CN102385312A - Serial PI(Proportional-Integral)-PI controller in quick tilting mirror control system - Google Patents

Abstract

The invention discloses a serial PI(Proportional-Integral)-PI controller in a quick tilting mirror control system, and the controller is composed of two serial PI controllers, wherein each controller is composed of two real-number zeros and two integrators. The parameter setting standard of the controller is characterized in that a controller gain is maximized under the condition of satisfying settable phase allowance and amplitude allowance; according to the standard, a parameter setting result can be obtained. Compared with the traditional PI controller, the controlled has the following advantage: experiments verify that the controller can be used for improving the system control performance on the premise that the tracking bandwidth is increased.

Description

The controller of tandem type PI-PI in a kind of quick titling mirror control system

Technical field

The present invention relates to the tracking Control field; The concrete controller that relates to tandem type PI-PI in a kind of quick titling mirror control system; Be used to realize the High Accuracy Control of light-beam position, this controller is equally applicable to other linear drives control system, such as the distorting lens system.

Background technology

Quick titling mirror be widely used in FSO, adaptive optics, the optical axis stable in, be a kind of light beam alignment technique of precision.The quick titling mirror control system generally is that the boresight error that utilizes tracking transducer (CCD, PSD, four-quadrant etc.) to provide carries out closed loop.In recent years, realized the dicyclo control structure that position closed loop and track loop combine both at home and abroad.The method of this dicyclo control structure mainly utilizes the position closed loop loop of high bandwidth to eliminate non-linear effects, for track loop provides a better controlling object.Referring to document (large high performance fast steering mirrors with fpga-embedded controls.felix E.morgan.SPIE Vol.7466), quick titling mirror position control method and realization approach have been provided in the document.Briefly, behind the position closed loop of employing high bandwidth, the track loop controlling object can be regarded a simple delay link as.

Realize good performance for tracking, normally improve track loop controller (all being PI usually) gain.But, be difficult to realize high bandwidth owing to receive the influence that tracking transducer postpones.Reduce to postpone all can bring influence for image quality, detection accuracy.In addition, high bandwidth is also brought more noise easily.

Summary of the invention

The technical matters that the present invention will solve is: overcome the deficiency of prior art, propose the controller of tandem type PI-PI in a kind of quick titling mirror control system, under the prerequisite that does not improve tracking bandwidth, improve system control performance.

The technical scheme that the present invention solves the problems of the technologies described above is: the controller of tandem type PI-PI in a kind of quick titling mirror control system; It is characterized in that: the controller of this tandem type PI-PI is not simple PI controller; But form by the PI controller of 2 tandem types; I.e. 2 real number zero points and 2 controllers that integrator constitutes are described below with formula:

$G_c\left(s\right)=\frac{K_p(T_{i}s+1)(T_{d}s+1)}{s^2}$

In the formula, G _c(s) be tracking control unit, K _pBe controller gain, T _i, T _dBe real number zero point.

And wherein 2 real number parameters at zero point satisfy T _i=4T _d

Further, the parameter tuning criterion of the controller of this tandem type PI-PI is can be provided with under phase margin (P.M.), magnitude margin (G.M.) condition satisfied, the maximization controller gain; Establish (P.M.) here and be not less than 45 °, (G.M.) and be not less than 6dB, be described below with mathematical function:

Max?K _p

$s.t.\left\{\begin{array}{c}G.M.\≥6\mathrm{dB}\\ P.M.\≥\frac{\mathrm{\π}}{4}\end{array}\right.$

The result is following based on the controlled device parameter tuning of this parameter tuning criterion:

$K_p=\frac{{\mathrm{\π}}^2}{40{\mathrm{\τ}}^2},$ $T_d=\frac{2\mathrm{\τ}}{\mathrm{\π}},$ $T_i=\frac{8\mathrm{\τ}}{\mathrm{\π}}$

In the formula, τ is the system delay time, and several times of sampling times to ccd sensor close.

Further, based on above-mentioned parameter tuning criterion, the controller implementation procedure of this tandem type PI-PI is following: according to phase margin definition and triangular transformation formula, with controller gain be converted into gain cross-over frequency and time delay like minor function:

$K_p=\frac{0.2w_g^2{\sin }^2(0.25\mathrm{\π}+w_g\mathrm{\τ})}{-5\cos (0.25\mathrm{\π}+w_g\mathrm{\τ})+\sqrt{9{\cos }^2(0.25\mathrm{\π}+w_g\mathrm{\τ})+16}}$

In the formula, w _gBe the gain cross-over frequency.

K _pThe condition that obtains extreme value is

So w is arranged _gτ ≈ 0.25 π; Just this result is brought in the equation of phase margin definition can controlled device parameter the result that adjusts; And this parameter tuning result brought in the magnitude margin definition, can obtain P.M.=0.25 π, G.M.=6.2dB satisfies above-mentioned parameter tuning criterion.

The present invention has with respect to the advantage of prior art:

(1) the present invention does not increase under the system bandwidth prerequisite, can improve low frequency performance effectively;

(2) the present invention has only utilized boresight error information, does not increase any burden, and system is simple and reliable;

(3) the present invention has adopted the method for designing based on phase place, magnitude margin, and closed-loop system has good stable property and robustness.

Description of drawings

Fig. 1 is quick titling mirror control synoptic diagram of the present invention;

Wherein, tracking transducer characteristic: e ^{τ s}The position loop closed loop characteristic is G ₀(s) ≈ 1;

Tracking control unit:

After the position loop closed loop, controlling object: G _p(s)=G ₀(s) * e ^{-τ s}=e ^{-τ s}Boresight error: tracking transducer (CCD, PSD, four-quadrant etc.) provides;

Fig. 2 is a quick titling mirror control system Experimental equipment;

Wherein, 1 is that PI quick titling mirror, 2 is that disturbance mirror, 3 is that CCD, 4 is beacon beam.

Fig. 3 is that the boresight error that utilizes CCD to provide is realized track loop, and the PI controller suppresses response with the error of the PI-PI controller of connecting.

Embodiment

Embodiments of the invention below are described.But following embodiment only limits to explain the present invention, and protection scope of the present invention should comprise the full content of claim, and promptly can realize the full content of claim of the present invention to the technician in this field through following examples.

(1) method for designing of embodiments of the invention

The position loop design

Document (large high performance fast steering mirrors with fpga-embedded controls.felix E.morgan.SPIE Vol.7466) has provided quick titling mirror position control method and realization approach.The position loop of high bandwidth can be thought Go (s) ≈ 1.In the design track loop, controlling object can be regarded simple delay link e-τ s as like this.

The PI-PI design of Controller

Through behind the position closed loop, the object of quick titling mirror (Fast steering mirror is called for short FSM) can be regarded simple delay link as, and the delay of system is mainly from handling and computing relay, so have:

G _p(s)＝e ^-τs (1)

τ is the system delay time, general several times to the sampling time of ccd sensor.

Series connection PI-PI controller is following:

$G_c\left(s\right)=\frac{K_p(T_{i}s+1)}{s}\×\frac{(T_{d}s+1)}{s}=\frac{K_p(T_{i}s+1)(T_{d}s+1)}{s^2}---\left(2\right)$

Convert in conjunction with formula (1), formula (2) problem: the following formula of system (3) that an integration is added delay is described, how the PID controller (4) of solving-optimizing:

$G_p\left(s\right)=\frac{e^{-\mathrm{\τs}}}{s}---\left(3\right)$

$G_c\left(s\right)=\frac{K_p(T_{i}s+1)(T_{d}s+1)}{s}---\left(4\right)$

Lot of documents and engineering practice draw: integral and differential term satisfy following relation in the PID controller parameter:

T _i＝4T _d (5)

The controlled variable criterion of adjusting: phase margin (P.M.), magnitude margin (G.M.) maximization controller gain can be set satisfying.Establish (P.M.) here and be not less than 45 °, (G.M.) and be not less than 6dB, be described below with mathematical function:

Max?K _p

$\left\{\begin{array}{c}G.M.\≥6\mathrm{dB}\\ P.M.\≥\frac{\mathrm{\π}}{4}\end{array}\right.---\left(6\right)$

Phase margin and magnitude margin have guaranteed the stability and the robustness of system, and the maximization ride gain means good system's low frequency performance.Definition by formula (3), formula (4), formula (5) and phase margin can obtain:

a?tan(T _dw _g)+a?tan(4T _dw _g)-w _gτ＝0.25π (7)

$K_p=\frac{w_g^2}{\sqrt{T_d^2{w}_g^2+1}\sqrt{16T_d^2{w}_g^2+1}}---\left(8\right)$

Wherein, w _gIt is the gain cross-over frequency.Obtain easily by formula (7):

$\frac{5T_d{w}_g}{\sqrt{T_d^2{w}_g^2+1}\sqrt{16T_d^2{w}_g^2+1}}=\sin (0.25\mathrm{\π}+w_g\mathrm{\τ})---\left(9\right)$

$\frac{1-4T_g^2{w}_g^2}{\sqrt{T_d^2{w}_g^2+1}\sqrt{16T_d^2{w}_g^2+1}}=\cos (0.25\mathrm{\π}+w_g\mathrm{\τ})---\left(10\right)$

Can get by formula (9), formula (10):

$\frac{1}{5T_d{w}_g}-\frac{4}{5}{T}_d{w}_g=c\tan (0.25\mathrm{\π}+w_g\mathrm{\τ})---\left(11\right)$

Can get by formula (11):

$T_d{w}_g=\frac{-5c\tan (0.25\mathrm{\π}+w_g\mathrm{\τ})+\sqrt{25c{\tan }^2(0.25\mathrm{\π}+w_g\mathrm{\τ})+16}}{8}---\left(12\right)$

Bringing formula (8) into by formula (9) can obtain:

$K_p=\frac{w_g^2}{5T_d{w}_g}\sin (0.25\mathrm{\π}+w_g\mathrm{\τ})---\left(13\right)$

Bringing formula (12) into formula (13) has:

$K_p=\frac{0.2w_g^2{\sin }^2(0.25\mathrm{\π}+w_g\mathrm{\τ})}{-5\cos (0.25\mathrm{\π}+w_g\mathrm{\τ})+\sqrt{9{\cos }^2(0.25\mathrm{\π}+w_g\mathrm{\τ})+16}}---\left(14\right)$

K _pObtain the condition of extreme value

So w is arranged _gτ ≈ 0.25 π, controller parameter is following:

$K_p=\frac{{\mathrm{\π}}^2}{40{\mathrm{\τ}}^2},$ $T_d=\frac{2\mathrm{\τ}}{\mathrm{\π}},$ $T_i=\frac{8\mathrm{\τ}}{\mathrm{\π}}---\left(15\right)$

If w _pBe the phase place cross-over frequency, can obtain by the magnitude margin definition:

a?tan(T _dw _p)+a?tan(T _iw _p)＝w _pτ (16)

In conjunction with formula (15) w is arranged _p=0.7638 π/τ, the open loop magnitude margin is like this:

$G_m=20\log 10\left[\frac{K_p\sqrt{T_d^2{w}_p^2+1}\sqrt{16T_d^2{w}_p^2+1}}{w_p^2}\right]=6.2>6\mathrm{dB}---\left(17\right)$

Owing to adopted maximum control device gain method based on phase place, amplitude information, both guaranteed the stability and the robustness of system, greatly guaranteed the performance of closed-loop system low frequency again.

(2) experimental verification

Method for designing above adopting; Quick titling mirror control system for a PI company is tested as follows; Install as shown in Figure 2ly, main parts are following: based on image detecting system (boresight error is provided), disturbance mirror, PI quick titling mirror, the beacon beam of CCD.Major technology parameter: CCD sampling time: τ=0.0005s; Delay time T=0.0015s, 3 times to the CCD sampling time.About PI quick titling mirror position closed loop bandwidth 1000Hz.The PI quick titling mirror is equipped with the position transducer foil gauge, and the analog driver that utilizes PI company to provide can be realized the position closed loop of high bandwidth.

The fundamental purpose of experiment is to utilize the boresight error that CCD provides to realize track loop, relatively the performance of PI controller and the PI-PI controller of connecting.Experimental result such as Fig. 3 can obtain table 1, and table 1 has shown the validity of PI-PI control method.

Table 1,2 kinds of different controller experimental results

The part that the present invention does not set forth in detail belongs to techniques well known.

Claims (3)

1. the controller of tandem type PI-PI in the quick titling mirror control system; It is characterized in that: the controller of this tandem type PI-PI is made up of the PI controller of 2 tandem types; I.e. 2 real number zero points and 2 controllers that integrator constitutes are described below with formula:

$G_c\left(s\right)=\frac{K_p(T_{i}s+1)(T_{d}s+1)}{s^2}$

In the formula, G _c(s) be tracking control unit, K _pBe controller gain, T _i, T _dBe real number zero point;

And wherein 2 real number parameters at zero point satisfy T _i=4T _d

2. the controller of tandem type PI-PI in a kind of quick titling mirror control system according to claim 1; It is characterized in that: the parameter tuning criterion of the controller of this tandem type PI-PI is can be provided with under phase margin (P.M.), magnitude margin (G.M.) condition satisfied, the maximization controller gain; Establish (P.M.) here and be not less than 45 °, (G.M.) and be not less than 6dB, be described below with mathematical function:

Max?K _p

$s.t.\left\{\begin{array}{c}G.M.\≥6\mathrm{dB}\\ P.M.\≥\frac{\mathrm{\π}}{4}\end{array}\right.$

The result is following based on the controlled device parameter tuning of this parameter tuning criterion:

$K_p=\frac{{\mathrm{\π}}^2}{40{\mathrm{\τ}}^2},$ $T_d=\frac{2\mathrm{\τ}}{\mathrm{\π}},$ $T_i=\frac{8\mathrm{\τ}}{\mathrm{\π}}$

In the formula, τ is the system delay time, and several times to the sampling time of ccd sensor.

3. the controller of tandem type PI-PI in a kind of quick titling mirror control system according to claim 2; It is characterized in that: described parameter tuning criterion; The controller implementation procedure of this tandem type PI-PI is following: according to phase margin definition and triangular transformation formula, with controller gain be converted into gain cross-over frequency and time delay like minor function:

$K_p=\frac{0.2w_g^2{\sin }^2(0.25\mathrm{\π}+w_g\mathrm{\τ})}{-5\cos (0.25\mathrm{\π}+w_g\mathrm{\τ})+\sqrt{9{\cos }^2(0.25\mathrm{\π}+w_g\mathrm{\τ})+16}}$

In the formula, w _gBe the gain cross-over frequency; K _pThe condition that obtains extreme value is

So w is arranged _gτ ≈ 0.25 π; Just this result is brought in the equation of phase margin definition can controlled device parameter the result that adjusts; And this parameter tuning result brought in the magnitude margin definition, can obtain P.M.=0.25 π, G.M.=6.2dB satisfies the described parameter tuning criterion of claim 2.

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