CN105573125A - Pneumatic system position adaption control method aiming at unknown control direction - Google Patents

Abstract

The invention discloses a pneumatic system position adaption control method aiming at a unknown control direction. The method comprises the following steps of step1) establishing a model of a pneumatic position servo system, wherein a control objective is that a displacement of a piston can track required expectation output when a proportional valve outputs positive and negative connection modes; step2) introducing an Nussbaum gain function and setting a self-adaptive controller of the pneumatic position servo system; step3) carrying out amplitude limiting on a control signal; step4) estimating a value of an unknown model parameter of the pneumatic position servo system and using an obtained estimated result to update a self-adaptive controller parameter in real time, wherein a computer outputs the control signal after amplitude limiting to the proportional valve through a D/A converter so as to adjust the displacement of the piston in a rodless cylinder in real time. By using the method in the invention, the control gain direction does not need to be known, a pressure detection hardware or software observation algorithm does not need to be added, a tracking effect is good and control precision is high.

Description

A kind of for the pneumatic system position self-adaptation control method of controlling party to the unknown

Technical field

The invention belongs to pneumatic system Position Tracking Control technical field, relate to a kind of for the pneumatic system position self-adaptation control method of controlling party to the unknown.

Background technology

The features such as pneumatic system (i.e. Pneumatic Position Servo System) is simple with its structure, power to volume ratio is high, safety anti-explosive, clean and long service life, are widely applied at industrial automation.But, pneumatic system has strong nonlinearity, parameter time varying and model uncertainty, these factors both increase the control difficulty of Pneumatic Position Servo System, how to improve the track following performance of Pneumatic Position Servo System, are important directions of current Pneumatic Position Servo System research.Pneumatic element is the raising of proportioning valve cost performance and improving constantly of microprocessor speed especially, brings opportunity to the pneumatic tracking control system of high-performance.

Pneumatic Position Servo System proportioning valve to the order of connection of cylinder both sides gas piping determines the direction of control action, and in reality, closure is fixed usually, but may make a fault in field-mounted process to some portable equipments and cause controlling party to uncertain.The control method of existing Pneumatic Position Servo System all needs the ride gain symbol of supposing the system known, and when Systematical control gain sign is unknown, existing a lot of control method is difficult to achieve effective control.

Summary of the invention

The object of the present invention is to provide a kind of for the pneumatic system position self-adaptation control method of controlling party to the unknown, solve the direction that prior art needs known Pneumatic Position Servo System ride gain in advance, and when Systematical control gain sign (direction) is unknown, existing a lot of self-adaptation control method is difficult to the problem realized.

The technical solution used in the present invention is, a kind of for the pneumatic system position self-adaptation control method of controlling party to the unknown, the method is specifically implemented according to following steps:

Step 1, set up the model of Pneumatic Position Servo System

According to the working mechanism of Pneumatic Position Servo System, ignore friction, carry out linearization process simultaneously, obtain linear numerical modei such as formula shown in (1):

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=x_3\\ {\stackrel{\·}{x}}_3=a_1{x}_1+a_2{x}_2+a_3{x}_3+bu\\ y=x_1\end{array}\right.,---\left(1\right)$

Wherein x ₁, x ₂, x ₃for system state variables, physical meaning represents the position of piston (1), speed and acceleration respectively, correspond to x respectively ₁, x ₂, x ₃first order derivative, u is control inputs, a ₁, a ₂, a ₃for unknown model parameters, the Systematical control gain that sized by b and direction is all unknown, control objectives is when proportioning valve exports positive and negative two kinds of connected modes, makes the displacement y of piston can follow the tracks of required desired output y _d;

Step 2, introducing Nussbaum gain function, arrange the adaptive controller of Pneumatic Position Servo System

Choose adaptive controller to above-mentioned formula (1), the model expression of adaptive controller is respectively such as formula shown in (2) and formula (3):

$\stackrel{\·}{\mathrm{\ξ}}=z_3(c_3{z}_3+{\widehat{\mathrm{\θ}}}^T\mathrm{\ω}),---\left(2\right)$

$u^{\′}=N\left(\mathrm{\ξ}\right)(c_3{z}_3+{\widehat{\mathrm{\θ}}}^T\mathrm{\ω}),---\left(3\right)$

Wherein N (ξ) is Nussbaum type even function, z ₁=x ₁-y _d, z ₂=x ₂-α ₁, z ₃=x ₃-α ₂, θ=[1a ₁a ₂a ₃] ^tfor parameter vector, for the estimated value of θ, for state vector, for desired output y _dfirst order derivative, for α ₁first order derivative, for α ₂first order derivative, α ₁, α ₂, z ₁, z ₂, z ₃for intermediate variable, c ₁, c ₂and c ₃for parameters;

Step 3, amplitude limit is carried out to control signal u ', such as formula (4):

$u=\left\{\begin{array}{cc}{U}_{max}& u^{\&prime;}>U_{max}\\ u^{\&prime;}& -U_{\max }\&le;u^{\&prime;}\&le;U_{max}\\ -U_{max}& u^{\&prime;}<-U_{max}\end{array}\right.,---\left(4\right)$

U _maxfor control output limitation value;

Step 4, the value of the unknown model parameters of Pneumatic Position Servo System to be estimated

The estimated value of unknown model parameters calculates with reference to formula (5):

$\stackrel{\&CenterDot;}{\widehat{\mathrm{\&theta;}}}={\mathrm{\&Gamma;\&omega;z}}_3,---\left(5\right)$

Γ is wherein positive definite matrix, is adaptive gain, for first order derivative,

Formula (5) estimation is obtained numerical value is used for the parameter in real-time update formula (2), and the control signal through amplitude limit is defeated by proportioning valve by D/A converter by computing machine, regulates the displacement y of piston in Rodless cylinder in real time.

The invention has the beneficial effects as follows, do not need the direction of known system ride gain in advance; Do not need to increase pressure detection hardware or software observation algorithm; Do not need nonlinear terms and uncertain parameter circle of the model of object, just can implement effective control; Compared with more existing control methods, the control accuracy of better tracking effect and Geng Gao can be obtained.

Accompanying drawing explanation

Fig. 1 is the structural representation of the control object (proportional valve control Rodless cylinder) of the inventive method;

Fig. 2 is the experimental result adopting the inventive method to follow the tracks of sinusoidal signal when proportioning valve forward connects;

Fig. 3 is the experimental result adopting the inventive method to follow the tracks of S curve when proportioning valve forward connects;

Fig. 4 is the experimental result adopting the inventive method to follow the tracks of multifrequency sine signal when proportioning valve forward connects;

Fig. 5 is the experimental result adopting the inventive method to follow the tracks of sinusoidal signal when proportioning valve Opposite direction connection;

Fig. 6 is the experimental result adopting the inventive method to follow the tracks of S curve when proportioning valve Opposite direction connection;

Fig. 7 is the experimental result adopting the inventive method to follow the tracks of multifrequency sine signal when proportioning valve Opposite direction connection;

Fig. 8 is the experimental result adopting sliding moding structure method 1 to follow the tracks of sinusoidal signal when proportioning valve forward connects;

Fig. 9 is the experimental result adopting sliding moding structure method 1 to follow the tracks of S curve when proportioning valve forward connects;

Figure 10 is the experimental result adopting sliding moding structure method 1 to follow the tracks of multifrequency sine signal when proportioning valve forward connects;

Figure 11 is the experimental result adopting sliding moding structure method 1 to follow the tracks of sinusoidal signal when proportioning valve Opposite direction connection;

Figure 12 is the experimental result adopting sliding moding structure method 1 to follow the tracks of S curve when proportioning valve Opposite direction connection;

Figure 13 is the experimental result adopting sliding moding structure method 1 to follow the tracks of multifrequency sine signal when proportioning valve Opposite direction connection;

Figure 14 is the experimental result adopting sliding moding structure method 2 to follow the tracks of sinusoidal signal when proportioning valve forward connects;

Figure 15 is the experimental result adopting sliding moding structure method 2 to follow the tracks of S curve when proportioning valve forward connects;

Figure 16 is the experimental result adopting sliding moding structure method 2 to follow the tracks of multifrequency sine signal when proportioning valve forward connects;

Figure 17 is the experimental result adopting contragradience adaptive approach 1 to follow the tracks of sinusoidal signal when proportioning valve forward connects;

Figure 18 is the experimental result adopting contragradience adaptive approach 1 to follow the tracks of S curve when proportioning valve forward connects;

Figure 19 is the experimental result adopting contragradience adaptive approach 1 to follow the tracks of multifrequency sine signal when proportioning valve forward connects;

Figure 20 is the experimental result adopting contragradience adaptive approach 2 to follow the tracks of sinusoidal signal when proportioning valve forward connects;

Figure 21 is the experimental result adopting contragradience adaptive approach 2 to follow the tracks of S curve when proportioning valve forward connects;

Figure 22 is the experimental result adopting contragradience adaptive approach 2 to follow the tracks of multifrequency sine signal when proportioning valve forward connects.

In figure, 1. piston, 2. load, 3. Rodless cylinder, 4. displacement detecting instrument, 5. proportioning valve, 6. computing machine, 7. reduction valve, 8. air pump, 9. gas-holder.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

Of the present invention for the pneumatic system position self-adaptation control method of controlling party to the unknown, specifically implement according to following steps:

Step 1, set up the model of Pneumatic Position Servo System

With reference to Fig. 1, the structure of the Pneumatic Position Servo System that the inventive method relies on is, the piston 1 of Rodless cylinder 3 is fixedly connected with load 2, and piston 1 also contacts with displacement detecting instrument 4 is corresponding, and the output signal of location detector 4 is by A/D converter access computing machine 6; The air cavity A side of Rodless cylinder 3 and air cavity B side respectively with two outlet sides (namely two Po hold) the corresponding UNICOM of proportioning valve 5, proportioning valve 5 is 3 position-5 way proportional servo valve, positive and negative direction two kinds of connected modes are defined as respectively according to the difference of two outlet sides (i.e. two the Po ends) order of connection, proportioning valve 5 inlet end (i.e. Pu end) is communicated with gas-holder 9, gas-holder 9 is by reduction valve 7 and air pump 8 UNICOM, computing machine 6 is connected with proportioning valve 5 by D/A converter, and the output signal of controller is sent to proportioning valve 5.

Suppose that above-mentioned Pneumatic Position Servo System meets following condition:

1) actuating medium (air) that system uses is ideal gas;

2) flow state of gas flow when valve port or other restriction is constant entropy adiabatic process;

3) in same cavity volume, gaseous tension and temperature are equal everywhere;

4) leakage is ignored;

5), during piston movement, the change procedure of two intracavity gas is adiabatic process;

6) bleed pressure and atmospheric pressure constant;

7) compared with system dynamic characteristic, the inertia of proportioning valve can be ignored.

According to the working mechanism of Pneumatic Position Servo System, ignore friction, carry out linearization process simultaneously, obtain linear numerical modei such as formula shown in (1):

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=x_3\\ {\stackrel{\&CenterDot;}{x}}_3=a_1{x}_1+a_2{x}_2+a_3{x}_3+bu\\ y=x_1\end{array}\right.,---\left(1\right)$

Wherein x ₁, x ₂, x ₃for system state variables, physical meaning represents the position of piston 1, speed and acceleration respectively, correspond to x respectively ₁, x ₂, x ₃first order derivative, u is control inputs, a ₁, a ₂, a ₃for unknown model parameters, the Systematical control gain that sized by b and direction (symbol) is all unknown, control objectives is when proportioning valve 5 exports positive and negative two kinds of connected modes, makes the displacement y of piston 1 can follow the tracks of required desired output y _d;

Step 2, introducing Nussbaum gain function, arrange the adaptive controller of Pneumatic Position Servo System

Choose adaptive controller to above-mentioned formula (1), the model expression of adaptive controller is respectively such as formula shown in (2) and formula (3):

$\stackrel{\&CenterDot;}{\mathrm{\&xi;}}=z_3(c_3{z}_3+{\widehat{\mathrm{\&theta;}}}^T\mathrm{\&omega;}),---\left(2\right)$

$u^{\&prime;}=N\left(\mathrm{\&xi;}\right)(c_3{z}_3+{\widehat{\mathrm{\&theta;}}}^T\mathrm{\&omega;}),---\left(3\right)$

Wherein N (ξ)=ξ ²cos (ξ) is Nussbaum type even function, z ₁=x ₁-y _d, z ₂=x ₂-α ₁, z ₃=x ₃-α ₂, θ=[1a ₁a ₂a ₃] ^tfor parameter vector, for the estimated value of θ, for state vector, for desired output y _dfirst order derivative, for α ₁first order derivative, for α ₂first order derivative, α ₁, α ₂, z ₁, z ₂, z ₃for intermediate variable, c ₁, c ₂and c ₃for parameters;

Step 3, amplitude limit is carried out to control signal u ', such as formula (4):

$u=\left\{\begin{array}{cc}{U}_{max}& u^{\&prime;}>U_{max}\\ u^{\&prime;}& -U_{\max }\&le;u^{\&prime;}\&le;U_{max}\\ -U_{max}& u^{\&prime;}<-U_{max}\end{array}\right.,---\left(4\right)$

U _maxfor control output limitation value, specifically according to actual ratio valve 5 and object determination numerical value;

Step 4, the value of the unknown model parameters of Pneumatic Position Servo System (adaptive controller) to be estimated

The estimated value of unknown model parameters calculates with reference to formula (5):

$\stackrel{\&CenterDot;}{\widehat{\mathrm{\&theta;}}}={\mathrm{\&Gamma;\&omega;z}}_3,---\left(5\right)$

Γ is wherein positive definite matrix, is adaptive gain, for first order derivative,

Formula (5) estimation is obtained numerical value is used for the parameter in real-time update formula (2), and the control signal through amplitude limit is defeated by proportioning valve 5 by D/A converter by computing machine 6, regulates the displacement y of piston 1 in Rodless cylinder 3 in real time.

Embodiment

The first, with reference to Fig. 1, select the model of all parts, build Pneumatic Position Servo System

Rodless cylinder 3 selects the Rodless cylinder of FESTO company DGPL-25-450-PPV-A-B-KF-GK-SV model; The 3 position-5 way proportioning valve of model MPYE-5-1/8-HF-010-B selected by proportioning valve 5; The swept resistance formula linear displacement detecting instrument of model MLO-POT-450-TLF selected by displacement detecting instrument 4; Computing machine 6 selects CPU to be the model of P21.2GHz; The model that universal data collection card is selected is PCI2306.The control software design employing VB establishment that computing machine 6 is built-in, demonstrates the change curve of correlated variables in control procedure by display screen.

The second, the control objectives of Pneumatic Position Servo System is set

Reference signal 1 is single frequency sinusoidal signal:

y _d＝111.65sin0.5πt，(6)

Reference signal 2 is S curve signal:

y _d＝-[55.825/(0.5π) ²]sin0.5πt+[55.825/(0.5π)]t，(7)

Reference signal 3 is multifrequency sine signal:

$\begin{array}{c}{y}_d=167.475\sin \mathrm{\&pi;}t+167.475\sin 0.5\mathrm{\&pi;}t+167.475\sin (2\mathrm{\&pi;}t/7)\\ +167.475\sin (\mathrm{\&pi;}t/6)+167.475\sin (2\mathrm{\&pi;}t/17)\end{array},---\left(8\right)$

3rd, adopt the adaptive controller of the inventive method through type (2)-Shi (5) to test

The occurrence of parameters is set, c ₁=c ₂=60, c ₃=0.1, Γ=diag ([0.010.010.01]), controls amplitude limit U _max=1.95V, when follow the tracks of expectation target be respectively formula (6)-Shi (8) time, proportioning valve 5 export for positive dirction connect time, aircraft pursuit course is as shown in Figure 2, Figure 3, Figure 4.Hold controller parameter constant, when proportioning valve 5 exports and connects in the other direction, aircraft pursuit course is as shown in Fig. 5, Fig. 6, Fig. 7.Visible, no matter the inventive method connects for servo-valve 5 forward or Opposite direction connection can both realize effective tracking.

4th, utilize the control method of following four kinds of prior aries to carry out contrast test

One) sliding moding structure method 1

Sliding moding structure method 1 reference literature [T.Nguyen, J.Leavitt, F.Jabbari, J.E.Bobrow.AccurateSlide-ModeControlofPneumaticSystemsUs ingLow-CostSolenoidValves.IEEE/ASMETransactionsonMechatr onics, 2007,12 (2): 216-219], the control expression formula of sliding moding structure method 1 is formula (9)-Shi (10):

$S=\stackrel{\&CenterDot;\&CenterDot;}{y}-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d+2\mathrm{\&zeta;}\mathrm{\&omega;}(\stackrel{\&CenterDot;}{y}-{\stackrel{\&CenterDot;}{y}}_d)+{\mathrm{\&omega;}}^2(y-y_d),---\left(9\right)$

u＝-k _s2sgn(S)，(10)

This sliding moding structure method 1 is for switch valve control cylinder, and actual control is provided by formula (10), k _s2the corresponding valve of=1, u=1 is opened, and the corresponding valve of u=-1 closes.Get k _s2the aperture amplitude of=1.56 volts of control ratio valves 5, controller parameter gets ξ=1, ω=50, controls result curve as shown in Fig. 8, Fig. 9, Figure 10.Hold controller parameter constant, when proportioning valve 5 exports and connects, controls result curve as shown in figure Figure 11, Figure 12, Figure 13 in the other direction.From Figure 11, Figure 12, Figure 13, sliding moding structure method 1 cannot realize the tracing control to reference signal.

Two) sliding moding structure method 2

Sliding moding structure method 2 reference literature [GaryM.Bone, ShuNing.ExperimentalComparisonofPositionTrackingControlA lgorithmsforPneumaticCylinderActuators.IEEE/ASMETransact ionsonMechatronics, 2007,12 (5): 557-561], the control expression formula of this sliding moding structure method 2 is formula (11)-Shi (14):

$S=\stackrel{\&CenterDot;\&CenterDot;}{y}-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d+2\mathrm{\&lambda;}(\stackrel{\&CenterDot;}{y}-{\stackrel{\&CenterDot;}{y}}_d)+{\mathrm{\&lambda;}}^2(y-y_d),---\left(11\right)$

$u_{eq}=\frac{1}{m_0}\&lsqb;{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{y}}_d+n_2\stackrel{\&CenterDot;\&CenterDot;}{y}+n_1\stackrel{\&CenterDot;}{y}+n_{0}y-2\mathrm{\&lambda;}(\stackrel{\&CenterDot;\&CenterDot;}{y}-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d)-{\mathrm{\&lambda;}}^2(\stackrel{\&CenterDot;}{y}-{\stackrel{\&CenterDot;}{y}}_d)\&rsqb;,---\left(12\right)$

u _s＝-k _s1sat(S/φ)，(13)

u′＝u _eq+u _s，(14)

The control of sliding moding structure method 2 reality is provided by formula (14), and the amplitude limit controlling to export provides such as formula (4), controling parameters n ₂=29.5544, n ₁=218.436, n ₀=0, m ₀=5531.3305, λ=50, k _s1=2.44 × 10 ⁴, φ=0.05, controls result curve as shown in Figure 14, Figure 15, Figure 16.Hold controller parameter constant, when proportioning valve 5 exports and connects in the other direction, be similar to the experimental result of sliding-mode control 1 when proportioning valve 5 exports reverse (with reference to Figure 11, Figure 12, Figure 13), this sliding moding structure method 2 cannot realize the tracing control to reference signal.

Three) contragradience adaptive approach 1

Contragradience adaptive approach 1 reference literature [RenHP, HuangC.AdaptiveBacksteppingControlofPneumaticServoSystem .InProceedingofthe2013IEEEInternationalSymposiumonIndust rialElectronics, Taibei, May28-31,2013:1-6], the control expression formula of contragradience adaptive approach 1 is formula (15)-Shi (16):

$u^{\&prime;}=\frac{1}{\hat{b}}(-z_2-{\hat{a}}_1{z}_1-{\hat{a}}_1{y}_d-{\hat{a}}_2{z}_2-{\hat{a}}_2{\mathrm{\&alpha;}}_1-{\hat{a}}_3{\mathrm{\&alpha;}}_2+{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_2),---\left(15\right)$

$\left\{\begin{array}{c}\frac{1}{\hat{b}}=\&Integral;(-\mathrm{\&lambda;})z_1{y}_{d}dt\\ {\stackrel{\&CenterDot;}{\hat{a}}}_1=-{\mathrm{\&beta;}}_1{z}_1{x}_1\\ {\stackrel{\&CenterDot;}{\hat{a}}}_2=-{\mathrm{\&beta;}}_2{z}_1{x}_2\\ {\stackrel{\&CenterDot;}{\hat{a}}}_3=-{\mathrm{\&beta;}}_3{z}_1{x}_3\end{array}\right.,---\left(16\right)$

The control of this contragradience adaptive approach 1 reality is provided by formula (15), controls the amplitude limit of output such as formula (4), controller parameter c ₁=c ₂=50, λ=β ₁=β ₂=β ₃=1, control result curve as shown in Figure 17, Figure 18, Figure 19.Hold controller parameter constant, when proportioning valve 5 exports and connects in the other direction, experimental result is similar to the experimental result of sliding-mode control 1 when proportioning valve 5 exports reverse (with reference to Figure 11, Figure 12, Figure 13), and contragradience adaptive approach 1 cannot realize the tracing control to reference signal.

Four) contragradience adaptive approach 2

Contragradience adaptive approach 2 reference literature [RenHP, HuangC.ExperimentalTrackingControlforPneumaticSystem.InP roceedingofthe2013IEEE39thAnnualConferenceonIndustrialEl ectronicsSociety, Vienna, Austria, November10-13,2013:4126-4130], contragradience adaptive approach 2 control expression formula be formula (17)-Shi (20):

$u=\hat{p}\stackrel{\&OverBar;}{u},---\left(17\right)$

$\stackrel{\&OverBar;}{u}={\mathrm{\&alpha;}}_2+{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{y}}_m,---\left(18\right)$

$\stackrel{\&CenterDot;}{\hat{p}}=-\mathrm{\&gamma;}\mathrm{sgn}\left(m_0\right)\stackrel{\&OverBar;}{u}{z}_3,---\left(19\right)$

$\stackrel{\&CenterDot;}{\hat{A}}=\mathrm{\&Gamma;}\mathrm{\&Phi;}\left(x\right)z_3,---\left(20\right)$

The control of this contragradience adaptive approach 2 reality is provided by formula (17), controls the amplitude limit of output such as formula (4), controller parameter c ₁=c ₂=50, λ=1, Γ=diag [111], controls result curve with reference to shown in Figure 20, Figure 21, Figure 22.Hold controller parameter constant, when proportioning valve 5 exports and connects in the other direction, experimental result is similar to the experimental result of sliding-mode control 1 when proportioning valve 5 exports reverse (with reference to Figure 11, Figure 12, Figure 13), and contragradience adaptive approach 2 cannot realize the tracing control to reference signal equally.

Visible by the contrast of above-mentioned four kinds of existing control technologys, the inventive method tracking effect is better.Especially when proportioning valve output connects in the other direction, all inefficacies of existing four kinds of control methods, and the inventive method still can realize the effective tracing control to reference signal.

5th, in order to the control effects of the inventive method is described more intuitively, calculate tracking error quantitatively when following the tracks of different expectation target, error is defined as root-mean-square error, and expression formula is as follows:

$RMSE=\sqrt{\frac{1}{N_2-N_1}\underset{k-N_1}{\overset{N_2}{\&Sigma;}}{e}_k^2},---\left(21\right)$

Wherein N ₁for comparing start time, N ₂for comparing finish time, e _k=y (k Δ T)-y _d(k Δ T), Δ T is sampling time interval, and k represents sampling instant.For avoiding the impact of different initial value and random disturbance, test of many times being carried out to the tracing control of often kind of reference signal, having provided the experimental result of wherein five tests.

Table 1 is that the inventive method and the error of existing four kinds of control methods when tracking mode (6) desired output signal contrast.

Table 1 the inventive method and the error of existing control method when tracking mode (6) desired output signal contrast

Table 2 is that the inventive method and the error of existing four kinds of control methods when tracking mode (7) desired output signal contrast.

Table 2 the inventive method and the error of existing control method when tracking mode (7) desired output signal contrast

Table 3 is that the inventive method and the error of existing four kinds of control methods when tracking mode (8) desired output signal contrast.

Table 3 the inventive method and the error of existing control method when tracking mode (8) desired output signal contrast

Contrast the data in above-mentioned table 1, table 2, table 3, obviously visible, in various expectation target situation, when proportioning valve exports positive and negative two kinds of connected modes, the inventive method all energy achieve effective controls, and average tracking error is all less than existing control method.

Claims (2)

1., for the pneumatic system position self-adaptation control method of controlling party to the unknown, it is characterized in that, the method is specifically implemented according to following steps:

Step 1, set up the model of Pneumatic Position Servo System

According to the working mechanism of Pneumatic Position Servo System, ignore friction, carry out linearization process simultaneously, obtain linear numerical modei such as formula shown in (1):

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=x_3\\ {\stackrel{\&CenterDot;}{x}}_3=a_1{x}_1+a_2{x}_2+a_3{x}_3+bu\\ y=x_1\end{array}\right.,---\left(1\right)$

Wherein x ₁, x ₂, x ₃for system state variables, physical meaning represents the position of piston (1), speed and acceleration respectively, correspond to x respectively ₁, x ₂, x ₃first order derivative, u is control inputs, a ₁, a ₂, a ₃for unknown model parameters, the Systematical control gain that sized by b and direction is all unknown, control objectives is when proportioning valve (5) exports positive and negative two kinds of connected modes, makes the displacement y of piston (1) can follow the tracks of required desired output y _d;

Step 2, introducing Nussbaum gain function, arrange the adaptive controller of Pneumatic Position Servo System

Choose adaptive controller to above-mentioned formula (1), the model expression of adaptive controller is respectively such as formula shown in (2) and formula (3):

$\stackrel{\&CenterDot;}{\mathrm{\&xi;}}=z_3(c_3{z}_3+{\widehat{\mathrm{\&theta;}}}^T\mathrm{\&omega;}),---\left(2\right)$

$u^{\&prime;}=N\left(\mathrm{\&xi;}\right)(c_3{z}_3+{\widehat{\mathrm{\&theta;}}}^T\mathrm{\&omega;}),---\left(3\right)$

Wherein N (ξ) is Nussbaum type even function, z ₁=x ₁-y _d, z ₂=x ₂-α ₁, z ₃=x ₃-α ₂, θ=[1a ₁a ₂a ₃] ^tfor parameter vector, for the estimated value of θ, for state vector, for desired output y _dfirst order derivative, for α ₁first order derivative, for α ₂first order derivative, α ₁, α ₂, z ₁, z ₂, z ₃for intermediate variable, c ₁, c ₂and c ₃for parameters;

Step 3, amplitude limit is carried out to control signal u ', such as formula (4):

$u=\left\{\begin{array}{cc}{U}_{max}& u^{\&prime;}>U_{max}\\ u^{\&prime;}& -U_{max}\&le;u^{\&prime;}\&le;U_{max}\\ -U_{max}& u^{\&prime;}<-U_{max}\end{array}\right.,---\left(4\right)$

U _maxfor control output limitation value;

Step 4, the value of the unknown model parameters of Pneumatic Position Servo System to be estimated

The estimated value of unknown model parameters calculates with reference to formula (5):

$\stackrel{\&CenterDot;}{\widehat{\mathrm{\&theta;}}}={\mathrm{\&Gamma;\&omega;z}}_3,---\left(5\right)$

Γ is wherein positive definite matrix, is adaptive gain, for first order derivative,

Formula (5) estimation is obtained numerical value is used for the parameter in real-time update formula (2), control signal through amplitude limit is defeated by proportioning valve (5) by D/A converter by computing machine (6), regulates the displacement y of piston (1) in Rodless cylinder (3) in real time.

2. according to claim 1 for the pneumatic system position self-adaptation control method of controlling party to the unknown, it is characterized in that: in described step 1, the structure of controlled Pneumatic Position Servo System is, the piston (1) of Rodless cylinder (3) is fixedly connected with load (2), piston (1) also contacts with displacement detecting instrument (4) is corresponding, and the output signal of location detector (4) accesses computing machine (6) by A/D converter; The air cavity A side of Rodless cylinder (3) and air cavity B side respectively with two corresponding UNICOMs in outlet side of proportioning valve (5), proportioning valve (5) is 3 position-5 way proportional servo valve, positive and negative direction two kinds of connected modes are defined as respectively according to the difference of two outlet side orders of connection, proportioning valve (5) inlet end is communicated with gas-holder (9), gas-holder (9) is by reduction valve (7) and air pump (8) UNICOM, and computing machine (6) is connected with proportioning valve (5) by D/A converter.