CN104714407B - A kind of rotating mechanism PID/H∞Control method - Google Patents

A kind of rotating mechanism PID/H∞Control method Download PDF

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CN104714407B
CN104714407B CN201310694471.2A CN201310694471A CN104714407B CN 104714407 B CN104714407 B CN 104714407B CN 201310694471 A CN201310694471 A CN 201310694471A CN 104714407 B CN104714407 B CN 104714407B
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CN104714407A (en
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胡平华
刘东斌
詹双豪
曲雪云
唐江河
李爱萍
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Beijing Automation Control Equipment Institute BACEI
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Abstract

The invention belongs to rotation modulation inertial navigation system control technology field, and in particular to a kind of rotating mechanism PID/H∞Control method.The control method comprises the following steps：1st, photoelectric encoder gathers the actual angular position θ of rotating frame in real time；2nd, actual angular position θ and control targe angle θrefMake difference, difference result is sent into position PID controller as input；Step 3, signals of the actual angular position θ after differentiator differential and the output of position PID controller done into difference, using differentiated result as input feeding speed loop H∞Controller；Step 4, speed loop H∞Torque motor is sent into the output of controller after power amplifier amplifies, and performs control result, drives rotating frame to be rotated by control rate.The control method of the present invention, can effectively eliminate the influence of moment of friction present in rotating mechanism and unbalanced moments, improve the control accuracy and dynamic reliability of rotating mechanism, and then improve the overall performance of inertial navigation system.

Description

A kind of rotating mechanism PID/H∞Control method
Technical field
The invention belongs to rotation modulation inertial navigation system control technology field, and in particular to a kind of bi-axial swivel mechanism PID/ H∞Control method.
Background technology
Moment of friction interference in bi-axial swivel mechanism, in shafting be present, the low speed rotation performance of rotating mechanism can be influenceed；This Outside, under airborne dynamic environment, the motion of carrier aircraft and random vibration can be produced by inertial navigation system pedestal couples into rotating mechanism Raw Ji trimming moment, influence the dynamic property of rotating mechanism.And traditional control method Ji can effectively handle in rotating mechanism and deposit Above-mentioned moment of friction and Ji trimming moment influenceed to caused by system, make rotating mechanism servo performance and robustness drop It is low.
The content of the invention
The technical problem to be solved in the invention is moment of friction and Ji equilibrant force present in effective elimination rotating mechanism Square influences to caused by the servo performance and robustness of system.
The rotating mechanism PID/H of the present invention∞Control method, comprise the following steps：
Step 1, photoelectric encoder gather the actual angular position θ of rotating frame in real time；
Step 2, actual angular position θ not control targe angle θrefMake difference, difference result is inputted to position PID controllers；
Step 3, the output of signals of the actual angular position θ after differentiator differential not position PID controller made into difference, it is poor Result after point is inputted to speed loop H∞Controller；
Step 4, speed loop H∞Torque motor is sent into the output of controller after power amplifier amplifies, and performs control knot Fruit, rotating frame is driven to be rotated by control rate；
Wherein, in the step 3, speed loop H∞The control rate of controller uses H∞Mixed Sensitivity PS/T methods are asked Solution draws, the H∞Mixed Sensitivity PS/T methods are shown below：
In formula, W1(s) it is the performances weighting functions of rotating mechanism control system, W2(s) it is the robust of rotating mechanism control system Stable weight function, P (s) are the transmission function of rotating mechanism controlled device, and S (s) is to characterize rotating mechanism panel level Sensitivity function, T (s) are the mending sensitivity function for the robust stability for characterizing rotating mechanism.
Preferably, the rotating mechanism control system performances weighting functions W1(s) expression formula is：
Wherein
ρ=ML/ωJK0
In formula, MLFor disturbance torque；ω is disturbance torque MLThe Output speed in the lower loop of effect；J is turning for rotating mechanism Dynamic inertia；K0For the gain coefficient of rotating mechanism controlled device；ξ is control output adjustment parameter；μ1、μ2、μ3For adjusting system Frequency characteristic parameter
The rotating mechanism control system performances weighting functions W2(s) expression formula is：
W2=k1λ1λ2
In formula, k1For gain coefficient；λ1For loop bandwidth restricted function；λ2For high-frequency noise inhibition function.
Preferably, ρ=1518, a width of 400Hz of rotating mechanism speed loop band, ξ=0.60;μ1=235; μ2=360;μ3 =780, then
λ1=0.0025 (s+1), λ2=(0.0003s+1), k1=1.2, then
W2(s)=1.2 × 0.0025 (s+1) (0.0003s+1)；
The H of speed loop∞The input/output model of controller is：
Preferably, position PID controller described in step 3 is PI structures, and its input/output model is：
Preferably, to the H of the speed loop∞The input/output model K of controllerv(s) depression of order simplification processing is carried out, is obtained H after simplification∞Controller input/output model is：
Brief description of the drawings
Fig. 1 is a kind of PID/H of rotating mechanism of the present invention∞The controlled rotating mechanism composition schematic diagram of control method；
Fig. 2 is a kind of PID/H of rotating mechanism of the present invention∞The control principle drawing of control method.
Embodiment
Embodiment 1,
A kind of as shown in Fig. 2 rotating mechanism PID/H of the present invention∞Control method, comprise the following steps：
Step 1, photoelectric encoder gather the actual angular position θ of rotating frame in real time；
Step 2, actual angular position θ not control targe angle θrefMake difference, difference result is sent into position PID controls as input Device processed；
Step 3, the output of signals of the actual angular position θ after differentiator differential not position PID controller done into difference, will Differentiated result is sent into speed loop H as input∞Controller；
Step 4, speed loop H∞Torque motor is sent into the output of controller after power amplifier amplifies, and performs control knot Fruit, rotating frame is driven to be rotated by control rate；
In the step 3, speed loop H∞The control rate of controller uses H∞Mixed Sensitivity PS/T methods are solved and drawn, The H∞Mixed Sensitivity PS/T methods such as following formula：
In formula
W1(s) it is the performances weighting functions of rotating mechanism control system；
W2(s) it is the robust stability weight function of rotating mechanism control system；
P (s) is the transmission function of the controlled device of rotating mechanism;
S (s) is the sensitivity function for characterizing rotating mechanism panel level, and its acquisition methods is known in the art often Know；
T (s) is the mending sensitivity function for the robust stability for characterizing rotating mechanism, and its acquisition methods is known in the art General knowledge；
Embodiment 2
The difference of the present embodiment not embodiment 1 is, W1(s) determination method is as follows：
Step 3.1.1, according to inner membrance principle, to eliminate loop steady-state error, W1(s) integral element 1/s should be contained in；
Step 3.1.2, it is delayed phase caused by decaying integral link, in W1(s) near increase loop Mid Frequency Zero point (μ s+1)；
Step 3.1.3, the AF panel performance indications T (s) of speed loop=ω (s) ML(s), to make in disturbance torque ML (s) the Output speed ω (s) under acting on is as far as possible small, in W1(s) gain coefficient ρ=M is set inL/ωJK0, wherein, MLIt is dry Disturb torque；ω is disturbance torque MLThe Output speed in the lower loop of effect；J is the rotary inertia of rotating mechanism；K0For rotating mechanism The gain coefficient of controlled device；
Step 3.4, in W1(s) increase inLink, to improve rotating mechanism The stability margin of speed loop, wherein ξ export adjustment parameter, μ for control1、μ2、μ3The frequency characteristic parameter of adjusting system；
It is final to determine W1(s) expression formula is：
W2(s) determination method is：
Step 3.2.1, in order to suppress the high frequency unmodelled dynamics of control loop, the bandwidth of limit circuit, in W2(s) Middle setting loop bandwidth limiting element λ1；
Step 3.2.2, in order to quickly suppress the high-frequency noise in loop, in W2(s) the high frequency link λ outside bandwidth is set in2；
The gain perturbation of system is considered as when step 3.2.3, designing, therefore W is set2(s) gain coefficient in is k1；
Then determine W2(s) expression formula is：
W2=k1λ1λ2
Embodiment 3
The difference of the present embodiment not embodiment 2 is：Take ρ=1518, the bandwidth of rotating mechanism speed loop in 400Hz, Take ξ=0.60;μ1=235;μ2=360;μ3=780, then
Take λ1=0.0025 (s+1), λ2=(0.0003s+1), the gain perturbation for considering system is ± 20%, takes k1=1.2, Then
W2(s)=1.2 × 0.0025 (s+1) (0.0003s+1)；
Therefore the H of speed loop∞The input/output model of controller is：
Embodiment 4
The difference of the present embodiment not embodiment 1 is, position PID controller described in step 3 is PI structures, proportional gain K=42, storage gain p=494, the input/output model of PID controller are：
Embodiment 5
The difference of the present embodiment not embodiment 3 is, H described in embodiment 3∞Speed control modular form（1）Exponent number Higher, Ji is beneficial to Project Realization, and depression of order processing need to be carried out to it, and depression of order principle is：
1st, the high frequency link much larger than system speed loop bandwidth influences smaller on the characteristic of the main frequency range of system, can be with Ignore；
2nd, closely located zero pole point is almost constant in the characteristic of middle low-frequency range, can be cancelled out each other；
3rd, when speed control designs, in order to meet H∞Solving condition and increased small perturbing term should reduce；
4th, the static gain Ji of speed control becomes before and after depression of order.
According to above-mentioned depression of order principle, to H∞Speed control modular form（1）Simplified, the H after must simplifying∞Controller Input/output model is：
。

Claims (4)

  1. A kind of 1. rotating mechanism PID/H∞Control method, comprise the following steps：
    Step 1, photoelectric encoder gather the actual angular position θ of rotating frame in real time；
    Step 2, actual angular position θ and control targe angle θrefMake difference, difference result is inputted to position PID controller；
    Step 3, difference of making the output of signals of the actual angular position θ after differentiator differential and position PID controller, after difference Result input to speed loop H∞Controller；
    Step 4, speed loop H∞Torque motor is sent into the output of controller after power amplifier amplifies, and performs control result, Rotating frame is driven to be rotated by control rate；
    It is characterized in that：In the step 3, speed loop H∞The control rate of controller uses H∞Mixed Sensitivity PS/T methods are asked Solution draws, the H∞Mixed Sensitivity PS/T methods are shown below：
    <mrow> <mo>|</mo> <mo>|</mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi>W</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mi>S</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>W</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mi>T</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>|</mo> <msub> <mo>|</mo> <mi>&amp;infin;</mi> </msub> <mo>&lt;</mo> <mn>1</mn> </mrow>
    In formula, W1(s) it is the performances weighting functions of rotating mechanism control system, W2(s) it is the robust stability of rotating mechanism control system Weight function, P (s) are the transmission function of rotating mechanism controlled device, and S (s) is the sensitive of sign rotating mechanism panel level Function is spent, T (s) is the mending sensitivity function for the robust stability for characterizing rotating mechanism；
    The rotating mechanism control system performances weighting functions W1(s) expression formula is：
    Wherein
    ρ=ML/ωJK0
    In formula, MLFor disturbance torque；ω is disturbance torque MLThe Output speed in the lower loop of effect；J is that the rotation of rotating mechanism is used to Amount；K0For the gain coefficient of rotating mechanism controlled device；ξ is control output adjustment parameter；μ1、μ2、μ3For the frequency of adjusting system Characterisitic parameter；
    The robust stability weight function W of the rotating mechanism control system2(s) expression formula is：
    W2=k1λ1λ2
    In formula, k1For gain coefficient；λ1For loop bandwidth restricted function；λ2For high-frequency noise inhibition function.
  2. 2. rotating mechanism PID/H as claimed in claim 1∞Control method, it is characterised in that：ρ=1518, rotating mechanism speed Loop bandwidth is 400Hz, ξ=0.60；μ1=235；μ2=360；μ3=780, then
    <mrow> <msub> <mi>W</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1518</mn> <mfrac> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mn>385</mn> </mfrac> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>(</mo> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>432</mn> <mi>s</mi> <mo>+</mo> <mn>129600</mn> <mo>)</mo> </mrow> <mrow> <mi>s</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>+</mo> <mn>235</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>s</mi> <mo>+</mo> <mn>780</mn> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
    λ1=0.0025 (s+1), λ2=(0.0003s+1), k1=1.2, then
    W2(s)=1.2 × 0.0025 (s+1) (0.0003s+1)；
    The H of speed loop∞The input/output model of controller is：
    <mrow> <msub> <mi>K</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>7881.665</mn> <msup> <mrow> <mo>(</mo> <mrow> <mi>s</mi> <mo>+</mo> <mn>5</mn> <mi>e</mi> <mn>004</mn> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mrow> <mi>s</mi> <mo>+</mo> <mn>2332</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mi>s</mi> <mo>+</mo> <mn>764.6</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mi>s</mi> <mo>+</mo> <mn>285.4</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>373.7</mn> <mi>s</mi> <mo>+</mo> <mn>3.63</mn> <mi>e</mi> <mn>004</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>s</mi> <mrow> <mo>(</mo> <mrow> <mi>s</mi> <mo>+</mo> <mn>5.247</mn> <mi>e</mi> <mn>004</mn> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mi>e</mi> <mn>005</mn> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mrow> <mi>s</mi> <mo>+</mo> <mn>3641</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mi>s</mi> <mo>+</mo> <mn>780</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mi>s</mi> <mo>+</mo> <mn>235</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>.</mo> </mrow>
  3. 3. rotating mechanism PID/H as claimed in claim 1∞Control method, it is characterised in that：Control position PID described in step 3 Device processed is PI structures, and its input/output model is：
    <mrow> <msub> <mi>K</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>42</mn> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>0.085</mn> <mi>s</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  4. 4. rotating mechanism PID/H as claimed in claim 3∞Control method, it is characterised in that：To the H of the speed loop∞Control The input/output model K of device processedv(s) depression of order simplification processing, the H after must simplifying are carried out∞Controller input/output model is：
    <mrow> <msubsup> <mi>K</mi> <mi>v</mi> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>0.0286</mn> <mrow> <mo>(</mo> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>373.7</mn> <mi>s</mi> <mo>+</mo> <mn>3.63</mn> <mi>e</mi> <mn>004</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>0.0035</mn> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>s</mi> <mrow> <mo>(</mo> <mn>0.0043</mn> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>.</mo> </mrow>
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