CN103997224B - A kind of static dust-removing power Fractional Order PID control method - Google Patents

Abstract

The invention discloses the Fractional Order PID control method of a kind of static dust-removing power, obtain open cycle system phase angle and gain in conjunction with high-frequency electrostatic dedusting power source transmission function and Fractional Order PID control method transmission function；Allowance relation is utilized to draw the K of Fractional Order PID control system_P,K_I,K_D.Draw according further to different integral calculus orders and organize K more_P,K_I,K_D；Fractional Order PID Controller output is calculated according to time-domain expression；The system output errors value of different group data is obtained according to ITAE weighing criteria；One group of data when using ITAE value minimum are as setting parameter；In conjunction with PID controller output and the linear relationship of IGBT driving frequency, obtain the driving frequency of conservative control IGBT.The present invention can accurately adjust Fractional Order PID parameter, it is achieved the preferable control to high-frequency electrostatic dust pelletizing system；Floating type DSP is used efficiently to process fractional calculus computing；There is the rise time short, the advantage such as steady-state error is little, strong robustness, applied range.

Description

A kind of static dust-removing power Fractional Order PID control method

Technical field

The present invention relates to the development of the control system of the high-frequency and high-voltage large power supply for electrostatic precipitation, belong to high-power High voltage power supply technical field.

Background technology

In the last few years, the industrial level of China and scale development and expansion, the discharge capacity of waste gas is also gradually increased, this A little flue dust carry a large amount of harmful substance and enter air, have a strong impact on ecological environment and human health.For reinforcing ring environment pollution Administering, many is national, and oneself is controlled by through listing dust emission in national standard, and discharge standard progressively tends to strict.

The most widely used electrostatic precipitation scheme is mainly based upon the power supply of power frequency.The letter of this kind of electric source structure List, capacity are big, the relatively simple maturation of technology.But having the disadvantage in that power-efficient is low, power factor is little；Output voltage arteries and veins Moving causes greatly efficiency of dust collection relatively low.High-frequency electrostatic precipitator power supplies can improve disadvantages mentioned above well, improves power-efficient, Increase power factor, it is achieved energy-conservation.The control system of high-frequency electrostatic dedusting power source typically uses integer rank PID side at present Method, integer rank PID approach owing to control algolithm is simple, strong robustness, the parameter feature such as be prone to adjust be widely used in industry The every field controlled.But owing to object of study or controlled device are generally not preferable integer level system, but by arbitrarily The differential equation on rank and integral equation are constituted, and therefore the limitation of integer rank PID can not meet the performance requirement of controlled device.

Summary of the invention

Goal of the invention: owing to high-frequency electrostatic dedusting power source structure is complicated, its transmission function is new fractional-order system, and fractional order The responding ability of PID control method and capacity of resisting disturbance and regulating power are better than integer rank PID control method, therefore to The deficiencies in the prior art, the present invention are overcome to provide the Fractional Order PID control method of a kind of static dust-removing power, it is possible to have The control of effect and regulation dedusting power source system.

Technical scheme:

High-frequency electrostatic dedusting power source of the present invention, its agent structure includes rectified three-phase circuit, high-frequency inverter circuit, height Frequently booster transformer, high-voltage rectifier, drives insulated gate bipolar transistor IGBT mode to use frequency conversion control technique i.e. PFM.Electrostatic precipitator control system based on Fractional Order PID method specifically includes that analog quantity acquisition circuit, Fractional Order PID control Device, IGBT drive circuit.

For solving above-mentioned technical problem, the Fractional Order PID control method of the static dust-removing power that the present invention provides is mainly IGBT is carried out VFC, and then the resonant process of high-frequency inverter circuit is controlled.Described static dust-removing power mark Rank PID control method comprises the following steps:

Step 1, according to the transmission function of Fractional Order PID control method, the frequency calculating Fractional Order PID Controller is rung Should, phase angle and gain:

The transmission function of Fractional Order PID control method is:

$G_c\left(s\right)=K_P+\frac{K_I}{s^{\mathrm{\λ}}}+K_D{s}^{\mathrm{\μ}}(\mathrm{\λ},\mathrm{\μ}>0)---\left(1.1\right);$

Wherein: λ, μ are differential order and integration order, the K of the Fractional Order PID control system set_P,K_I,K_DFor PID

Proportionality coefficient, integral coefficient, differential coefficient in control system；

According to phase margin and magnitude margin relation, the frequency response calculating Fractional Order PID Controller is:

$G_c\left(j\mathrm{\ω}\right)=\[K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}cos\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}cos\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)\]+j\[K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)\]---\left(1.3\right);$

The phase angle and the gain that draw Fractional Order PID Controller be:

$Arg\[G_c\left(j\mathrm{\ω}\right)\]=arctan\frac{K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)}{K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}\cos \left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}\cos \left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)}---\left(1.4\right);$

$\left|G_c\left(j\mathrm{\ω}\right)\right|={\{{\[K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}cos\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}cos\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)\]}^2+{\[K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)\]}^2\}}^{\frac{1}{2}}---\left(1.5\right).$

Step 2, Fractional Order PID control system based on high-frequency electrostatic dedusting power source system, in conjunction with power supply architecture medium-high frequency The known parameter of transformer circuit parameter, calculates high-frequency electrostatic dedusting power source transmission function according to first-harmonic approximation principle, and then Calculate phase angle and the gain of this system:

Calculating high-frequency electrostatic dedusting power source transmission function according to first-harmonic approximation principle is:

$G_s\left(s\right)=\frac{R_e{C}_i{C}_s{s}^2}{L_s{C}_i{C}_s{s}^3+(L_s{R}_e{C}_s+R_e{C}_i{C}_s)s^2+C_{i}s+R_e}---\left(1.6\right);$

Wherein:

$R_e=\frac{{\[1+0.27sin(\mathrm{\θ}/2)\]}^2{R}_{LD}}{2n^2}---\left(1.7\right);$

C_i=C_p+C_e(1.8)；

$C_e=\frac{2n^{2}tan(-25sin\mathrm{\θ})}{{\[1+0.27sin(\mathrm{\θ}/2)\]}^2{\mathrm{\ω}}_s{R}_{LD}}---\left(1.9\right);$

$\mathrm{\θ}=2{\tan }^{-1}\sqrt{\frac{n^2}{4f_s{C}_p{R}_{LD}}}---\left(1.10\right);$

${\mathrm{\ω}}_s=\frac{1}{\sqrt{L_s{C}_s}}---\left(1.11\right);$

Wherein: high frequency transformer turn ratio n, high frequency transformer interelectrode capacity C_pWith leakage inductance L_s, resonance circuit series capacitance C_s, load resistance R_LD, resonant frequency f_sFor the known parameter of circuit parameter.When the circuit structure design of high-frequency electrostatic cleaner unit completes Time, now system transter can be calculated according to the parameter in circuit；

The phase angle of this system can be calculated according to formula 1.6 and gain is:

$Arg\left|G_s\left(j\mathrm{\ω}\right)\right|=-arctan\frac{D\mathrm{\ω}-{\mathrm{B\ω}}^3}{E-{\mathrm{C\ω}}^2}---\left(1.12\right);$

$\left|G_s\left(j\mathrm{\ω}\right)\right|=\sqrt{\frac{1}{{(E-{\mathrm{C\ω}}^2)}^2+{(D\mathrm{\ω}-{\mathrm{B\ω}}^3)}^2}}---\left(1.13\right);$

Wherein:

B=L_sC_iC_s；

C=L_sR_eC_s+R_eC_iC_s；

D=C_i, E=R_e。

Step 3, obtains in conjunction with the transmission function of high-frequency electrostatic dedusting power source and the transmission function of Fractional Order PID control method The phase angle of system open loop and gain:

According to formula 1.4 to formula 1.13, phase angle and the gain of obtaining open cycle system be:

$Arg\left|G_s\left(j\mathrm{\ω}\right)G_c\left(j\mathrm{\ω}\right)\right|=arctan\frac{K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)}{K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}\cos \left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}\cos \left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)}-arctan\frac{D\mathrm{\ω}-{\mathrm{B\ω}}^3}{E-{\mathrm{C\ω}}^2}---\left(1.14\right);$

$\left|G_s\left(j\mathrm{\ω}\right)G_c\left(j\mathrm{\ω}\right)\right|=\frac{{\{{\[K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}cos\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}cos\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)\]}^2+{\[K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)\]}^2\}}^{\frac{1}{2}}}{{\[{(E-{\mathrm{C\ω}}^2)}^2+{(D\mathrm{\ω}-{\mathrm{B\ω}}^3)}^2\]}^{1/2}}---\left(1.15\right);$

Step 4, sets differential order and the integration order of Fractional Order PID control system, and the phase place according to open cycle system is abundant Amount and magnitude margin relation, determines the ratio of static dust-removing power Fractional Order PID control method mid score rank PID control system Coefficient, integral coefficient and differential coefficient, to realize the control to high-frequency electrostatic dust pelletizing system of the fractional order control device:

The differential order of setting Fractional Order PID control system and integration order λ, the value of μ, abundant according to phase place under open cycle system Amount and the relation of magnitude margin:

Arg|G_s(jω)G_c(j ω) |=-π (1.16)

|G_s(jω)G_c(jω)|_dB=1 (1.17)

$\frac{d\left(G_s\right(j\mathrm{\ω})G_c\left(j\mathrm{\ω}\right))}{d\mathrm{\ω}}=0---\left(1.18\right)$

To setting known λ, μ value, calculate K according to formula 1.16 to formula 1.18_P,K_I,K_DValue.Above method according to High-frequency electrostatic dedusting power source system transter, to the differential set, integration order, can obtain correspondence and remove based on high-frequency electrostatic The Fractional Order PID parameter of dirt power supply, thus realize the control to high-frequency electrostatic dust pelletizing system of the fractional order control device.

Further, static dust-removing power Fractional Order PID control method of the present invention also includes:

Step 5, differential order and integration order according to setting calculate proportionality coefficient, integral coefficient, differential coefficient After, the controller controlled quentity controlled variable calculating Fractional Order PID according to the time-domain expression of Fractional Order PID exports:

Can show that the time-domain expression of Fractional Order PID control method is as shown in following formula 1.2: wherein e (t) according to formula 1.1 It is the real output value difference with setting value of high-frequency electrostatic dedusting power source system:

U (t)=K_Pe(t)+K_ID^-λe(t)+K_DD^μe(t) (1.2)。

When calculating the controller controlled quentity controlled variable output of Fractional Order PID according to formula 1.2, proportional component computing is relatively simple, and divides The computing of number rank differential and integration is complex, and the computing of mid score rank differential of the present invention and integration is completed by floating type DSP, its Computing Principle defines according to Gr ü nwald-Letnicov Fractional Calculus, takes finite term approximate processing, thus the most in the time domain The method using transform calculates fractional order differential and integration, in conjunction with scale operation result and fractional calculus result of calculation U (t) can be drawn.

Step 6, according to ITAE weighing criteria, is drawn the proportionality coefficient calculated in step 5, amasss by data simulation The system output errors value of these group data of point coefficient, differential coefficient:

The computing formula of ITAE is:

$J=\underset{0}{\overset{\mathrm{\∞}}{\∫}}t\left|e\left(t\right)\right|dt---\left(1.19\right).$

Step 7, sets different differential orders and integration order, and the PID controller calculating different order corresponding controls Amount output area and system output errors value, differential order when using ITAE value minimum and integration order and the ratio of its correspondence Example coefficient, integral coefficient, differential coefficient, as the setting parameter of Fractional Order PID control method:

According to being continually changing λ, the value of μ, calculate the ITAE value of system under different value, when taking ITAE value minimum λ, μ and K_P,K_I,K_DValue, be defined as Fractional Order PID setting parameter in high-frequency electrostatic dedusting power source system, it is achieved to base In accurately adjusting of high-frequency electrostatic dedusting power source Fractional Order PID parameter.

Step 8, according to Fractional Order PID Controller controlled quentity controlled variable output area and IGBT driving frequency scope meter in power supply architecture Calculate and draw the output of Fractional Order PID Controller controlled quentity controlled variable and the linear relationship of IGBT driving frequency.

Step 9, according to the Fractional Order PID Controller controlled quentity controlled variable output that the setting parameter described in step 7 is corresponding, and step Linear relationship described in 8, obtains controlling the driving frequency of IGBT in high-frequency electrostatic dedusting power source.Realize fractional order control device to height Frequently the preferable control of electrostatic precipitation system.

Beneficial effect: the present invention uses relatively advanced Fractional Order PID method because the differential order of Fractional Order PID and Integration order can value continuously, this makes Fractional Order PID flexible structure, can select differential and integration according to controlled device Order, thus obtain the control effect excellent to high-frequency and high-voltage electrostatic precipitator；It has greater advantage than traditional PID approach, passes System pid algorithm is the most applicable to integer rank control object, and Fractional Order PID algorithm is to non-integral order control object and integer rank Control object is all suitable for, and range of application is relatively broad；The present invention, according to high-frequency electrostatic dedusting power source system transter, can obtain Corresponding differential order and the Fractional Order PID parameter of integration order, thus realize fractional order control device to high-frequency electrostatic dedusting system The control of system；And can realize based on high-frequency electrostatic dedusting power source Fractional Order PID parameter according to ITAE weighing criteria further Accurately adjust, realize the preferable control to high-frequency electrostatic dust pelletizing system of the fractional order control device further；Mid score rank PID of the present invention Controller uses floating type DSP processing unit, and the execution for complicated algorithm provides basis, it is possible to process fractional order fast and effectively The computing of calculus；Compared with the PID control method of integer rank, it is short that the present invention has the rise time, and steady-state error is little, robustness By force, the advantage of applied range.

Accompanying drawing explanation

Fig. 1 is high-frequency electrostatic dedusting power source system global structure block diagram based on Fractional Order PID control method；

Fig. 2 is high-frequency electrostatic dedusting power source structure chart；

Fig. 3 is Fractional Order PID control method calculation flow chart；

Fig. 4 is Fractional Order PID Controller block diagram.

Detailed description of the invention

Below in conjunction with embodiment, the present invention is described in further detail, and this enforcement row do not constitute restriction to the present invention.

High-frequency electrostatic dedusting power source of the present invention, its agent structure includes rectified three-phase circuit, high-frequency inverter circuit, height Frequently booster transformer, high-voltage rectifier.In the present embodiment, rectified three-phase circuit uses three-phase uncontrollable rectifier mode, and high frequency is inverse Power transformation road uses the inverter circuit structure of LCC resonance manner, drives insulated gate bipolar transistor IGBT mode to use frequency conversion control Technology processed i.e. PFM, high-frequency step-up transformer uses high turn ratio high frequency transformer, and high-voltage rectifier uses bridge plate rectifier system. The Fractional Order PID control method of static dust-removing power of the present invention mainly carries out VFC to IGBT, and then to high frequency The LCC resonant process of inverter circuit is controlled.Described electrostatic precipitator control system based on Fractional Order PID method mainly wraps Include: analog quantity acquisition circuit, Fractional Order PID Controller, IGBT drive circuit.Described in the present embodiment, analog quantity acquisition circuit is adopted Use Phototube Coupling mode, it is ensured that sampling precision and enhance the anti-interference of system, front end signal is filtered, at amplification Reason, thus for late-class circuit A/D sampling stability and accuracy provide safeguard.

Electrostatic precipitator control system based on Fractional Order PID method of the present invention is as core by floating type DSP device The data collected are analyzed and computing by the heart.IGBT drive circuit described in the present embodiment is by company of Infineon 2SD315AI drives module directly to drive IGBT, and this module has the electric interfaces of isolation, has power supply and monitors and device Self-checking function.

The control process of high-frequency electrostatic dedusting power source Fractional Order PID control method of the present invention is as follows: adopted by simulation The output voltage of collection plate sampling electrostatic precipitator and output electric current and the resonance current of inverter circuit, sampled signal is through second order Butterworth filter output connects amplifying circuit, and signal amplitude is amplified to zone of reasonableness, and its output signal passes through linear optical coupling Isolation, is eventually connected to follower, and final signal transfers to the internal A/D unit of floating type DSP to carry out digital-to-analogue conversion, Fractional Order PID Control method carries out Fractional Order PID calculating to the output voltage of high-frequency electrostatic dedusting power source, further, according to calculating mark The output of rank PID controller controlled quentity controlled variables, obtains the frequency of rational driving IGBT, wherein the output of Fractional Order PID Controller controlled quentity controlled variable and The proportional relation of driving frequency of IGBT.

In the present embodiment, high-frequency electrostatic dedusting power source system global structure based on Fractional Order PID control method such as Fig. 1 institute Showing, whole system input power is three-phase alternating current, Guan Bi main body loop A.C. contactor 1, gives electric capacity pre-by current-limiting resistance 3 Charging, the charging interval is 3-5s, is further closed A.C. contactor 2, main body loop normal power supply, and the purpose of precharge is to reduce Excessive voltage changes the impact causing IGBT, thus reduces the electromagnetic interference thus brought.Three-phase alternating current is through three-phase not Control rectification module 4 rectification output 530V unidirectional current, then carry out inversion through IGBT inverter circuit 5, for reducing in reversals Hardware deterioration, inverter structure uses LCC resonance manner, further, enters high frequency transformer 6 and boost, and boosting output connects height Voltage rectifier 7, the direct current of output 70KV～80KV, finally accesses cleaner unit body 8.Its output HVDC is adopted through simulation Collection plate 9 sampling and outputting voltage and electric current, entered conditioning, enters Fractional Order PID Controller 10, and via controller is according to Fractional Order PID Algorithm, determine drive IGBT frequency, by IGBT drive plate 12 complete the driving to IGBT, the power supply of controller unit by AC/DC power module 11 provides.

Fig. 2 is high-frequency electrostatic dedusting power source structure chart, approximates principle according to the parameters in power supply architecture according to first-harmonic Can calculate high-frequency electrostatic dedusting power source system transter is:

$G_s\left(s\right)=\frac{R_e{C}_i{C}_i{s}^2}{L_s{C}_i{C}_s{s}^3+\left(L_s{R}_e{C}_s+R_e{C}_i{C}_s\right)s^2+C_{i}s+R_e}---\left(1.6\right);$

Wherein:

$R_e=\frac{{\[1+0.27sin(\mathrm{\θ}/2)\]}^2{R}_{LD}}{2n^2}---\left(1.7\right);$

C_i=C_p+C_e(1.8)；

$C_e=\frac{2n^{2}tan(-25sin\mathrm{\θ})}{{\[1+0.27sin(\mathrm{\θ}/2)\]}^2{\mathrm{\ω}}_s{R}_{LD}}---\left(1.9\right);$

$\mathrm{\θ}=2{\tan }^{-1}\sqrt{\frac{n^2}{4f_s{C}_p{R}_{LD}}}---\left(1.10\right);$

${\mathrm{\ω}}_s=\frac{1}{\sqrt{L_s{C}_s}}---\left(1.11\right);$

As in figure 2 it is shown, n is the turn ratio of high frequency transformer, C_p,L_sIt is interelectrode capacity and leakage inductance, the C of high frequency change device_sIt is humorous Shake the series capacitance in circuit, R_LDIt is load resistance, f_sIt is the resonant frequency in resonance circuit, all known parameters, according to Above parameter can calculate high-frequency electrostatic dedusting power source system transter.

Fractional Order PID control method calculation flow chart is as it is shown on figure 3, according to the transmission function of Fractional Order PID control method It is formula 1.3 that formula 1.1 can calculate the frequency response formula of this transmission function:

$G_c\left(s\right)=K_P+\frac{K_I}{s^{\mathrm{\λ}}}+K_D{s}^{\mathrm{\μ}}(\mathrm{\λ},\mathrm{\μ}>0)---\left(1.1\right);$

$G_c\left(j\mathrm{\ω}\right)=\[K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}cos\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}cos\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)\]+j\[K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)\]---\left(1.3\right);$

Phase angle formula 1.4 and the gain formula 1.5 of this transmission function can be write out according to formula 1.3:

$Arg\[G_c\left(j\mathrm{\ω}\right)\]=\arctan \frac{K_D{\mathrm{\ω}}^{\mathrm{\μ}}\sin \left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}\sin \left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)}{K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}\cos \left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}\cos \left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)}---\left(1.4\right);$

$\left|G_c\left(j\mathrm{\ω}\right)\right|={\{{\[K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}cos\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}cos\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)\]}^2+{\[K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)\]}^2\}}^{\frac{1}{2}}---\left(1.5\right);$

Wherein: ω=2 π f_s；

Phase angle formula 1.12 He of this transmission function can be write out according to high-frequency electrostatic dedusting power source system transter Gain formula 1.13:

$Arg\left|G_s\left(j\mathrm{\ω}\right)\right|=-arctan\frac{D\mathrm{\ω}-{\mathrm{B\ω}}^3}{E-{\mathrm{C\ω}}^2}---\left(1.12\right);$

$\left|G_s\left(j\mathrm{\ω}\right)\right|=\sqrt{\frac{1}{{(E-{\mathrm{C\ω}}^2)}^2+{(D\mathrm{\ω}-{\mathrm{B\ω}}^3)}^2}}---\left(1.13\right);$

Wherein:

B=L_sC_iC_s；

C=L_sR_eC_s+R_eC_iC_s；

D=C_i, E=R_e；

The phase angle of open cycle system can be calculated according to formula 1.4 to formula 1.13 and gain is respectively as follows:

$Arg\left|G_s\left(j\mathrm{\ω}\right)G_c\left(j\mathrm{\ω}\right)\right|=arctan\frac{K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)}{K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}\cos \left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}\cos \left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)}-arctan\frac{D\mathrm{\ω}-{\mathrm{B\ω}}^3}{E-{\mathrm{C\ω}}^2}---\left(1.14\right);$

$\left|G_s\left(j\mathrm{\ω}\right)G_c\left(j\mathrm{\ω}\right)\right|=\frac{{\{{\[K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}cos\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}cos\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)\]}^2+{\[K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)\]}^2\}}^{\frac{1}{2}}}{{\[{(E-{\mathrm{C\ω}}^2)}^2+{(D\mathrm{\ω}-{\mathrm{B\ω}}^3)}^2\]}^{1/2}}---\left(1.15\right);$

Relation index according to phase margin under open cycle system and magnitude margin, the phase angle of open cycle system and gain should meet Following relational expression:

Arg|G_s(jω)G_c(j ω) |=-π (1.16)；

|G_s(jω)G_c(jω)|_dB=1 (1.17)；

$\frac{d\left(G_s\right(j\mathrm{\ω})G_c\left(j\mathrm{\ω}\right))}{d\mathrm{\ω}}=0---\left(1.18\right);$

If the value of known λ, μ, K can be calculated according to formula 1.16, formula 1.17 and formula 1.18_P,K_I,K_DValue, as quiet The parameter of electric dust-removing power supply Fractional Order PID control method mid score rank PID control system.

The span setting λ, μ is 0～1, and step value is 0.1.First μ=0.1 is made, λ=0.1,0.2 ... 1.0, point Do not calculate 10 groups of K_P,K_I,K_DValue, secondly μ=0.2, λ=0.1,0.2 ... 1.0 are calculated other 10 groups of K again_P,K_I, K_DValue, by that analogy, can obtain 100 groups of K_P,K_I,K_D, the value of λ, μ.

Using emulation tool to emulate these 100 groups of parameters determined, artificial circuit principle, according to as shown in Figure 4, is adopted Using ITAE weighing criteria, drawn the system output errors often organizing data by emulation data, the computing formula of ITAE is:

$J=\underset{0}{\overset{\mathrm{\∞}}{\∫}}t\left|e\left(t\right)\right|dt---\left(1.19\right);$

Use 100 groups of K_P,K_I,K_D, in λ, μ value, one group of data of ITAE value minimum are as the essence of Fractional Order PID control algolithm Really setting parameter.

Determine setting parameter K_P,K_I,K_D, after the value of λ, μ, the difference e (t) of output voltage is counted according to formula 1.2 Calculate, obtain Fractional Order PID Controller controlled quentity controlled variable and export:

U (t)=K_Pe(t)+K_ID^-λe(t)+K_DD^μe(t) (1.2)；

Wherein proportional component computing is relatively simple, and the computing of fractional order differential and integration is complex, fractional order differential and The computing of integration is completed by floating type DSP, and its Computing Principle defines according to Gr ü nwald-Letnicov Fractional Calculus, has taken Limit item approximate processing, thus directly use the method for transform to calculate fractional order differential and integration in the time domain, transport in conjunction with ratio Calculate result and fractional calculus result of calculation can draw u (t).

The most as shown in Figure 4, the driving frequency of IGBT is exported by the controlled quentity controlled variable of Fractional Order PID control method and determines, it is right Should be related to for linear corresponding relation: permissible with IGBT driving frequency scope according to Fractional Order PID Controller controlled quentity controlled variable output area Calculate the output of Fractional Order PID Controller controlled quentity controlled variable and the linear corresponding relation of IGBT driving frequency；True according to above-mentioned steps Determine setting parameter and be calculated u (t), it is thus achieved that corresponding Fractional Order PID Controller controlled quentity controlled variable output, in conjunction with above-mentioned linear correspondence Relation, thus obtain the driving frequency of IGBT in conservative control high-frequency electrostatic dedusting power source, it is achieved to high-frequency electrostatic dedusting power source Rationally ideally control.

Claims (5)

1. a static dust-removing power Fractional Order PID control method, it is characterised in that: comprise the following steps,

Step 1, according to the transmission function of Fractional Order PID control method, calculate Fractional Order PID Controller frequency response, Phase angle and gain；

Step 2, Fractional Order PID control system based on high-frequency electrostatic dedusting power source system, in conjunction with power supply architecture medium-high frequency transformation The known parameter of device circuit parameter, calculates high-frequency electrostatic dedusting power source transmission function according to first-harmonic approximation principle, calculates The phase angle of this system and gain；

Step 3, obtains system in conjunction with the transmission function of high-frequency electrostatic dedusting power source and the transmission function of Fractional Order PID control method The phase angle of open loop and gain；

Step 4, sets the differential order of Fractional Order PID control system and integration order, according to the phase margin of open cycle system and Magnitude margin relation, determines the ratio system of static dust-removing power Fractional Order PID control method mid score rank PID control system Number, integral coefficient and differential coefficient, to realize the control to high-frequency electrostatic dust pelletizing system of the fractional order control device.

Static dust-removing power Fractional Order PID control method the most according to claim 1, it is characterised in that: also include following Step,

Step 5, after calculating proportionality coefficient, integral coefficient, differential coefficient according to the differential order set and integration order, root The controller controlled quentity controlled variable output of Fractional Order PID is calculated according to the time-domain expression of Fractional Order PID；

Step 6, according to ITAE weighing criteria, draws proportionality coefficient, the integration system calculated in step 5 by data simulation The system output errors value of these group data of number, differential coefficient；

Step 7, sets different differential orders and integration order, calculates PID controller controlled quentity controlled variable corresponding during different order Output area and system output errors value, differential order when using ITAE value minimum and integration order and the ratio of its correspondence Coefficient, integral coefficient, differential coefficient, as the setting parameter of Fractional Order PID control method；

Step 8, obtains with IGBT driving frequency range computation in power supply architecture according to Fractional Order PID Controller controlled quentity controlled variable output area Go out the output of Fractional Order PID Controller controlled quentity controlled variable and the linear relationship of IGBT driving frequency；

Step 9, according to the Fractional Order PID Controller controlled quentity controlled variable output that the setting parameter described in step 7 is corresponding, with in step 8 Described linear relationship, obtains controlling the driving frequency of IGBT in high-frequency electrostatic dedusting power source.

Static dust-removing power Fractional Order PID control method the most according to claim 1, it is characterised in that:

In described step 1, the transmission function of Fractional Order PID control method is:

$G_c\left(s\right)=K_P+\frac{K_I}{s^{\mathrm{\λ}}}+K_D{s}^{\mathrm{\μ}}(\mathrm{\λ},\mathrm{\μ}>0)---\left(1.1\right);$

Wherein: λ, μ are differential order and integration order, the K of the Fractional Order PID control system set_P,K_I,K_DFor PID

Proportionality coefficient, integral coefficient, differential coefficient in control system；

According to phase margin and magnitude margin relation, the frequency response calculating Fractional Order PID Controller is:

$G_c\left(j\mathrm{\ω}\right)=\[K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}cos\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}cos\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)\]+j\[K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)\]---\left(1.3\right);$

The phase angle and the gain that draw Fractional Order PID Controller be:

$Arg\[G_c\left(j\mathrm{\ω}\right)\]=arctan\frac{K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)}{K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}\cos \left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}\cos \left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)}---\left(1.4\right);$

$\left|G_c\left(j\mathrm{\ω}\right)\right|={\{{\[K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}cos\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}cos\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)\]}^2+{\[K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)\]}^2\}}^{\frac{1}{2}}---\left(1.5\right);$

In described step 2, Fractional Order PID control system based on high-frequency electrostatic dedusting power source system, according to high in power supply architecture The known parameter of frequency power transformer circuit parameter, calculating high-frequency electrostatic dedusting power source transmission function according to first-harmonic approximation principle is:

$G_s\left(s\right)=\frac{R_e{C}_i{C}_s{s}^2}{L_s{C}_i{C}_s{s}^3+(L_s{R}_e{C}_s+R_e{C}_i{C}_s)s^2+C_{i}s+R_e}---\left(1.6\right);$

Wherein:

$R_e=\frac{{\[1+0.27sin(\mathrm{\θ}/2)\]}^2{R}_{LD}}{2n^2}---\left(1.7\right);$

C_i=C_p+C_e(1.8)；

$C_e=\frac{2n^{2}tan(-25sin\mathrm{\θ})}{{\[1+0.27sin(\mathrm{\θ}/2)\]}^2{\mathrm{\ω}}_s{R}_{LD}}---\left(1.9\right);$

$\mathrm{\θ}=2{\tan }^{-1}\sqrt{\frac{n^2}{4f_s{C}_p{R}_{LD}}}---\left(1.10\right);$

${\mathrm{\ω}}_s=\frac{1}{\sqrt{L_s{C}_s}}---\left(1.11\right);$

Wherein: high frequency transformer turn ratio n, high frequency transformer interelectrode capacity C_pWith leakage inductance L_s, resonance circuit series capacitance C_s, negative Carry resistance R_LD, resonant frequency f_sFor the known parameter of circuit parameter；

The phase angle and the gain that calculate this system be:

$Arg\left|G_s\left(j\mathrm{\ω}\right)\right|=-arctan\frac{D\mathrm{\ω}-{\mathrm{B\ω}}^3}{E-{\mathrm{C\ω}}^2}---\left(1.12\right);$

$\left|G_s\left(j\mathrm{\ω}\right)\right|=\sqrt{\frac{1}{{(E-{\mathrm{C\ω}}^2)}^2+{(D\mathrm{\ω}-{\mathrm{B\ω}}^3)}^2}}---\left(1.13\right);$

Wherein:

B=L_sC_iC_s；

C=L_sR_eC_s+R_eC_iC_s；

D=C_i, E=R_e；

In described step 3, ask in conjunction with the transmission function of high-frequency electrostatic dedusting power source and the transmission function of Fractional Order PID control method The phase angle and the gain that go out open cycle system be:

$Arg\left|G_s\left(j\mathrm{\ω}\right)G_c\left(j\mathrm{\ω}\right)\right|=arctan\frac{K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)}{K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}\cos \left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}cos\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)}-arctan\frac{D\mathrm{\ω}-{\mathrm{B\ω}}^3}{E-{\mathrm{C\ω}}^2}---\left(1.14\right);$

$\left|G_s\left(j\mathrm{\ω}\right)G_c\left(j\mathrm{\ω}\right)\right|=\frac{{\{{\[K_P+\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}cos\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)+K_D{\mathrm{\ω}}^{\mathrm{\μ}}cos\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)\]}^2+{\[K_D{\mathrm{\ω}}^{\mathrm{\μ}}sin\left(\frac{\mathrm{\π}\mathrm{\μ}}{2}\right)-\frac{K_I}{{\mathrm{\ω}}^{\mathrm{\λ}}}sin\left(\frac{\mathrm{\π}\mathrm{\λ}}{2}\right)\]}^2\}}^{\frac{1}{2}}}{{\[{(E-{\mathrm{C\ω}}^2)}^2+{(D\mathrm{\ω}-{\mathrm{B\ω}}^3)}^2\]}^{1/2}}---\left(1.15\right);$

In described step 4, setting differential order and the integration order λ of Fractional Order PID control system, the value of μ, according to open cycle system Phase margin and magnitude margin relation:

Arg|G_s(jω)G_c(j ω) |=-π (1.16)

|G_s(jω)G_c(jω)|_dB=1 (1.17)

$\frac{d\left(G_s\right(j\mathrm{\ω}\left)G_c\right(j\mathrm{\ω}\left)\right)}{d\mathrm{\ω}}=0---\left(1.18\right)$

Calculate Proportional coefficient K in described Fractional Order PID control system_P, integral coefficient K_I, differential coefficient K_DValue.

Static dust-removing power Fractional Order PID control method the most according to claim 2, it is characterised in that:

In described step 5, the time-domain expression of described Fractional Order PID is:

U (t)=K_Pe(t)+K_ID^-λe(t)+K_DD^μe(t) (1.2)；

Wherein: e (t) is the real output value difference with setting value of high-frequency electrostatic dedusting power source system, λ, μ are the mark set The differential order of rank PID control system and integration order, K_P,K_I,K_DFor proportionality coefficient in PID control system, integral coefficient, micro- Divide coefficient；

In described step 6, the computing formula of described ITAE weighing criteria is

$J=\underset{0}{\overset{\mathrm{\∞}}{\∫}}t\left|e\left(t\right)\right|dt---\left(1.19\right).$

5. according to the static dust-removing power Fractional Order PID control method described in claim 2 or 4, it is characterised in that: described step When in 5, time-domain expression according to Fractional Order PID calculates the controller controlled quentity controlled variable output of Fractional Order PID, fractional order differential and long-pending The computing divided is completed by floating type DSP, and its principle defines according to Gr ü nwald-Letnicov Fractional Calculus, takes finite term near Like processing, thus directly use the method for transform to calculate Fractional Order PID in the time domain.