CN104570734B - A kind of all-coefficient adaptive control method based on single order characteristic model - Google Patents

Abstract

The invention discloses a kind of all-coefficient adaptive control method based on single order characteristic model, according to formula <maths num=" 0001 " > </maths> calculates the preliminary parameters estimate vector θ of current period ₁(k); According to the preliminary parameters estimate vector θ of current period ₁(k) and a upper cycle estimated parameter vector θ (k) by what estimate that parameter vector θ (k-1) calculates current period; Parameter is estimated according to current period with carry out the controlled quentity controlled variable u (k) that linear Feedback Control obtains current period.All-coefficient adaptive control method based on single order characteristic model of the present invention, parameter is few, and algorithm is simple, and greatly and easily determine, the dynamic gain tracking velocity calculated by estimates of parameters is fast, adaptable for parameter area.

Description

Full-coefficient self-adaptive control method based on first-order feature model

Technical Field

The invention relates to the field of intelligent and self-adaptive control, in particular to a full-coefficient self-adaptive control method based on a first-order feature model.

Background

The existing full-coefficient adaptive control method based on the feature model is based on the feature model with the second order or more, for example, in 1998, "manned spacecraft full-coefficient adaptive reentry lift control" published in aerospace science (vol.19, No.1, jan, 1998, p8-12), the paper proposes a full-coefficient adaptive control method based on the drop point prediction and adopting the second-order feature model. The second-order characteristic model is adopted, the upper and lower limits are required to be carried out on each model parameter, and the upper and lower limits are also required to be carried out on the sum of the model parameters, so that the stability of the closed-loop system can be ensured. For a feature model with a second order or more, the upper and lower limit values of the parameter are related to the ratio of the control period to the time constant, and because the controlled object is unknown and the time constant is unknown, the upper and lower limit values of the parameter can only be determined empirically. The method is adopted for controlling the jumping reentry lift force of certain types of spaceflight. In the process of carrying out deep research on the control of the jumping reentry lift force of a certain model, the fact that model parameters sometimes touch or stay at the boundary due to large dynamic change of a controlled object is found, and the parameter tracking and self-adaptive capacity is lost, so that the further improvement of the reentry guidance precision is limited.

Disclosure of Invention

The invention aims to solve the technical problem of providing a full-coefficient self-adaptive control method based on a first-order characteristic model, the adopted first-order characteristic model has few parameters, only limits the parameter range, does not have the limitation of the sum of the parameters, has simple algorithm and large parameter range, and the dynamic gain tracking speed calculated by the parameter estimation value is high, the adaptive capacity is strong, and the first-order characteristic model is constant and stable, and the control effect on a reentry vehicle is superior to that of the full-coefficient self-adaptive control method of the second-order characteristic model.

The technical scheme of the invention is as follows:

a full-coefficient self-adaptive control method based on a first-order feature model is a first-order variable coefficient difference equation and is represented as follows:

y(k+1)＝α(k)y(k)+β₀(k)u(k)

wherein y (k) is the output transformation quantity of the current period of the controlled object, y (k +1) is the output transformation quantity of the next period of the controlled object, u (k) is the control quantity of the current period, α (k), β₀(k) Time-varying parameters of a current period of the first-order feature model;

the full-coefficient self-adaptive control method based on the first-order feature model in each period comprises the following steps:

according to the formula ${\mathrm{\&theta;}}_1\left(k\right)=\mathrm{\&theta;}(k-1)+\frac{{\mathrm{\&lambda;}}_1\mathrm{\&phi;}(k-1)}{{\mathrm{\&phi;}}^T(k-1)\mathrm{\&phi;}(k-1)+{\mathrm{\&lambda;}}_2}[y\left(k\right)-{\mathrm{\&phi;}}^T(k-1)\mathrm{\&theta;}(k-1)]$ Calculating a preliminary parameter estimation vector theta for the current cycle₁(k) Wherein λ is₁Is a gain factor, λ₂To remove the zero protection factor, 0<λ₁<1,λ₂>0; phi (k-1) is the regression vector of the previous cycle, phi^T(k-1)＝[y(k-1),u(k-1)]^T(ii) a Theta (k-1) is the estimated parameter vector of the previous cycle,

estimating a vector theta from the preliminary parameters of the current period₁(k) And calculating the estimated parameter vector theta (k) of the current period by using the estimated parameter vector theta (k-1) of the previous period, wherein theta (k) is F_θ1θ₁(k)+(1-F_θ1) Theta (k-1) wherein F_θ1Is a filter coefficient, 0<F_θ1Less than or equal to 1; determining the estimated time-varying parameter of the current period according to the estimated parameter vector theta (k) of the current periodWherein, ${\mathrm{\&theta;}}^T\left(k\right)={[\widehat{\mathrm{\&alpha;}}\left(k\right),{\widehat{\mathrm{\&beta;}}}_0\left(k\right)]}^T;$

judging the estimated time-varying parameter of the current periodWhether or not to satisfy $\widehat{\mathrm{\&alpha;}}\left(k\right)\&Element;\left[\begin{array}{cc}\underset{\&OverBar;}{\mathrm{\&alpha;}}& 0.99\end{array}\right],$ αIs the minimum value of the estimated time-varying parameter, if satisfied, the estimated time-varying parameter of the current period is retainedIf it is not $\widehat{\mathrm{\&alpha;}}\left(k\right)>0.99,$ Then order $\widehat{\mathrm{\&alpha;}}\left(k\right)=0.99,$ If it is not $\widehat{\mathrm{\&alpha;}}\left(k\right)\&le;\underset{\&OverBar;}{\mathrm{\&alpha;}},$ Then order $\widehat{\mathrm{\&alpha;}}\left(k\right)=\underset{\&OverBar;}{\mathrm{\&alpha;}};$ The estimated time-varying parameter of the current period is judged by the same methodWhether or not to satisfy $\widehat{\mathrm{\&beta;}}\left(k\right)\&Element;\left[\begin{array}{cc}0.003& 1.00\end{array}\right];$

Estimated parameters according to the current cycleAndlinear feedback control is performed to obtain a controlled variable u (k) in the current cycle, u (k) ═ L α (k) y (k)/(β)₀(k) + λ), L, λ are gain adjustment parameters, 0, respectively<L≤1，λ≥0。

The method is used for the jump-reentry lift control of the reentry vehicle.

Minimum of estimated time-varying parametersαThe value range is as follows: 0.01<α≤0.4。

αTake 0.3.

And the control quantity u (k) is subjected to output conversion to obtain a control quantity for feedback, and the control quantity for feedback is applied to a controlled object.

The control quantity u (k) is subjected to integration and output transformation to obtain a lift force control quantity for feedback, and the control quantity for feedback is applied to a controlled object; the formula for the integral is: u. of₁(k)＝u₁(k-1) + u (k), wherein u₁(k) Is the integrated control quantity of the current period, u₁And (k-1) is the control quantity after integration of the previous period.

The output conversion amount y (k) is determined by the following method: and calculating the error between the output of the controlled object and the reference output, and then performing input transformation on the error to obtain an output transformation quantity y (k).

Compared with the prior art, the invention has the advantages that:

(1) the invention provides a first-order variable coefficient feature model for the first time, wherein the first-order feature model has few parameters, and the first-order feature model has only 2 parameters compared with 3 parameters of a second-order feature model.

(2) The dynamic gain calculated by the parameter estimation value has high tracking speed and strong adaptability. Compared with a second-order characteristic model and a first-order characteristic model, the dynamic gain tracking speed calculated by the parameter estimation value is high and the adaptability is strong because the parameter sum limitation does not exist.

(3) The parameter range is large and easy to determine. Compared with the parameter range of the second-order characteristic model, the parameter range of the first-order characteristic model is large, and the dynamic gain variation range calculated by the method is also large.

(4) The method is already used in the actual flight of the jump reentry of the reentry aircraft, and the high-precision control effect is achieved.

Drawings

FIG. 1 is a block diagram of an incremental first-order feature model and its full-coefficient adaptive control method;

FIG. 2 is a block diagram of a full-scale first-order feature model and its full-coefficient adaptive control method;

FIG. 3 is a graph of height (m) versus time(s) for an example;

FIG. 4 is a plot of velocity (m/s) versus time(s) of the reflector of an embodiment relative to the earth's surface;

FIG. 5 is an axial apparent velocity increment VXP (m/s) versus time(s) plot for an embodiment;

FIG. 6 is an Nx-time(s) curve of an axial overload of an embodiment.

Detailed Description

The conventional full-coefficient adaptive control based on the feature model is based on the feature model of more than or equal to the second order, but the conventional full-coefficient adaptive control based on the feature model is only applied to the second order feature model. The full-coefficient self-adaptive control based on the first-order feature model provided by the invention provides a lower-order first-order feature model only with the lower order, and the effectiveness of the method is shown for the mathematical simulation and the actual flight application of certain type of jump reentry. The full-coefficient adaptive control based on the first-order feature model is not available in the field of intelligent adaptive control in the past, is innovative and developed in the field of intelligent adaptive control, and has great significance for the development of the intelligent adaptive control. Since the first-order feature model is applied to the reentry aircraft in many design steps compared with the first-order feature model applied to other fields, the specific implementation steps are described by taking the first-order feature model as an example, and other applications can be referred to or reduced for use.

(1) Input and output of definite controlled object and input and output of controller

The input of the controlled object is recorded as u_allThe output is r; the required reference output is r₀The error of the output from the reference output is y₁＝r-r₀(ii) a For y₁The error result after input transformation is y, and the output u is output after the controller based on the first-order characteristic model.

If the incremental controller is selected according to the characteristics of the controlled object(see figure 1), u is the increment of the control quantity, and the control quantity u is obtained by integration₁U obtained by output conversion₂Is a feedback control amount;

if a full-scale controller (see FIG. 2) is selected according to the characteristics of the controlled object, u is the controlled variable, and u is obtained by output conversion₂Is a feedback control amount;

feedback control quantity u₂And a reference input u₀The sum is the input u of the controlled object_allIt is the total control quantity of the controlled object.

Here, the reference input, the reference output, the input transformation and the output transformation are determined off-line in the task preparation process. For an incremental controller, the integrator is invariant and does not fit within the adaptive controller. Therefore, the relation between y and u is the real-time algorithm of the adaptive controller.

The invention proposes for the first time to represent the relationship between y and u with a first order feature model,

the first-order feature model is a first-order coefficient-of-variation difference equation expressed as follows:

y(k+1)＝α(k)y(k)+β₀(k)u(k)

wherein y (k) is the output quantity of the current period of the controlled object, u (k) is the control quantity of the current period, y (k +1) is the output quantity of the next period of the controlled object, y (k) and y (k +1) are obtained by measuring values or transforming the measuring values, α (k) and β₀(k) Time-varying parameters of the current period of the first-order feature model;

the process of the full-coefficient self-adaptive control method based on the first-order feature model in each period is as follows:

defining a regression vector phi^T(k-1)＝[y(k-1),u(k-1)]^TPhi (k-1) is the regression vector of the previous cycle;

defining estimated parameter vectorsθ (k) is the estimated parameter vector of the period;

calculating a preliminary parameter estimation vector theta of the current period according to the following formula₁(k)，

Wherein λ₁Is a gain factor, λ₂To remove the zero protection factor, 0<λ₁<1,λ₂>0。

θ(k)＝F_θ1θ₁(k)+(1-F_θ1)θ(k-1)，

Wherein F_θ1Is a filter coefficient, 0<F_θ1≤1。

Determining the estimated time-varying parameter of the current period according to the estimated parameter vector theta (k) of the current period Wherein, ${\mathrm{\&theta;}}^T\left(k\right)={[\widehat{\mathrm{\&alpha;}}\left(k\right),{\widehat{\mathrm{\&beta;}}}_0\left(k\right)]}^T;$

judging the estimated time-varying parameter of the current periodWhether or not to satisfy $\widehat{\mathrm{\&alpha;}}\left(k\right)\&Element;\left[\begin{array}{cc}\underset{\&OverBar;}{\mathrm{\&alpha;}}& 0.99\end{array}\right],$ αIs the minimum value of the estimated time-varying parameter, if satisfied, the estimated time-varying parameter of the current period is retainedIf it is not $\widehat{\mathrm{\&alpha;}}\left(k\right)>0.99,$ Then order $\widehat{\mathrm{\&alpha;}}\left(k\right)=0.99,$ If it is not $\widehat{\mathrm{\&alpha;}}\left(k\right)\&le;\underset{\&OverBar;}{\mathrm{\&alpha;}},$ Then order $\widehat{\mathrm{\&alpha;}}\left(k\right)=\underset{\&OverBar;}{\mathrm{\&alpha;}};$ Judging the estimated time-varying parameter of the current periodWhether or not to satisfy $\widehat{\mathrm{\&beta;}}\left(k\right)\&Element;\left[\begin{array}{cc}0.003& 1.00\end{array}\right];$ If it is not ${\widehat{\mathrm{\&beta;}}}_0\left(k\right)>1.00,$ Then order ${\widehat{\mathrm{\&beta;}}}_0\left(k\right)=1.00;$ If it is notThen orderWherein 0.01<αLess than or equal to 0.4, and is determined according to simulation research on an actual object.

Estimated parameters according to the current cycleAndlinear feedback control is performed to obtain a controlled variable u (k) in the current cycle, u (k) ═ L α (k) y (k)/(β)₀(k) + λ), L, λ are gain adjustment parameters, 0, respectively<L≤1，λ≥0。

In the first period, the initial values of the parameters are α (k) ═ α (k-1) ═ 0.9, and β (k) ═ β (k-1) ═ 0.1; u (k-1) ═ 0.

Examples

Aiming at the jump type reentry lift control of the reentry aircraft, a full-coefficient adaptive controller based on a first-order characteristic model is designed according to a block diagram shown in figure 1, and the reference input is a nominal roll angle u₂Is a lift feedback control quantity; input transformationOutput conversion toA takes the value 36 and D (tcf) is a known dynamic gain function.

Multiple iterations through design and mathematical simulation to determineα＝0.3、λ₁＝1、λ₂＝4、F_θ10.1, 0.012 and 1. The actual flight has good effect, the expected aim is achieved, the parachute opening point error is 680m, and the control precision is at the international leading level.

Fig. 3-6 show the altitude curve, the speed curve, the axial apparent speed increment curve, and the axial overload curve, respectively. 3-6, the returner realizes perfect jump reentry, the primary reentry section attenuates the speed from 10.674km/s to 7.2km/s within the first cosmic speed, the secondary reentry section reduces the speed from 7.2km/s to 0.143km/s of the parachute opening point, and the speed attenuation and overload process of the primary reentry section, the leap-out section and the secondary reentry section of the whole process are clearly distinguished.

Claims (7)

1. A full-coefficient self-adaptive control method based on a first-order feature model is characterized in that the first-order feature model is a first-order variable coefficient difference equation and is expressed as follows:

y(k+1)＝α(k)y(k)+β₀(k)u(k)

wherein y (k) is the output transformation quantity of the current period of the controlled object, y (k +1) is the output transformation quantity of the next period of the controlled object, u (k) is the control quantity of the current period, α (k), β₀(k) Time-varying parameters of the current period of the first-order feature model;

the full-coefficient self-adaptive control method based on the first-order feature model in each period comprises the following steps:

according to the formula ${\mathrm{\&theta;}}_1\left(k\right)=\mathrm{\&theta;}(k-1)+\frac{{\mathrm{\&lambda;}}_1\mathrm{\&phi;}(k-1)}{{\mathrm{\&phi;}}^T(k-1)\mathrm{\&phi;}(k-1)+{\mathrm{\&lambda;}}_2}\&lsqb;y\left(k\right)-{\mathrm{\&phi;}}^T(k-1)\mathrm{\&theta;}(k-1)\&rsqb;$ Calculating a preliminary parameter estimation vector theta for the current cycle₁(k) Wherein λ is₁Is a gain factor, λ₂To remove the zero protection factor, 0<λ₁<1,λ₂>0; phi (k-1) is the regression vector of the previous cycle, phi^T(k-1)＝[y(k-1),u(k-1)]^T(ii) a Theta (k-1) is the estimated parameter vector of the previous cycle, ${\mathrm{\&theta;}}^T(k-1)={\&lsqb;\widehat{\mathrm{\&alpha;}}(k-1),{\widehat{\mathrm{\&beta;}}}_0(k-1)\&rsqb;}^T;$ estimated time-varying parameters for the previous cycle;

estimating a vector theta from the preliminary parameters of the current period₁(k) And calculating the estimated parameter vector theta (k) of the current period by using the estimated parameter vector theta (k-1) of the previous period, wherein theta (k) is F_θ1θ₁(k)+(1-F_θ1) Theta (k-1) wherein F_θ1Is a filter coefficient, 0<F_θ1Less than or equal to 1; determining the estimated time-varying parameter of the current period according to the estimated parameter vector theta (k) of the current period Wherein, ${\mathrm{\&theta;}}^T\left(k\right)={\&lsqb;\widehat{\mathrm{\&alpha;}}\left(k\right),{\widehat{\mathrm{\&beta;}}}_0\left(k\right)\&rsqb;}^T;$

judging the estimated time-varying parameter of the current control periodWhether or not to satisfy $\widehat{\mathrm{\&alpha;}}\left(k\right)\&Element;\&lsqb;\begin{array}{cc}\underset{\&OverBar;}{\mathrm{\&alpha;}}& 0.99\end{array}\&rsqb;,$ αIs the minimum value of the estimated time-varying parameter, if satisfied, the estimated time-varying parameter of the current period is retainedIf it is not $\widehat{\mathrm{\&alpha;}}\left(k\right)>0.99,$ Then order $\widehat{\mathrm{\&alpha;}}\left(k\right)=0.99,$ If it is not $\widehat{\mathrm{\&alpha;}}\left(k\right)<\underset{\&OverBar;}{\mathrm{\&alpha;}},$ Then order $\widehat{\mathrm{\&alpha;}}\left(k\right)=\underset{\&OverBar;}{\mathrm{\&alpha;}},$ Judging the estimated time-varying parameter of the current periodWhether or not to satisfy ${\widehat{\mathrm{\&beta;}}}_0\left(k\right)\&Element;\&lsqb;\begin{array}{cc}0.003& 1.00\end{array}\&rsqb;,$ If it is not ${\widehat{\mathrm{\&beta;}}}_0\left(k\right)>1.00,$ Then order ${\widehat{\mathrm{\&beta;}}}_0\left(k\right)=1.00;$ If it is not ${\widehat{\mathrm{\&beta;}}}_0\left(k\right)<0.003,$ Then order ${\widehat{\mathrm{\&beta;}}}_0\left(k\right)=0.003;$

Estimated parameters according to the current control periodAndlinear feedback control is performed to obtain a controlled variable u (k) in the current cycle, u (k) ═ L α (k) y (k)/(β)₀(k) + λ), L, λ are gain adjustment parameters, 0, respectively<L≤1，λ≥0。

2. The full-coefficient adaptive control method based on the first-order feature model is used for the jump-type reentry lift control of the reentry vehicle according to claim 1.

3. The full-coefficient adaptive control method based on the first-order feature model as claimed in claim 1, wherein the minimum value of the estimated time-varying parameterαThe value range is as follows: 0.01 < (R) >α≤0.4。

4. The full-coefficient adaptive control method based on the first-order feature model according to claim 1,αtake 0.3.

5. The full-coefficient adaptive control method based on the first-order feature model of claim 1, wherein the control quantity u (k) is subjected to output transformation to obtain a control quantity for feedback, and the control quantity for feedback is applied to a controlled object.

6. The full-coefficient adaptive control method based on the first-order feature model is characterized in that the control quantity u (k) is subjected to integration and output transformation to obtain a lift control quantity for feedback, and the lift control quantity for feedback is applied to a controlled object; the formula for the integral is: u. of₁(k)＝u₁(k-1) + u (k), wherein u₁(k) Is the integrated control quantity of the current period, u₁And (k-1) is the control quantity after integration of the previous period.

7. The full-coefficient adaptive control method based on the first-order feature model of claim 1, wherein the determination method of the output transformation quantity y (k) is as follows: and calculating the error between the output of the controlled object and the reference output, and then performing input transformation on the error to obtain an output transformation quantity y (k).