CN109507870A - The fractional order proportional integration or proportional plus derivative controller design method of structure adaptive - Google Patents
The fractional order proportional integration or proportional plus derivative controller design method of structure adaptive Download PDFInfo
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B11/00—Automatic controllers
- G05B11/01—Automatic controllers electric
- G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
- G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P.I., P.I.D.
Abstract
The invention discloses a kind of fractional order proportional integration of structure adaptive or the design methods of proportional plus derivative controller；First by inputting sinusoidal signal and capture output signal to controlled device, amplitude and phase of the open cycle system of controlled device at specified gain-crossover frequency are obtained；By inputting another sinusoidal signal and capture output signal to controlled device, the phase frequency curve slope of controlled device is obtained；By the relational expression between amplitude, phase and the phase slope and three parameters of fractional order control device that obtain the controlled device transmission function that three experimental datas are updated to building, three parameters of fractional order control device can be obtained by resolving, including proportionality coefficient, time constant and calculus order, wherein calculus order determines that fractional order control device is proportional integration or proportion differential structure.This method does not depend on the mathematical model of controlled device, is able to pass through the controller the Self-tuning System process of parameter, calculates controller parameter automatically, and determine controller architecture.
Description
Technical field
The present invention relates to automatic field more particularly to the fractional order proportional integrations or proportion differential of a kind of structure adaptive
The design method of controller.
Background technique
In closed loop controller in industrial processes, the simple proportional, integral of structure (PI) control or proportional-plus-derivative (PD)
Control method has a very wide range of applications.As industrial process requires control performance higher and higher, traditional integer rank
PI or PD control have been difficult to meet the requirements.Engineers and technicians are forced to find the more superior control method of performance, Er Qieyou
Ensure that control method is easy to use, is convenient for Project Realization.
Fractional calculus theory has the history in more than 300 years.By people in recent years to its it is theoretical constantly improve and
The rapid progress of science and technology, fractional calculus theory also gradually start to be applied in control field.Use fractional order
Calculus link replaces the integer rank calculus link in PI control and PD control, to derive fractional order PI control and divide
Number rank PD control.Many scholars demonstrate from theory analysis and practical application, and the PI or PD control method of fractional order can determine that
Better control effect.
In conventional controller architecture design, either integer rank or fractional order control device are required to being controlled pair
The physical characteristic of elephant has certain understanding, and then determines it is using PI control or PD control.In practical applications, especially one
A little large scale industry processes with subsystem interaction, structure and operation mechanism are complicated, are generally difficult to obtain its accurately dynamic
Characteristic and priori knowledge can not determine actually using PI control or PD control, and the parameter of controller is also difficult to determine,
It needs to gather through a large number of experiments to carry out examination, this brings bigger difficulty for the structure design of controller, increases control
Device designs complexity.
Summary of the invention
In view of this, the present invention provides the design method of a kind of fractional order PI of structure adaptive or PD control device, it should
Mathematical model of the method independent of controlled device is able to pass through the controller the Self-tuning System process of parameter, calculates control automatically
The parameter of device, while determining the structure of controller.
In order to solve the above-mentioned technical problem, the specific design process of controller of the present invention is as follows:
The expression of the transmission function of fractional order PI or PD control device is indicated in the form of formula (1).
Hc(s)=Kp(1+Tis-λ) (1)
In formula (1), HcIt (s) is the transmission function of controller, the parameter comprising there are three, wherein T is time constant, KpFor
Proportionality coefficient, λ are real number, indicate calculus order.As λ < 0, controller described in formula (1) is fractional order PD control device；
As λ > 0, controller described in formula (1) is fractional order PI controller, it can be seen that the symbol of parameter lambda determines controller
Specific structure.It can determine the structure of controller and the parameter of controller by the size of automatic adjusting above three parameter.
In the present invention, by meeting three following conditions, to obtain three equations, and then according to obtained three sides
Journey can solve three parameter T in controlleri, Kp, λ.
Condition 1: controlled device open cycle system has specified gain-crossover frequency ωgc
Gain-crossover frequency is on the Bode diagram of controlled system transmission function, and amplitude-versus-frequency curve amplitude passes through 0 decibel of line
Corresponding angular frequency.One biggish gain-crossover frequency of design can effectively shorten the regulating time of closed-loop control system.Make
Controlled closed-loop system obtains specified gain-crossover frequency, and condition described in formula (2) must be satisfied for.
|H(jωgc) |=| Hc(jωgc)|·|P(jωgc) |=1 (2)
Transmission function in formula (2) is described in a frequency domain, wherein H (j ωgc) be controlled system open loop transmitting
Function, Hc(jωgc) be controller transmission function, P (j ωgc) be then controlled device transmission function.
Condition 2: open cycle system has specified phase margin
Phase margin is the value and -180 ° of difference of phase frequency curve corresponding to open loop system gain cross-over frequency, it
Size is related with the overshoot size of closed-loop system step response.Under normal conditions, reasonable phase margin is about at 45~65 °
Section in choose.In order to make closed-loop system obtain specified phase margin, condition described in formula (3) be must be satisfied for.
Symbol ∠ in formula (3) indicates phase angle.
Condition 3: at gain-crossover frequency have etc. damping characteristics
Etc. damping characteristics refer on the open loop Bode diagram of controlled system that phase frequency curve is flat, i.e., in specified frequency
Upper corresponding phase slope is 0.It means that controller has very strong robust for the change of controlled device open-loop gain
Property.In order to make system the damping characteristics such as obtain at gain-crossover frequency, condition described in formula (4) be must be satisfied for.
ω indicates angular frequency in formula (4), according to above three condition, so that it may obtain formula (2), (3), (4) three equations.
By s=j ω substitute into formula (1) can goals for rank controller transmission function frequency domain plural number description:
It is then possible to which amplitude of the fractional order control device under frequencies omega is calculated | HC(j ω) | and phase ∠ HC(j ω),
Respectively as shown in formula (6) and formula (7):
Formula (6) are substituted into formula (2), can be obtained:
Formula (7) are substituted into formula (3), can be obtained:
Formula (7) are substituted into formula (4), can be obtained:
Above-mentioned formula (8) (9) (10) is controlled device transmission function P (j ωgc) amplitude | P (j ωgc) |, phase ∠ P
(jωgc) and phase slopeWith the relational expression between three parameters of fractional order control device.As long as can calculate
Place's controlled device is located at gain-crossover frequency ωgcThe amplitude at place | P (j ωgc) |, phase ∠ P (j ωgc) and phase slopeValue, so that it may calculate the parameter of controller in formula (1), the specific steps of which are as follows:
Step 1: calculating controlled device open cycle system in specified gain-crossover frequency ωgcThe amplitude M and phase at place
A sinusoidal signal u (t) is inputted to controlled device:
U (t)=Aisin(ωgct) (11)
Wherein the amplitude of input signal u (t) is Ai, angular frequency is gain-crossover frequency ωgc, t is the time.
Under the excitation of above-mentioned sinusoidal signal, controlled device output a cycle is identical and there are transit times and vibration
The sinusoidal signal of width difference.The output signal for defining controlled device is y (t), amplitude Ao, transition between input/output signal
Time is τ, τ=ti-to, wherein tiFor the time to peak of a peak value x in input signal u (t), toFor in output signal y (t)
The time to peak of same peak value x.Open cycle system then can be obtained and be located at gain-crossover frequency ωgcThe amplitude M and phase at place:
φ=∠ P (j ωgc)=ωgcτ=ωgc(ti-to) (13)
Step 2: calculating the Bode figure phase frequency curve slope of controlled device, be expressed as
A sinusoidal signal u is inputted to controlled device again1(t):
u1(t)=Ai1sin(ω1t) (14)
Wherein input signal u1(t) amplitude is Ai1, preferably desirable Ai1=Ai, angular frequency ω1=ωgc(1+ α),
α is a given positive real number less than 0.1, preferably desirable α=0.01.The purpose for setting a difference α is that formula (16) is
It is differentiated using approximate mode, it is therefore desirable to the difference on the angular frequency of two signals, and this difference approach is 0,
Therefore value α one small is set here to meet the requirement.
Then controlled device is located at angular frequency1The phase at place1Are as follows:
φ1=∠ P (j ω1)=ω1τ1=ω1(ti1-to1) (15)
In above formula (15), ti1For input signal u1(t) time to peak of a peak value x1, t ino1For by u1(t) it is motivated
Output signal y out1(t) time to peak of same peak value x1 in.
It can go out controlled device when constant α obtains smaller value according to the basic definition of derivative with approximate calculation and be located at
Gain-crossover frequency ωgcThe phase frequency curve slope at place:
Step 3: controller parameter calculates:
It will be according to the calculated experimental data of formula (12), (13) and (16) institute, including controlled device transmission function P (j ωgc)
Amplitude | P (j ωgc) |, phase ∠ P (j ωgc) and phase slopeIt is brought into formula (8), (9) and (10)
In can solve three parameter T of controlleri、Kp,λ.Wherein parameter TiAnd KpIt is the real number greater than zero, and λ is then any
Real number, if λ < 0, controller is substantially fractional order PD control device；If λ > 0, controller is substantially fractional order PI
Controller.
The utility model has the advantages that
(1) the fractional order proportional integration of structure adaptive proposed by the present invention or the design method of proportional plus derivative controller,
It is not necessary that the specific structure of controller is determined in advance, according to the result of parameter automatic adjusting be assured that using PI control or
PD control.
(2) controller design method proposed by the present invention does not need the mathematical model for obtaining controller in advance and related ginseng
Number, it is only necessary to the parameter of controller can be calculated by the method for experiment.
Detailed description of the invention
Fig. 1 is fractional order control device closed-loop system structure.
Fig. 2 is the input and output signal of open loop sine experiment.
Fig. 3 is the first time open loop experiment under specified gain-crossover frequency.
Fig. 4 is second of open loop experiment under specified gain-crossover frequency.
Specific embodiment
The present invention will now be described in detail with reference to the accompanying drawings and examples.
Using following time lag of first order process as controlled device, i.e.,
In formula, K=1 is open-loop gain, and T=3 is time constant, and L=0.1 is Slack time.
Fractional order control device as shown in Fig. 1 is designed above-mentioned controlled device, and wherein R (s) is the transmitting of input signal
Function, E (s) are the transmission function of error signal, P (s) is the transmission function of controlled device, U (s) is the transmitting letter for controlling signal
Number, Y (s) are the transmission function of output signal, KPProportional parts, T for controlleris-λFor the differential or integral part of controller
Transmission function.
In this embodiment it is assumed that the structural parameter K of controlled device, T, L are unknown.Since controlled device is a tool
There is a linear system of lag, therefore inputs a sinusoidal excitation signal to controlled device, then it is identical to obtain a cycle, and
There are the sinusoidal signals of transit time and amplitude difference, as shown in Fig. 2.
In controller design, following Control performance standard is designed, it may be assumed that gain-crossover frequency ωgc=1rad/s, phase
NarginSpecific controller design process is as follows:
Step 1: calculating the amplitude M and phase at gain-crossover frequency
Sinusoidal signal u (t)=sin (t), amplitude A are inputted to controlled devicei=1, angular frequency is that more frequency is handed in gain
Rate ωgc=1rad/s.Under the excitation of above-mentioned sinusoidal signal, it is identical that a period as shown in Figure 3 can be obtained, and existed
Cross the sinusoidal signal of time and amplitude difference.The one of time to peak of input signal u (t) is ti=32.987s, it is corresponding defeated
The time to peak of signal y (t) is t outo=34.336s, amplitude Ao=0.3163.Controlled device can be obtained and be located at gain-crossover frequency
The amplitude at place isPhase is φ=ωgc·(ti-to)=- 77.29 °.
Step 2: calculate phase frequency curve slope:
α=0.01 is enabled, inputs sinusoidal signal u (t)=sin (1.01*t) to controlled device.Obtain input as shown in Figure 4
And output signal, wherein input signal u1(t) a time to peak is ti1=32.660s, corresponding is output signal
y1(t) time to peak to1=34.000s, can obtain the phase that controlled device is located at the frequency is φ1=ω1(ti1-to1)=-
77.54o.Controlled device is located at the phase slope at gain-crossover frequency
Step 3: controller parameter calculates:
The amplitude that experiment is obtained | P (j ωgc) |=M, phase ∠ P (j ωgc)=φ and phase slope
It substitutes into following three formulas
Wherein,For the phase margin of specified open cycle system.
Three Nonlinear System of Equations to be solved can be obtained after substitution, control can be found out using calculating instruments such as Matlab
Three parameters of device are as follows:
Kp=1.9667, Ti=1.1921, λ=0.9563.Then, fractional order control device made of being adjusted:
As it can be seen that the controller is fractional order PI structure type.
In conclusion the above is merely preferred embodiments of the present invention, being not intended to limit the scope of the present invention.
All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in of the invention
Within protection scope.
Claims (2)
1. a kind of fractional order proportional integration of structure adaptive or the design method of proportional plus derivative controller, which is characterized in that packet
It includes:
Step 1: obtaining the open cycle system of controlled device in specified gain-crossover frequency ωgcThe amplitude M and phase at place；
A sinusoidal signal u (t) is inputted to controlled device, the amplitude of u (t) is Ai, angular frequency is the gain-crossover frequency
ωgc；At this time controlled device output a cycle it is identical, there are the sinusoidal signal y (t) of transit time τ and amplitude difference, y's (t)
Amplitude is Ao；Then,
Open cycle system is located at gain-crossover frequency ωgcThe amplitude at place
Open cycle system is located at gain-crossover frequency ωgcThe phase at place=∠ P (j ωgc)=ωgcτ (2)
Step 2: obtaining the Bode figure phase frequency curve slope of controlled device
Inputting an angular frequency to controlled device is ω1=ωgcThe sinusoidal signal u of (1+ α)1(t), α is being less than for a setting
0.1 positive real number；Obtain u1(t) the output signal y corresponding to1(t) transit time is τ1；Controlled device position can then be calculated
In gain-crossover frequency ωgcThe phase frequency curve slope at place are as follows:
Wherein, φ1For output signal y1(t) in sinusoidal input signal u1(t) angular frequency1The phase at place, φ1=ω1τ1；
Step 3: calculating fractional order control device Hc(s)=Kp(1+Ts-λ) in parameter, including Proportional coefficient Kp, time constant TiWith
Calculus order λ；
In this step, controlled device transmission function P (j ω is constructedgc) amplitude | P (j ωgc) |, phase ∠ P (j ωgc) and phase
Position slopeRelational expression (4) (5) (6) between three parameters of fractional order control device:
Wherein, in formula (5)For the phase margin of specified open cycle system；
Then, P (j ω formula (1) (2) (3) obtainedgc)、|P(jωgc) | andIt substitutes into relational expression (4) (5)
(6), three parameters of fractional order control device are calculated.
2. the method as described in claim 1, which is characterized in that α=0.01.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110389320A (en) * | 2019-06-10 | 2019-10-29 | 浙江大学 | A kind of Adaptable System between array element tile based on digital simulation transmission line |
| CN110531612A (en) * | 2019-08-16 | 2019-12-03 | 佛山科学技术学院 | A kind of parameter tuning method of Fractional Order PID Controller |
| CN114244169A (en) * | 2021-12-16 | 2022-03-25 | 山东大学 | Fractional order-based multi-index cooperative control method and system for three-level inverter |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103279034A (en) * | 2013-05-15 | 2013-09-04 | 哈尔滨工业大学 | Parameter setting method for fractional-order robust controller |
| CN103558755A (en) * | 2013-11-05 | 2014-02-05 | 四川理工学院 | Fractional order integration PID controller setting and self-setting method |
| CN104777746A (en) * | 2015-04-09 | 2015-07-15 | 长春理工大学 | Enhanced gain robust fractional-order PID (proportion integration differentiation) controller parameter setting method |
| CN106338913A (en) * | 2016-11-04 | 2017-01-18 | 河北省科学院应用数学研究所 | Fractional-order PID control design method based on phase margin and cutoff frequency |
| CN107505834A (en) * | 2017-08-31 | 2017-12-22 | 东北石油大学 | A kind of design method of fractional order pi controller |
-
2018
- 2018-11-21 CN CN201811388969.5A patent/CN109507870B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103279034A (en) * | 2013-05-15 | 2013-09-04 | 哈尔滨工业大学 | Parameter setting method for fractional-order robust controller |
| CN103558755A (en) * | 2013-11-05 | 2014-02-05 | 四川理工学院 | Fractional order integration PID controller setting and self-setting method |
| CN104777746A (en) * | 2015-04-09 | 2015-07-15 | 长春理工大学 | Enhanced gain robust fractional-order PID (proportion integration differentiation) controller parameter setting method |
| CN106338913A (en) * | 2016-11-04 | 2017-01-18 | 河北省科学院应用数学研究所 | Fractional-order PID control design method based on phase margin and cutoff frequency |
| CN107505834A (en) * | 2017-08-31 | 2017-12-22 | 东北石油大学 | A kind of design method of fractional order pi controller |
Non-Patent Citations (3)
| Title |
|---|
| YING LUO；CHUNYANG WANG；YANGQUAN CHEN: "Tuning fractional order proportional integral controllers for fractional order systems", 《2009 CHINESE CONTROL AND DECISION CONFERENCE》 * |
| 余伟: "永磁同步电动机的分数阶建模研究", 《中国博士学位论文全文数据库工程科技Ⅱ辑》 * |
| 郑伟佳: "永磁同步电动机分数阶建模与控制研究", 《中国博士学位论文全文数据库工程科技Ⅱ辑》 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110389320A (en) * | 2019-06-10 | 2019-10-29 | 浙江大学 | A kind of Adaptable System between array element tile based on digital simulation transmission line |
| CN110531612A (en) * | 2019-08-16 | 2019-12-03 | 佛山科学技术学院 | A kind of parameter tuning method of Fractional Order PID Controller |
| CN110531612B (en) * | 2019-08-16 | 2022-06-17 | 佛山科学技术学院 | Parameter setting method of fractional order PID controller |
| CN114244169A (en) * | 2021-12-16 | 2022-03-25 | 山东大学 | Fractional order-based multi-index cooperative control method and system for three-level inverter |
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