching variable S, | S | ≧ S _min (27) The error e at that time and the first-order time derivative of the error By forcibly setting the decision constant λ from the following equation based on the value e ′, λ = −e ′ / e (28) The switching variable S can be forcibly set to zero. Therefore, the determination constant λ
A desired error converging characteristic can be given by arbitrarily changing. For example, in the modified mode, when e = 1, e ′ = 100 as the initial state of the control state, the initial value of the decision constant λ is, for example, −1 from the equation (28).
If 00, the switching variable S becomes 0. Then, after that, the determination constant λ may be changed based on the equation (23). According to this embodiment, it is possible to forcibly eliminate the case of the control state (S ≠ 0) in which it is impossible to predict how the error will converge, whereby the error e can be converged to an arbitrary convergence characteristic. And, it can be converged in a short time. According to this embodiment, the decision constant λ is forcibly set, and further the switching variable S is forcibly set to 0,
The curve C3 of FIG. 8 shows the simulation result of the step response of the rotation angle θ when the above-mentioned determination constant λ is changed so as to simulate the secondary system obtained by using the equation (23). Further, FIG. 9 shows the result of changing the decision constant λ at this time. In each of the above-described embodiments, the servo control system 1 of FIG. 1 has been described.
The controller 8 can be applied to the conventional servo control system 21 _a (FIG. 11) and the servo control system 21 _b (FIG. 12), and the configuration corresponding to these can be applied to the servo control system shown in FIG. a 1 _a, or a servo control system shown in FIG. 3 1 _b
Is. For these servo control systems 1 _a and 1 _b ,
With respect to the setting change of the determination constant λ, it is possible to obtain the same operation effects as the operation effects according to the changing modes 1 to 3 shown in the servo control system 1.

[0017]

The present invention is constructed as described above. As a result, the decision constant can be arbitrarily set and changed to a value that can obtain the error convergence characteristic suitable for the control state of the controlled object. Therefore, the above-mentioned controlled object is controlled with high accuracy by the sliding mode control system according to a suitable error convergence characteristic. For example, the above-mentioned decision constant is appropriately set and changed so as to suppress chattering in the sliding mode control system, so that the steady-state error can be reduced, and further, any desired error convergence can be achieved. The characteristic makes it possible to control the controlled object. Further, by forcing the control state of the controlled object to converge on the control slip surface, it is possible to prevent the convergence of the error from becoming unpredictable.

[Brief description of drawings]

FIG. 1 is a block diagram showing a servo control system including a sliding mode control system according to an embodiment of the present invention.

FIG. 2 is a block diagram showing a servo control system including a disturbance estimation observer.

FIG. 3 is a block diagram showing a configuration of a servo control system in which a nonlinear compensation system is added to the servo control system of FIG.

4 is a step response result regarding a rotation angle θ when a secondary system is simulated by using a sliding mode control system in which an error convergence characteristic in the servo control system of FIG. 1 is expressed by using a transfer function. The graph figure which shows.

5 is a graph showing the change over time of the decision constant λ corresponding to the step response result of the rotation angle θ shown in FIG.

FIG. 6 is a graph showing a step response result when a time response having a shortest error convergence time at a constant angular acceleration (maximum acceleration) set in the motor system is simulated.

FIG. 7 is a graph showing a change with time of a decision constant λ corresponding to the step response result of FIG.

FIG. 8 is a graph showing a step response result of a rotation angle θ obtained by a simulation of a secondary system under a condition different from the condition shown in FIG.

9 is a graph showing a change with time of a decision constant λ corresponding to the step response result of FIG.

FIG. 10 is a block diagram corresponding to FIG. 1 showing a conventional servo control system as an example of the background of the present invention.

FIG. 11 is a block diagram showing a servo control system which is another example of the conventional art and corresponds to the servo control system of FIG. 2.

12 is a block diagram corresponding to the servo control system of FIG. 3 showing a servo control system as still another example of the conventional art.

[Explanation of symbols]

1, 1 _a , 1 _b , 21, 21 _a , 21 _b ... Servo control system 2 ... Motor system (control target) 3, 23 ... Sliding mode control system 4 ... Model 5 ... Filter 6 ... Non-linear compensation system 8 ... λ adjustment Τ ... Torque (control command value) λ ... Determination constant a ... Maximum angular acceleration e ... Error e '... First time differential value of error ΔT ... Sampling cycle (switching output cycle)

Claims (5)

[Claims] 1. A control state of a control target on a control slip surface for bringing an error of a control amount close to 0 converges in accordance with a preset decision constant for determining a convergence characteristic of the error. In a control method using a sliding mode control system for switching and outputting a control command value to the controlled object, the determination constant is set to be changeable based on at least the error and a first-order time differential value of the error. A control method using a sliding mode control system characterized by the above. 2. The control method using a sliding mode control system according to claim 1, wherein the decision constant is changed so as to be increased as the error decreases. 3. The following conditional expression λ <0.5 / ΔT (where λ: the above-mentioned decision constant), which shows the relationship between the above-mentioned decision constant and the switching output cycle ΔT of the above-mentioned control command value, is satisfied. The control method using the sliding mode control system according to claim 1, wherein the setting is changed so as to be large within the range. 4. When the maximum acceleration of the controlled object is preset, the following constant expression λ ′ = (a · e · sgn (e− (e ′) ² / 2a) −
(E ′) ² ) / e ² where λ ′: first-order differential value of the above-mentioned determination constant e: the above-mentioned error e ′: first-order time differential value of the above-mentioned a: maximum acceleration sgn (x): x The value is 1 when ≧ 0, and the value is 0 when x <0. The setting is changed based on the first-order time differential value of the decision constant calculated by the sign function. A control method using a sliding mode control system. 5. The control using the sliding mode control system according to claim 1, wherein the decision constant is forcibly set by the error and the first-order time derivative of the error when the error is extremely large. Method.