CN108828958A - It is a kind of to inhibit the discrete time controller of strategy to attract rule design method without switching using interference difference - Google Patents
It is a kind of to inhibit the discrete time controller of strategy to attract rule design method without switching using interference difference Download PDFInfo
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract
It is a kind of to inhibit the discrete time controller of strategy to attract rule design method without switching using interference difference, it gives module and generates reference signal；According to the concrete form for giving reference signal, corresponding interference differential compensation feedback element is constructed, output signal is for the interference compensation in digitial controller；Based on rule building perfect error is attracted dynamically without switching, according to perfect error dynamic design digitial controller, current controller is calculated into the signal obtained as the input of target servo.Specific attitude conirol can be carried out according to the index of characterization system convergence performance, provide the steady-state error band of characterization tracking error convergence process, the expression of absolute attractable layer and monotone decreasing region.It is provided by the invention to attract rule design method without switching, according to given reference signal, using corresponding interference differential compensation measure, servo-system tracking accuracy is improved by inhibiting to interfere, has the control effect for eliminating system chatter concurrently.
Description
Technical field
The digitial controller of strategy is inhibited to attract rule design method without switching using interference difference the present invention relates to a kind of, it should
Method is suitable for positional servosystem, is also applied for other industrial applications.
Background technique
Reaching law method is the effective tool of servo system sliding-mode controller design, due to using Reaching Law, closed-loop system
Dynamic process shows as approach procedure and sliding mode, and stability and convergence are by specific Reaching Law and switching function form
It is determined.Practical controller design need to consider the influence of various disturbances, by Method of suppression disturbance " insertion " in former Reaching Law, repair
Reaching Law after changing forms ideal switching dynamic.In this way, the controller according to ideal switching dynamic design can effectively inhibit to disturb
It is dynamic.
Rule method is attracted to directly adopt tracking error signal, without defining switching function, controller design is more direct, simple
It is clean.Rule is attracted to reflect desired systematic error dynamic characteristic when not considering disturbance；In the case of there is interference, direct basis
Controller caused by restraining is attracted to cannot achieve.Interference suppression measure " insertion " can be attracted and be restrained, building has Disturbance Rejection effect
Perfect error dynamic.Perfect error dynamical equation according to construction designs digitial controller, and closed-loop system dynamic process is by managing
The expectation tracking performance thinking that error dynamics are determined, and being characterized with perfect error dynamic.
Rule method is attracted to be different from the reaching law method of discrete sliding mode control.The main distinction of the two is shown：Attract rule
Tracking error is replaced switching function, origin to replace diverter surface by method；Reaching law method requires finite time to reach diverter surface, and
Attract rule method that finite time is required to reach origin；The closed-loop system of rule method design is attracted still to have about parameter drift and outer
The robust performance of portion's interference, only sliding formwork control focuses on the invariance of sliding formwork movement, and rule method is attracted to pursue systematic steady state
Invariance.
When attracting rule method discrete controller, the index for portraying tracking error transient state and stable state behavior can be by ideal
Error dynamics provide, and specifically have following four indexs：Steady-state error band, absolute attractable layer, monotone decreasing region and tracking miss
Difference first enters most step numbers needed for steady-state error band.In fact, the specific value of four indexs depends on controller parameter,
Controller parameter is different, and the value of four indexs is also different.Once given perfect error dynamic-form, can provide four fingers in advance
Target expression is used for attitude conirol.In the attraction rule method delivered at present, four indexs are all relied on
Imitate the boundary of interference signal.Effectively inhibit interference, reduce the boundary of equivalent interference signal to be the problem for attracting rule method urgently to be resolved.
Summary of the invention
The present invention provides a kind of Design of Digital Controller suitable for positional servosystem and attracts rule method without switching.For suppression
Influence of the interference signal processed to servo-system performance improves tracing control precision, using interference differential compensation technology, is embedded into
Attract in rule without switching, to construct the perfect error dynamic with Disturbance Rejection ability.According to perfect error dynamic design
Digitial controller, so that the characteristic that there is closed-loop system perfect error dynamic to be portrayed, so that it is anti-dry to improve positional servosystem
Disturb ability and tracking performance.Controller design, which is used, attracts rule without switching, can eliminate chattering phenomenon.The present invention specifically gives surely
State error band, absolute attractable layer, monotone decreasing region and tracking error first enter most step numbers etc. needed for steady-state error band
The expression of four indexs can be used for instructing attitude conirol.
The present invention solve the technical solution that uses of above-mentioned technical problem for：
It is a kind of to inhibit the discrete time controller of strategy to attract rule design method without switching using interference difference including following
Step：
Step 1. gives reference signal rkFor the multinomial of time variable k, M indicates the polynomial highest power, three kinds
Reference signal is as follows：
1) square-wave signal, M=0
2) triangular signal, M=1
3) S curve, M=3
Wherein, A is amplitude, and N is the sampling number of reference signal in one cycle；
Step 2. constructs perfect error dynamic
Attract rule for without switching
ek+1=(1- ρ (ek))ek (4)
Wherein, δ > 0 is for adjusting the parameter for attracting speed, ek=rk-ykFor the system tracking error at k moment, ykFor k
Interference suppression measure is embedded in attraction rule, construction perfect error dynamic by the system real output signal at moment
Wherein, dk+1For the equivalent interference at k+1 moment,For compensating equivalent interference,For equivalent interference benefit
Repay error；
Step 3. interferes differential compensation strategy
The effect of equivalent interference compensation is taken to be
Equivalent interference is defined for specific reference signal, form is
Equivalent interference signal when M=0
dk+1=wk+1 (7)
Equivalent interference signal when M=1
dk+1=wk+1-wk (8)
Equivalent interference signal when M=3
dk+1=[(wk+1-wk)-(wk-wk-1)]-[(wk-wk-1)-(wk-1-wk-2)] (9)
Wherein, wk+1For the interference at k+1 moment；
Definition interference difference step number is L, and L indicates that interference compensation error includes the interference of L successive one, such as formula (7), two
Step interference difference dk+1-dk=wk+1-wk, include wk+1With wkTwo moment interference are selecting equivalent interference effectively to inhibit interference
When, following condition should be met
Wherein,For not less than smallest positive integral；
Step 4. controller design
According to perfect error dynamic (6) and equivalent interference signal dk+1, provide the expression formula of device control as follows：
1) for square wave reference signal formula (1),
Wherein, F (q-1)=B (q-1)-b0。
2) for triangle reference signal wave formula (2),
Wherein,
3) for S curve reference signal formula (3),
Formula (11) is into formula (13), A (q-1)、B(q-1) it is servo-system
A(q-1)yk=q-1B(q-1)uk+wk (14)
About q-1Parametric polynomial：
A(q-1)=1+a1q-1+a2q-2+……+anq-n
B(q-1)=b0+b1q-1+b2q-2+……+bmq-m
Wherein, ukWith ykThe respectively input and output signal at servo-system k moment, q-1For One-step delay operator, m, n divide
It Wei not A (q-1)、B(q-1) order, b0≠ 0,1≤m≤n.
Further, the method also includes：
Step 5. performance evaluation
It provides steady-state error band, absolute attractable layer, monotone decreasing region and tracking error and first enters steady-state error band institute
The expression for needing most four indexs of step number, for describing system tracking performance and instructs attitude conirol, wherein
Steady-state error band, absolute attractable layer and monotone decreasing region are defined as follows：
1) steady-state error band (ΔSSE)
2) absolute attractable layer (ΔAAL)
3) monotone decreasing region (ΔMDR)
Equivalent interference compensation error meetsWhen, the expression formula of each index is as follows：
Steady-state error band (ΔSSE)
Absolute attractable layer (ΔAAL)
Monotone decreasing region (ΔMDR)
Restrain step number
Wherein, e0For tracking error initial value.
The technology of the present invention is contemplated that：A kind of restraining without switching attraction for positional servosystem Tracking Control Design is provided
Method.Equivalent interference is defined according to given reference signal, interference suppression measure insertion is attracted in rule without switching, formation has dry
Disturb the perfect error dynamic of inhibiting effect.According to perfect error dynamic design digitial controller, to realize to given reference signal
Accurate tracking.
Beneficial effects of the present invention are mainly manifested in：According to given reference signal, differential compensation measure is interfered using corresponding,
Tracking accuracy is improved by inhibiting to interfere.Meanwhile attracting rule using without switching discrete time, eliminate system chatter.
Detailed description of the invention
Fig. 1 is servo-system block diagram.
Fig. 2-Fig. 4 is rk=10sin (2 π fkTs) deg, f=10Hz, Ts=0.01, when Δ=0.6, using controller formula
(20) Numerical Simulation Results, wherein tracking error signal e when Fig. 2 is δ=1.9 Δk；Tracking when Fig. 3 is δ=3 Δ misses
Difference signal ek；Fig. 4 is mushing error compensation
Fig. 5-Fig. 8 is reference signal rkSuch as formula (1), A=5, TsWhen=0.005, δ=0.8, using controller formula (20)
Numerical Simulation Results, wherein Fig. 5 is reference signal rkWith output signal yk；Fig. 6 is tracking error signal ek；Fig. 7 is that interference misses
Difference compensationFig. 8 is control signal uk。
Fig. 9-Figure 12 is reference signal rkIt is imitative using the numerical value of controller formula (20) when A=10, δ=0.8 such as formula (2)
Very, wherein Fig. 9 is reference signal rkWith output signal yk；Figure 10 is tracking error signal ek；Figure 11 is mushing error compensationFigure 12 is control signal uk。
Figure 13-Figure 16 is reference signal rkSuch as formula (2), A=10, TsWhen=0.005, δ=0.8, using controller formula
(21) Numerical Simulation Results, wherein Figure 13 is reference signal rkWith output signal yk；Figure 14 is tracking error signal ek；Figure 15
It is mushing error compensationFigure 16 is control signal uk。
Figure 17-Figure 20 is reference signal rkSuch as formula (3), A=5, TsWhen=0.005, δ=0.8, using controller formula (20)
Numerical Simulation Results, wherein Figure 17 is reference signal rkWith output signal yk；Figure 18 is tracking error signal ek；Figure 19 is dry
Disturb error compensationFigure 20 is control signal uk。
Figure 21-Figure 24 is reference signal rkSuch as formula (3), A=5, TsWhen=0.005, δ=0.8, using controller formula (21)
Numerical Simulation Results, wherein Figure 21 is reference signal rkWith output signal yk；Figure 22 is tracking error signal ek；Figure 23 is dry
Disturb error compensationFigure 24 is control signal uk。
Figure 25-Figure 28 is reference signal rkSuch as formula (3), A=5, TsWhen=0.005, δ=0.8, using controller formula (22)
Numerical Simulation Results, wherein Figure 25 is reference signal rkWith output signal yk；Figure 26 is tracking error signal ek；Figure 27 is dry
Disturb error compensationFigure 28 is control signal uk。
Figure 29-Figure 30 is reference signal rkSuch as formula (1), A=15deg, TsWhen=0.2ms, δ=0.8, using controller formula
(20) experimental result, wherein Figure 29 is to be followed successively by reference signal rkWith output signal yk, control signal uk, tracking error signal
ekIt is compensated with mushing errorFigure 30 is tracking error signal ekHistogram.
Figure 31-Figure 32 is reference signal rkSuch as formula (2), A=90deg, TsWhen=0.2ms, δ=0.8, using controller formula
(20) experimental result, wherein Figure 31 is to be followed successively by reference signal rkWith output signal yk, control signal uk, tracking error signal
ekIt is compensated with mushing errorFigure 32 is tracking error signal ekHistogram.
Figure 33-Figure 34 is reference signal rkSuch as formula (2), A=90deg, TsWhen=0.2ms, δ=0.8, using controller formula
(21) experimental result, wherein Figure 33 is to be followed successively by reference signal rkWith output signal yk, control signal uk, tracking error signal
ekIt is compensated with mushing errorFigure 34 is tracking error signal ekHistogram.
Figure 35-Figure 36 is reference signal rkSuch as formula (3), A=135deg, TsWhen=0.2ms, δ=0.8, using controller
The experimental result of formula (20), wherein Figure 35 is to be followed successively by reference signal rkWith output signal yk, control signal uk, tracking error letter
Number ekIt is compensated with mushing errorFigure 36 is tracking error signal ekHistogram.
Figure 37-Figure 38 is reference signal rkSuch as formula (3), A=135deg, TsWhen=0.2ms, δ=0.8, using controller
The experimental result of formula (21), wherein Figure 37 is to be followed successively by reference signal rkWith output signal yk, control signal uk, tracking error letter
Number ekIt is compensated with mushing errorFigure 38 is tracking error signal ekHistogram.
Figure 39-Figure 40 is reference signal rkSuch as formula (3), A=135deg, TsWhen=0.2ms, δ=0.8, using controller
The experimental result of formula (22), wherein Figure 39 is to be followed successively by reference signal rkWith output signal yk, control signal uk, tracking error letter
Number ekIt is compensated with mushing errorFigure 40 is tracking error signal ekHistogram.
Specific embodiment
The specific embodiment of the invention is described further with reference to the accompanying drawing.
Fig. 1 is servo-system block diagram.Referring to Fig. 2-Figure 40, a kind of discrete time control inhibiting strategy using interference difference
Device processed attracts rule design method without switching, includes the following steps：
Step 1. gives reference signal rk
Reference signal rkFor the multinomial of time variable k, M indicates the polynomial highest power；Three kinds of reference signals are such as
Under：
1) square-wave signal, M=0
2) triangular signal, M=1
3) S curve, M=3
Wherein, A is amplitude, and N is the sampling number of reference signal in one cycle；
Step 2. constructs perfect error dynamic
Attract rule for without switching
ek+1=(1- ρ (ek))ek (4)
Wherein, δ > 0 is for adjusting the parameter for attracting speed, ek=rk-ykFor the system tracking error at k moment, ykFor k
The system real output signal at moment；Sign function is free of in formula (4), therefore can eliminate system chatter phenomenon.By AF panel
Measure is embedded in attraction rule, construction perfect error dynamic
Wherein, dk+1For the equivalent interference at k+1 moment,For compensating equivalent interference.For equivalent interference benefit
Repay error；
Step 3. interferes differential compensation measure
There is provided equivalent interference compensation measure be
Equivalent interference is defined for given reference signal, form is
Equivalent interference signal when M=0
dk+1=wk+1 (7)
Equivalent interference signal when M=1
dk+1=wk+1-wk (8)
Equivalent interference signal when M=3
dk+1=[(wk+1-wk)-(wk-wk-1)]-[(wk-wk-1)-(wk-1-wk-2)] (9)
Wherein, wk+1For the interference at k+1 moment；
Definition interference difference step number is L, and L indicates that interference compensation error includes the interference of L successive one, such as formula (7), two
Step interference difference dk+1-dk=wk+1-wk, include wk+1With wkTwo moment interference are selecting equivalent interference effectively to inhibit interference
When, following condition should be met
Wherein,For not less than smallest positive integral；
Step 4. controller design
According to perfect error dynamic (6) and equivalent interference signal dk+1Expression formula, provide device control as follows：
1) for square wave reference signal formula (1), controller is
2) for triangle reference signal wave formula (2), controller is
3) for S curve reference signal formula (3), controller is
In formula (11), formula (12) and formula (13), a1, a2, b0, b1For servo-system
yk+1+a1yk+a2yk-1=b0uk+b1uk-1+wk+1 (14)
Parameter.
Step 5. performance evaluation
It provides steady-state error band, absolute attractable layer, monotone decreasing region and tracking error and first enters steady-state error band institute
The expression for needing most four indexs of step number, for describing system tracking performance and instructs attitude conirol, wherein
Steady-state error band, absolute attractable layer and monotone decreasing region are defined as follows
1) steady-state error band (ΔSSE)
2) absolute attractable layer (ΔAAL)
3) monotone decreasing region (ΔMDR)
Equivalent interference compensation error meetsWhen, the expression formula of each index is as follows：
Steady-state error band (ΔSSE)
Absolute attractable layer (ΔAAL)
Monotone decreasing region (ΔMDR)
Restrain step number
Wherein, e0For tracking error initial value.
Known by formula (15), the steady-state error band of tracking error reduces with the reduction of Δ, therefore by using interference difference
Control precision can be improved in indemnifying measure.
In the present embodiment, the accurate tracing task of permanent magnet synchronous motor device execution position, design digitial controller is used for position
Ring control is set, wherein electric current loop is provided with speed ring controller by ELMO driver；Position ring controller is by DSP development board
TMS320F2812 is provided.
The mathematical model of servo-system is as follows
yk+1-1.5001yk+0.4989yk-1=2.1589uk-0.5113uk-1+wk+1 (19)
For M=0, known by formula (10)
For M=1, known by formula (11)
For M=3, known by formula (12)
It is provided by numerical simulation and the experiment show present invention and interferes differential compensation measure in discrete servo-system
Validity.
It emulates and is divided into two parts, the performance indicator expression that first part's verification expression (15) is provided to formula (18), the
The interference suppressioning effect of two parts verifying interference differential compensation measure.
(1) it gives with reference to letter rk=10sin (2 π fkTs) deg, frequency f=10Hz, sampling period Ts=0.01, it interferes and is
wk=0.12 | mod (k, 20) -10 |+0.16 | mod (k+7,20) -10 |.Under controller formula (20) effect, parameter δ difference is taken
Value, the performance indicator of system (19) also can be different, see Fig. 2-Fig. 4
(i) when controller parameter is Δ=0.38, δ=1.9 Δ (referring to fig. 2 and Fig. 4), performance indicator is
ΔAAL=ΔSSE=ΔMDR=1.267
(ii) when controller parameter is Δ=0.38, δ=3 Δ (referring to Fig. 3 and Fig. 4), performance indicator is
ΔAAL=ΔSSE=0.9 < ΔMDR=1.682
Pass through emulation, the results showed that steady-state error band ΔSSE, absolute attractable layer ΔAAL, monotone decreasing region ΔMDRIt is walked with convergence
NumberDo not meet formula (15), formula (16), formula (17) and formula (18).
(2) reference signal is respectively square-wave signal formula (1), triangular signal formula (2) and S curve formula (3), amplitude A difference
It is 5,10,5.It is verifying interference difference step number L at full formula (10), the controller of design can be realized to corresponding reference signal
Accurate tracking, disturbing signal are selected as wk=0.2rk, sampling period Ts=0.005, controller parameter δ=0.8.
1) reference signal rkFor formula (1), using controller formula (20), simulation result is shown in Fig. 5-Fig. 8, in figure, ΔSSE=
0deg。
2) reference signal rkFor formula (2), use controller for formula (20), simulation result is shown in Fig. 9-Figure 12, in figure, Δ=
0.05deg, ΔSSE=0.053deg.
3) reference signal rkFor formula (2), use controller for formula (21), simulation result is shown in Figure 13-Figure 16, in figure, ΔSSE
=0deg.
4) reference signal rkFor formula (3), use controller for formula (20), simulation result is shown in Figure 17-Figure 20, in figure, Δ=
0.04deg, ΔSSE=0.042deg.
5) reference signal rkFor formula (3), use controller for formula (21), simulation result is shown in Figure 21-Figure 24, in figure, Δ=
0.0015deg, ΔSSE=0.0015deg.
6) reference signal rkFor formula (3), use controller for formula (22), simulation result is shown in Figure 25-Figure 28, in figure, ΔSSE
=0deg.
By emulation (2), show when M and L meet formula (10), it can be real using the controller of interference differential compensation design
Now to the accurate tracking of given reference signal, when M and L is unsatisfactory for formula (10), L is closerTracking effect is better, and
Control process is without buffeting.
Control method provided by the invention is verified on position servo device, Fig. 1 is positional servosystem block diagram.With reference to letter
Number be respectively square-wave signal formula (1), triangular signal formula (2) and S curve formula (3), this 3 kinds of reference signals about variable k most
Big power is respectively 0,1 and 3.Controller formula (20), formula (21) and formula (22) verifying interference differential compensation technology is respectively adopted
Effect.Sampling period T in experiments=0.2ms, controller parameter δ=0.8, the width of reference signal formula (1), formula (2) and formula (3)
Value A is respectively 15deg, 90deg and 135deg.Experimental result is as follows：
1) reference signal rkSuch as formula (1), using controller (20), experimental result is shown in Figure 29-Figure 30 figure, ΔSSE=
0.05deg。
2) reference signal rkSuch as formula (2), using controller (20), experimental result is shown in Figure 31-Figure 32.In figure, ΔSSE=
0.2deg。
3) reference signal rkSuch as formula (2), using controller (21), experimental result is shown in Figure 33-Figure 34.In figure, ΔSSE=
0.05deg。
4) reference signal rkSuch as formula (3), using controller (20), experimental result is shown in Figure 35-Figure 36.In figure, ΔSSE=
0.15deg。
5) reference signal rkSuch as formula (3), using controller (21), experimental result is shown in Figure 37-Figure 38.In figure, ΔSSE=
0.1deg。
6) reference signal rkSuch as formula (3), using controller (22), experimental result is shown in Figure 39-Figure 40.In figure, ΔSSE=
0.05deg。
The experimental results showed that can be realized when M and L meet formula (10) using the controller of interference differential compensation design
Accurate tracking to given reference signal, when M and L is unsatisfactory for formula (10), L is closerSystem tracking performance is better,
And control process is without buffeting.
Claims (2)
1. a kind of inhibit the discrete time controller of strategy to attract rule design method without switching using interference difference, feature exists
In including the following steps：
Step 1. gives reference signal rkFor the multinomial of time variable k, M indicates the polynomial highest power, and three kinds with reference to letter
It is number as follows：
1) square-wave signal, M=0
2) triangular signal, M=1
3) S curve, M=3
Wherein, A is amplitude, and N is the sampling number of reference signal in one cycle；
Step 2. constructs perfect error dynamic
Attract rule for without switching
ek+1=(1- ρ (ek))ek (4)
Wherein, δ > 0 is for adjusting the parameter for attracting speed, ek=rk-ykFor the system tracking error at k moment, ykFor the k moment
System real output signal, by interference suppression measure be embedded in the attraction rule, construction perfect error dynamic
Wherein, dk+1For the equivalent interference at k+1 moment,For compensating equivalent interference,For equivalent interference compensation mistake
Difference；
Step 3. interferes differential compensation strategy
The effect of equivalent interference compensation is taken to be
Equivalent interference is defined for specific reference signal, form is
Equivalent interference signal when M=0
dk+1=wk+1 (7)
Equivalent interference signal when M=1
dk+1=wk+1-wk (8)
Equivalent interference signal when M=3
dk+1=[(wk+1-wk)-(wk-wk-1)]-[(wk-wk-1)-(wk-1-wk-2)] (9)
Wherein, wk+1For the interference at k+1 moment；
Definition interference difference step number is L, and L indicates that interference compensation error includes the interference of L successive one, and such as formula (7), two steps are dry
Disturb difference dk+1-dk=wk+1-wk, include wk+1With wkTwo moment interference, effectively to inhibit interference, when selecting equivalent interference,
Following condition should be met
Wherein,For not less than smallest positive integral；
Step 4. controller design
According to perfect error dynamic (6) and equivalent interference signal dk+1, provide the expression formula of device control as follows：
1) for square wave reference signal formula (1),
Wherein, F (q-1)=B (q-1)-b0；
2) for triangle reference signal wave formula (2),
Wherein,
3) for S curve reference signal formula (3),
Formula (11) is into formula (13), A (q-1)、B(q-1) it is servo-system
A(q-1)yk=q-1B(q-1)uk+wk (14)
About q-1Parametric polynomial：
A(q-1)=1+a1q-1+a2q-2+……+anq-n
B(q-1)=b0+b1q-1+b2q-2+……+bmq-m
Wherein, ukWith ykThe respectively input and output signal at servo-system k moment, q-1For One-step delay operator, m, n are respectively A
(q-1)、B(q-1) order, b0≠ 0,1≤m≤n.
2. a kind of discrete time controller using interference difference inhibition strategy as described in claim 1 attracts rule to set without switching
Meter method, which is characterized in that the method also includes：
Step 5. performance evaluation
Steady-state error band, absolute attractable layer, monotone decreasing region and tracking error is provided to first enter needed for steady-state error band most
The expression of four indexs of multistep number for describing system tracking performance and instructs attitude conirol, wherein stable state
Error band, absolute attractable layer and monotone decreasing region are defined as follows：
1) steady-state error band (ΔSSE)
2) absolute attractable layer (ΔAAL)
3) monotone decreasing region (ΔMDR)
Equivalent interference compensation error meetsWhen, the expression formula of each index is as follows：
Steady-state error band (ΔSSE)
Absolute attractable layer (ΔAAL)
Monotone decreasing region (ΔMDR)
Restrain step number
Wherein, e0For tracking error initial value.
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| CN110658719A (en) * | 2019-09-27 | 2020-01-07 | 浙江工业大学 | Servo system non-switching attraction repetitive control method adopting equivalent disturbance compensation |
| CN110673477A (en) * | 2019-09-27 | 2020-01-10 | 浙江工业大学 | Design method of discrete time power attraction controller adopting interference difference suppression strategy |
| CN114326372A (en) * | 2021-12-08 | 2022-04-12 | 北京理工大学 | Non-smooth feedback optimal tracking control method of position servo system |
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