CN105045092A - PI^lambdaD^mu controller parameter optimization method for unmanned intelligent automobile - Google Patents

Abstract

The invention discloses a PI^lambdaD^mu controller parameter optimization method for an unmanned intelligent automobile. The PI^lambdaD^mu controller parameter optimization method includes steps: firstly, obtaining a parameter stability domain of a system according to a D partition principle, then designing a strategy for obtaining a fractional order PI^lambdaD^mu controller parameter solution set under constraint of the region pole index, obtaining the controller parameter solution set under the constraint of the region pole index, and synthesizing the parameter stability domain and the controller parameter solution set so as to obtain a fractional order PI^lambdaD^mu controller parameter solution set which meets the region pole index. The fractional order PI^lambdaD^mu controller parameter optimization method based on the region pole index assigns a system pole into a certain region of a left half complex plane, and thereby enables a system to obtain expected transient response performance.

Description

PI of unmanned intelligent automobileλDμParameter optimization method of controller

The application requires 2014-08-15 as filed date, 201410403638.X as filed name, and is fractional order PI based on regional pole index^λD^μThe parameters of the controller optimize the priority of the method.

Technical Field

The invention relates to a fractional order PI^λD^μA parameter optimization method of a controller, in particular to a PI of an unmanned intelligent automobile^λD^μA parameter optimization method for a controller.

Background

In the industrial production process, the temperature of a production device,Process variables such as pressure, flow, liquid level, etc. are often required to be maintained at a certain value or to be changed according to a certain rule so as to meet the requirements of the production process. The PID controller adjusts the deviation of the whole control system according to the PID control principle, so that the actual value of the controlled variable is consistent with the preset value required by the process. Different control laws are suitable for different production processes, and the corresponding control laws must be reasonably selected, otherwise the PID controller cannot achieve the expected control effect. A PID controller (proportionality integration differentiation controller) is composed of a proportional unit P, an integral unit I, and a differentiation unit D. By K_p，K_iAnd K_dSetting three parameters. PID controllers are primarily suitable for systems where the basic linearity and dynamics do not change over time.

A PID controller is a feedback loop component that is common in industrial control applications. The controller compares the collected data to a reference value and then uses the difference to calculate a new input value that is intended to allow the data of the system to reach or remain at the reference value. Different from other simple control operations, the PID controller can adjust the input value according to historical data and the occurrence rate of differences, so that the system is more accurate and more stable. It can be shown mathematically that a PID feedback loop can maintain the stability of the system in the event that other control methods result in a system with a stability error or process iteration.

Fractional order PI^λD^μThe controller is a novel controller, and compared with the traditional PID controller, the controller has two more adjustable parameters, namely differential order lambda and integral order mu, and fractional order PI^λD^μThe controller can achieve better control effect than the conventional PID controller. In addition, fractional order PI^λD^μThe method also has the advantages of strong robustness, easy operation and realization, fractional order PI^λD^μThe advantages of the controller have been widely recognized. Albeit fractional order PI^λD^μThe controller makes the parameter adjustment of the controller more flexible, the parameter more optimized and the effectThe result is better, but the design of the controller and the difficulty of parameter setting are increased.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides a PI of an unmanned intelligent automobile^λD^μMethod for optimizing parameters of a controller, wherein the fractional order PI^λD^μThe controller is used in a control and stabilization system, and comprises:

s101: transfer function according to speed control process of unmanned intelligent automobileAnd fractional order PI^λD^μController transfer functionEstablishing unmanned intelligent automobile closed-loop systemAnd establishing a fractional order PI according to the stability of the unmanned intelligent automobile closed-loop system^λD^μController parameter space (k)_p,k_i,k_dλ, μ), the transfer function of the vehicle speed control process of the unmanned intelligent vehicle takes the speed v(s) of the unmanned intelligent vehicle as a controlled variable, takes the rotating speed RPM(s) of the direct current motor as a manipulated variable, and v(s) ═ G(s) RPM(s);

s102: performing fractional order PI according to D division principle^λD^μController parameter space (k)_p,k_i,k_dλ, μ) to obtain (k)_p,k_i) The parameter stability domain of (1);

s103: according to a preset regional pole index, carrying out fractional order PI^λD^μController parameter space (k)_p,k_i,k_dLambda, mu) to obtain the fingers satisfying the poles of the regionTarget first parameter solution set Q_θ；

S104: according to the parameter stable domain phi and the first parameter solution set Q_θThe intersection of the two sets of the partial order PI meets the regional pole index^λD^μA second parameter solution set of the controller, the second parameter solution set being a fractional order PI satisfying a speed control optimization of the unmanned smart car^λD^μA controller parameter solution set.

Further, the step S104 is followed by a step S105: optionally, a parameter (k) is solution-set from the second parameter_p,k_i) Substituting into the fractional order PI^λD^μAnd a controller.

Further, the regional pole index constraint range is an angular region D (α, θ). Wherein α is a decay rate (or a decay coefficient), θ is a regional pole index angle, and a region determined by α and θ is D (α, θ) to represent the regional pole index.

Further, the first parameter solution set is: a system pole is arranged in an area D (alpha, theta) restricted by an area pole index, and the value range [ omega ] of the preset frequency omega_min,ω_max]And obtaining a first parameter solution set meeting the regional pole index.

Further, (K) in the step 102 is obtained from a characteristic equation 1+ G (j ω) C (j ω) of the control system being 0_P,K_i) The parameter stability domain of (2).

Compared with the prior art, the invention has the beneficial effects that:

the invention discloses a method for designing a fractional controller under the constraint of regional pole indexes, which is used for allocating a system pole to a certain specific region of a left half complex plane, so that the system can obtain expected transient response performance. The invention designs a fractional order PI for a certain control system^λD^μThe controller can be used for an industrial control system, and simultaneously, the controller design meets the regional pole index configuration and designs the fractional order PI^λD^μWhen the controller is used, the pole of the closed-loop system is arranged in a certain specific area of the left half complex plane, the dynamic response performance of the system is ensured, and the fractional order PI is effectively solved^λD^μThe controller meets the design problem of regional pole requirement to make fractional order PI^λD^μThe controller performance is more excellent.

Drawings

Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:

FIG. 1 is a block diagram of a control system according to the present invention;

FIG. 2 is a geometric representation of a regional pole index;

FIG. 3 shows PI at λ change^λD^μA controller stability domain;

FIG. 4 is PI^0.3D^0.8A controller stability domain;

FIG. 5 is a fractional order PI satisfying regional pole criteria^λD^μA controller parameter solution set;

FIG. 6 is a diagram of an integer order PI satisfying a regional pole index^λD^μSolving the parameters of the controller;

FIG. 7 is a fractional order PI based on regional pole index^λD^μA flow chart of a parameter optimization method of the controller;

FIG. 8 is a graph of the control results of the controller of the present invention for an unmanned intelligent vehicle with three sets of parameters.

Detailed Description

The present invention will be described in detail below by way of specific embodiments with reference to the accompanying drawings. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the spirit of the invention. All falling within the scope of the present invention.

Specifically, the structure of the control system to which the present invention is directed is shown in fig. 1. The system is a unit negative feedback system, in fig. 1, r (t) is system input quantity, y (t) is system output quantity, e (t) is deviation between the input quantity and the output quantity, and a proper fractional order PI is designed for a certain unmanned intelligent automobile G(s)^λD^μA controller c(s) operable to cause the system output to track the value of the system input.

Step S101 shown in fig. 7: according to the transfer function and fractional order PI of the speed control process of the unmanned intelligent automobile^λD^μThe method comprises the steps of establishing a closed loop system of the unmanned intelligent automobile by using a transfer function of a controller, and establishing a fractional order PI according to the stability of the closed loop system of the unmanned intelligent automobile^λD^μController parameter space (k)_p,k_i,k_dLambda and mu) of the unmanned intelligent automobile, wherein the transfer function of the speed control process of the unmanned intelligent automobile takes the speed of the unmanned intelligent automobile as a controlled variable and takes the rotating speed of the direct current motor as a manipulated variable.

<math> <mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>D</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>b</mi> <mi>n</mi> </msub> <msup> <mi>s</mi> <msub> <mi>&beta;</mi> <mi>n</mi> </msub> </msup> <mo>+</mo> <msub> <mi>b</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msup> <mi>s</mi> <msub> <mi>&beta;</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msup> <mo>+</mo> <mn>...</mn> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <msup> <mi>s</mi> <msub> <mi>&beta;</mi> <mn>1</mn> </msub> </msup> <mo>+</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <msup> <mi>s</mi> <msub> <mi>&beta;</mi> <mn>0</mn> </msub> </msup> </mrow> <mrow> <msub> <mi>a</mi> <mi>n</mi> </msub> <msup> <mi>s</mi> <msub> <mi>a</mi> <mi>n</mi> </msub> </msup> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msup> <mi>s</mi> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msup> <mo>+</mo> <mn>...</mn> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <mi>s</mi> <msub> <mi>a</mi> <mn>1</mn> </msub> </msup> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msup> <mi>s</mi> <msub> <mi>a</mi> <mn>0</mn> </msub> </msup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>r</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>b</mi> <mi>r</mi> </msub> <msup> <mi>s</mi> <msub> <mi>&beta;</mi> <mi>r</mi> </msub> </msup> </mrow> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>r</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>a</mi> <mi>r</mi> </msub> <msup> <mi>s</mi> <msub> <mi>a</mi> <mi>r</mi> </msub> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>

G(s) is a transfer function of the unmanned smart car, wherein_n，…，β₁，β₀；α_n，…，α₁，α₀；a_n，…，a₁，a₀；b_n，…，b₁，b₀Is a constant coefficient related to the structure and parameters of the unmanned intelligent automobile system. Wherein beta is_n＞…＞β₁＞β₀≥0,α_n＞…＞α₁＞α₀≥0.

<math> <mrow> <mi>C</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>+</mo> <mfrac> <msub> <mi>k</mi> <mi>i</mi> </msub> <msup> <mi>s</mi> <mi>&lambda;</mi> </msup> </mfrac> <mo>+</mo> <msub> <mi>k</mi> <mi>d</mi> </msub> <msup> <mi>s</mi> <mi>&mu;</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

Where 0 < lambda, mu < 2, C(s) represents a fractional order PI^λD^μA controller transfer function, wherein: k is a radical of_pRepresenting fractional order PI^λD^μProportional coefficient of controller, k_iRepresenting fractional order PI^λD^μIntegral coefficient of controller, k_dRepresenting fractional order PI^λD^μThe derivative coefficient of the controller.

The transfer function of the closed loop system of the unmanned intelligent automobile is as follows:

<math> <mrow> <mi>&Phi;</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>C</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>C</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>

substituting the formula (1) and the formula (2) into the formula (3) to obtain a characteristic polynomial of the unmanned intelligent automobile closed-loop system:

Ψ(s)＝s^λD(s)+(k_ps^λ+k_i+k_ds^μ+λ)N(s)(4)

for a set of parameters (k)_p,k_i,k_dλ, μ), the criterion is: if it makes the root of the system characteristic equation Ψ(s) ═ 0 have complex real parts, then the subsystem is input-output stable.

For step S102: performing fractional order PI according to D division principle^λD^μController parameter space (k)_p,k_i,k_dLambda, mu) to obtain a parameter stable domain;

by the principle of D division, (k) can be divided_p,k_i,k_dλ, μ) of a parameter space_ΦDividing the system into a region Z with a Real Root Boundary (RRB), a Complex Root Boundary (CRB) and an Infinite Root Boundary (IRB) as boundaries, wherein the region Z is a stable region, coordinates of all points in the stable region correspond to points of a parameter set which can stabilize the system, and the boundary of the D division is defined as follows:

<math> <mrow> <mo>&part;</mo> <mi>D</mi> <mo>&equiv;</mo> <mo>&part;</mo> <msub> <mi>D</mi> <mn>0</mn> </msub> <mo>&cup;</mo> <mo>&part;</mo> <msub> <mi>D</mi> <mi>&infin;</mi> </msub> <mo>&cup;</mo> <mo>&part;</mo> <msub> <mi>D</mi> <mrow> <mi>j</mi> <mi>w</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <mo>&part;</mo> <msub> <mi>D</mi> <mn>0</mn> </msub> <mo>&equiv;</mo> <mrow> <mo>{</mo> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>,</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>,</mo> <mi>&lambda;</mi> <mo>,</mo> <mi>&mu;</mi> </mrow> <mo>)</mo> </mrow> <mo>&Element;</mo> <mi>&Phi;</mi> <mo>|</mo> <mi>&Psi;</mi> <mrow> <mo>(</mo> <mrow> <mi>j</mi> <mi>&omega;</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>&omega;</mi> <mo>=</mo> <mn>0</mn> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&part;</mo> <msub> <mi>D</mi> <mi>&infin;</mi> </msub> <mo>&equiv;</mo> <mrow> <mo>{</mo> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>,</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>,</mo> <mi>&lambda;</mi> <mo>,</mo> <mi>&mu;</mi> </mrow> <mo>)</mo> </mrow> <mo>&Element;</mo> <mi>&Phi;</mi> <mo>|</mo> <mi>&Psi;</mi> <mrow> <mo>(</mo> <mrow> <mi>j</mi> <mi>&omega;</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>&omega;</mi> <mo>=</mo> <mi>&infin;</mi> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&part;</mo> <msub> <mi>D</mi> <mrow> <mi>j</mi> <mi>&omega;</mi> </mrow> </msub> <mo>&equiv;</mo> <mrow> <mo>{</mo> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>,</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>,</mo> <mi>&lambda;</mi> <mo>,</mo> <mi>&mu;</mi> </mrow> <mo>)</mo> </mrow> <mo>&Element;</mo> <mi>&Phi;</mi> <mo>|</mo> <mi>&Psi;</mi> <mrow> <mo>(</mo> <mrow> <mi>j</mi> <mi>&omega;</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mo>&ForAll;</mo> <mi>&omega;</mi> <mo>&Element;</mo> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <mi>&infin;</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein,the boundary of the real root is represented,which represents the boundary of an infinite root,representing a multi-root boundary.

Substituting s ═ j ω into the characteristic polynomial (4), the characteristic equation can be expressed as:

Ψ(jω)＝(jω)^λD(jω)+(k_d(jω)^λ+μ+k_p(jω)^λ+k_i)N(jω)(7)

fractional order PI for a given controlled system according to the D-segmentation principle^λD^μParameter space (k) of controller_p,k_i,k_dλ, μ) is divided into several regions by a possible plane (a), a possible plane (b) and a curved surface (c).

Wherein the possible plane (a) is a Real Root Boundary (RRB)

According to the first equation of equation (6), the real root boundary can be obtained as: k is a radical of_i＝0。

The possible plane (b) is the Infinite Root Boundary (IRB):

the infinite root boundary is represented as:

<math> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>n</mi> </msub> <mo>&lt;</mo> <msub> <mi>&beta;</mi> <mi>n</mi> </msub> <mo>+</mo> <mi>&mu;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&PlusMinus;</mo> <msub> <mi>a</mi> <mi>n</mi> </msub> <mo>/</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>&beta;</mi> <mi>n</mi> </msub> <mo>+</mo> <mi>&mu;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>n</mi> <mi>o</mi> <mi>n</mi> <mi>e</mi> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>n</mi> </msub> <mo>&gt;</mo> <msub> <mi>&beta;</mi> <mi>n</mi> </msub> <mo>+</mo> <mi>&mu;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein: k is a radical of_dIs the differential coefficient of the fractional order PID controller, and u is the differential order of the fractional order PID controller.

The curved surface (c) is a Complex Root Boundary (CRB) according to the formulaAnd Euler formula e^jxSubstituting cosx + jsinx into the characteristic equation (7) can obtain a fractional order PI^λD^μThe parameters to be set of the controller are as follows:

<math> <mrow> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mi>A</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>I</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>B</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> </math>

k_i＝C(ω)+D(ω)-R(ω)(10)

wherein:

<math> <mrow> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <mi>A</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mi>d</mi> </msub> <msup> <mi>&omega;</mi> <mrow> <mi>&lambda;</mi> <mo>+</mo> <mi>&mu;</mi> </mrow> </msup> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> <mo>(</mo> <mrow> <mi>&lambda;</mi> <mo>+</mo> <mi>&mu;</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>B</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>&omega;</mi> <mi>&lambda;</mi> </msup> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> <mi>&lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>C</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mi>d</mi> </msub> <msup> <mi>&omega;</mi> <mrow> <mi>&lambda;</mi> <mo>+</mo> <mi>&mu;</mi> </mrow> </msup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> <mo>(</mo> <mrow> <mi>&lambda;</mi> <mo>+</mo> <mi>&mu;</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>D</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mi>d</mi> </msub> <msup> <mi>&omega;</mi> <mrow> <mi>&lambda;</mi> <mo>+</mo> <mi>&mu;</mi> </mrow> </msup> <mi>sin</mi> <mo>(</mo> <mrow> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mrow> <mi>&lambda;</mi> <mo>+</mo> <mi>&mu;</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>+</mo> <mi>I</mi> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> <mo>)</mo> </mrow> <mfrac> <mn>1</mn> <mrow> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> <mi>&lambda;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>Re</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mi>&omega;</mi> <mi>&lambda;</mi> </msup> <mrow> <mo>(</mo> <mi>cos</mi> <mo>(</mo> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> <mo>)</mo> <mi>&lambda;</mi> <mo>+</mo> <mi>sin</mi> <mo>(</mo> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> <mo>)</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> <mi>D</mi> <mrow> <mo>(</mo> <mi>j</mi> <mi>&omega;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mi>j</mi> <mi>&omega;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>I</mi> <mi>m</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mi>&omega;</mi> <mi>&lambda;</mi> </msup> <mrow> <mo>(</mo> <mi>cos</mi> <mo>(</mo> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> <mo>)</mo> <mi>&lambda;</mi> <mo>+</mo> <mi>sin</mi> <mo>(</mo> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> <mo>)</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> <mi>D</mi> <mrow> <mo>(</mo> <mi>j</mi> <mi>&omega;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mi>j</mi> <mi>&omega;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> </math>

by the above formulas (9) and (10),given a value of one (k) _d Value of λ, μ)When the frequency ω changes from 0 to ∞ may be at (k)_p,k_i) The plane gets a Complex Root Boundary (CRB).

In summary, the two curved surfaces are divided by the possible plane (a), the possible plane (b) and the curved surface (c) andgiven a value of one (k) _d λ, μ) of Value ofObtaining (k)_p,k_i) The parameter stability domain of (2).

For step S103: according to a predetermined regional poleIndex for the fractional order PI^λD^μController parameter space (k)_p,k_i,k_dλ, μ) to obtain a first parameter solution set satisfying the regional pole index.

The predetermined regional pole index of the present invention is an angular region D (α, θ), as shown in fig. 2. The regional pole index refers to a constraint range that constrains the system poles to a particular region of the complex plane.

As shown in fig. 2, the poles of the system are arranged in the pole indexes D (α, θ). The pole index constraint region used by the present invention is an angular region, i.e., D (0, α).

Combining the controlled system G(s) and the pole region index constraint range D (0, theta) as shown in FIG. 1, calculating the fractional order PI again^λD^μParameter space (k) of controller_p,k_i,k_dλ, μ) of the parameter space (k)_p,k_i,k_dλ, μ) is divided into several areas by a possible plane (a), a possible plane (b) and a curved surface (c).

In this case, the closed loop system characteristic equation is:

Δ(s,θ)＝s^λe^jλθD(se^jθ)+(k_ds^λ+μe^jθ(λ+μ)+k_ps^λe^jλ+k_i)N(se^jθ)(12)

wherein: theta is the angle value of the index of the regional pole, k_pRepresenting fractional order PI^λD^μProportional coefficient of controller, k_iRepresenting fractional order PI^λD^μIntegral coefficient of controller, k_dRepresenting fractional order PI^λD^μThe derivative coefficient of the controller.

The following can be obtained: possible planes (a): if a₀Not equal to 0, then k_i0; otherwise, the plane does not exist.

Possible planes (b): if m is n-1, then k_d＝-1/a_m(ii) a Otherwise, the plane does not exist.

Curved surface (c): fractional order PI meeting regional pole index^λD^μThe parameters to be set of the controller are as follows:

<math> <mrow> <mrow> <mo>{</mo> <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <msub> <mi>A</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>I</mi> <mrow> <mo>(</mo> <mrow> <mi>&omega;</mi> <mo>,</mo> <mi>&theta;</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>A</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>k</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>A</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <msub> <mi>B</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>I</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <msub> <mi>B</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>A</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> <msub> <mi>B</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>R</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> <mi>&theta;</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>0</mn> <mo>,</mo> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> <mo>&rsqb;</mo> <mo>,</mo> <mi>&omega;</mi> <mo>&Element;</mo> <mi>&Lambda;</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>&omega;</mi> <mo>,</mo> <mi>&theta;</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>Re</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mi>j</mi> <mi>&lambda;</mi> </msup> <msup> <mi>&omega;</mi> <mi>&lambda;</mi> </msup> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mi>&lambda;</mi> <mi>&theta;</mi> </mrow> </msup> <mi>D</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>j&omega;e</mi> <mrow> <mi>j</mi> <mi>&theta;</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>j&omega;e</mi> <mrow> <mi>j</mi> <mi>&theta;</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <mrow> <mi>&omega;</mi> <mo>,</mo> <mi>&theta;</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>Im</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mi>j</mi> <mi>&lambda;</mi> </msup> <msup> <mi>&omega;</mi> <mi>&lambda;</mi> </msup> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mi>&lambda;</mi> <mi>&theta;</mi> </mrow> </msup> <mi>D</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>j&omega;e</mi> <mrow> <mi>j</mi> <mi>&theta;</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>j&omega;e</mi> <mrow> <mi>j</mi> <mi>&theta;</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&Lambda;</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> <mo>,</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> <mo>&cup;</mo> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <mi>&infin;</mi> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mo>&ForAll;</mo> <mi>&omega;</mi> <mo>&Element;</mo> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> <mo>,</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> <mo>&cup;</mo> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <mi>&infin;</mi> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mi>N</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>j&omega;e</mi> <mrow> <mi>j</mi> <mi>&theta;</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>&NotEqual;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <msub> <mi>&Lambda;</mi> <mo>+</mo> </msub> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>&ForAll;</mo> <mi>&omega;</mi> <mo>&Element;</mo> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> <mo>,</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> <mo>&cup;</mo> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <mi>&infin;</mi> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mo>&Exists;</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>></mo> <mn>0</mn> <mo>,</mo> <mi>N</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>j&omega;</mi> <mi>i</mi> </msub> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mi>&theta;</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <msub> <mi>&Lambda;</mi> <mo>-</mo> </msub> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>&ForAll;</mo> <mi>&omega;</mi> <mo>&Element;</mo> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> <mo>,</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> <mo>&cup;</mo> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <mi>&infin;</mi> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mo>&Exists;</mo> <msub> <mi>&omega;</mi> <mi>p</mi> </msub> <mo>></mo> <mn>0</mn> <mo>,</mo> <mi>N</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>j&omega;</mi> <mi>p</mi> </msub> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mi>&theta;</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <msub> <mi>&Lambda;</mi> <mo>+</mo> </msub> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>&cup;</mo> <mover> <msub> <mi>&Lambda;</mi> <mo>-</mo> </msub> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>&ForAll;</mo> <mi>&omega;</mi> <mo>&Element;</mo> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> <mo>,</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> <mo>&cup;</mo> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <mi>&infin;</mi> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mo>&Exists;</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>></mo> <mn>0</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>j&omega;</mi> <mi>i</mi> </msub> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mi>&theta;</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>=</mo> <mn>0</mn> <mo>;</mo> <mo>&Exists;</mo> <msub> <mi>&omega;</mi> <mi>p</mi> </msub> <mo>&lt;</mo> <mn>0</mn> <mo>,</mo> <mi>N</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>j&omega;</mi> <mi>i</mi> </msub> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mi>&theta;</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <msub> <mi>&Lambda;</mi> <mo>+</mo> </msub> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <msub> <mi>&omega;</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>&cup;</mo> <mrow> <mo>&lsqb;</mo> <mrow> <munderover> <mrow> <mi></mi> <mo>&cup;</mo> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <mo>(</mo> <mrow> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&omega;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&rsqb;</mo> </mrow> <mo>&cup;</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>&omega;</mi> <mi>k</mi> </msub> <mo>,</mo> <mi>&infin;</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <msub> <mi>&Lambda;</mi> <mo>-</mo> </msub> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <msub> <mi>&omega;</mi> <mi>l</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>&cup;</mo> <mrow> <mo>&lsqb;</mo> <mrow> <munderover> <mrow> <mi></mi> <mo>&cup;</mo> </mrow> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>l</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <mo>(</mo> <mrow> <msub> <mi>&omega;</mi> <mrow> <mi>l</mi> <mo>+</mo> <mn>1</mn> <mo>-</mo> <mi>p</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&omega;</mi> <mrow> <mi>l</mi> <mo>-</mo> <mi>p</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&rsqb;</mo> </mrow> <mo>&cup;</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>&omega;</mi> <mn>1</mn> </msub> <mo>,</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>k</mi> <mo>,</mo> <mn>0</mn> <mo>&lt;</mo> <msub> <mi>&omega;</mi> <mn>1</mn> </msub> <mo>&lt;</mo> <msub> <mi>&omega;</mi> <mn>2</mn> </msub> <mo>&lt;</mo> <mn>...</mn> <mo>&lt;</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>&lt;</mo> <mn>...</mn> <mo>&lt;</mo> <msub> <mi>&omega;</mi> <mi>k</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>..</mn> <mo>,</mo> <mi>l</mi> <mo>,</mo> <msub> <mi>&omega;</mi> <mi>l</mi> </msub> <mo>&lt;</mo> <mn>...</mn> <mo>&lt;</mo> <msub> <mi>&omega;</mi> <mi>p</mi> </msub> <mo>&lt;</mo> <mn>...</mn> <mo>&lt;</mo> <msub> <mi>&omega;</mi> <mn>2</mn> </msub> <mo>&lt;</mo> <msub> <mi>&omega;</mi> <mn>1</mn> </msub> <mo>&lt;</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow> </math>

where ω represents frequency and θ is the angle value of the pole index of the region.

By the above formula (13), for a given parameter k_dλ, μ, when the frequency ω changes from 0 to ∞, a first parameter solution set Q can be obtained that satisfies the pole index of the region_θ。

Then, as in step S104 in fig. 7: obtaining a fractional order PI meeting the regional pole index according to the intersection of the parameter stable region and the first parameter solution set^λD^μA second parameter solution set of the controller, the second parameter solution set being a fractional order PI satisfying a speed control optimization of the unmanned smart car^λD^μA controller parameter solution set. At this time, the second parameter solution set is the final optimized fractional order PI of the invention^λD^μController parameter set, arbitrarily taking one (k) in second parameter solution set_p,k_i) Can satisfy fractional order PI^λD^μControl requirements of the controller.

The step S104 is followed by a step S105: optionally, a parameter (k) is solution-set from the second parameter_p,k_i) Substituting into the fractional order PI^λD^μAnd a controller.

The unmanned intelligent automobile integrates functions of environmental perception, planning decision, automatic driving and the like, is intensively applied to a plurality of subjects such as automatic control, mode recognition, sensor technology, electricity, computers, machinery and the like, and is a typical high-technology comprehensive body. The key technology of the unmanned intelligent automobile is the control of the speed, namely the tracking of the preset target speed is realized. Compared with the traditional PID controller for controlling the speed of the intelligent automobile, the speed of the intelligent automobile can be controlled more stably by using the method and the device.

Based on the above formula derivation process, the speed of the unmanned intelligent vehicle is used as the controlled variable (v), and the rotation speed of the dc motor is used as the manipulated variable (RPM), and in one embodiment, the transfer function of the speed control process of the unmanned intelligent vehicle is:

$G\left(s\right)=\frac{1}{s^3+s^2+3s+1}---\left(15\right)$

namely:

v(s)＝G(s)RPM(s)(16)

as can be seen from the method described in step S101, the closed loop transfer function is:

<math> <mrow> <mi>&Phi;</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>C</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mi>s</mi> <mn>3</mn> </msup> <mo>+</mo> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>3</mn> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mi>C</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> </math>

the characteristic polynomial of the closed loop system is:

<math> <mrow> <mi>&Psi;</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msup> <mi>s</mi> <mi>&lambda;</mi> </msup> <mrow> <msup> <mi>s</mi> <mn>3</mn> </msup> <mo>+</mo> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>3</mn> <mi>s</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mi>p</mi> </msub> <msup> <mi>s</mi> <mi>&lambda;</mi> </msup> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mi>d</mi> </msub> <msup> <mi>s</mi> <mrow> <mi>&mu;</mi> <mo>+</mo> <mi>&lambda;</mi> </mrow> </msup> </mrow> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow> </math>

fractional order PI^λD^μThe controller parameter space is (k)_p,k_i,k_d,λ,μ)。

Then, according to the method of step S102, a fractional order PI is taken^λD^μThe controller satisfies the area pole constraint index α of 0 and θ of pi/3, i.e., D (0, pi/3).

First, the measured value is mu-K_dThe order λ is a variable with a constant value of 1, and different stable regions are calculated by changing the value of the order λ, and as shown in fig. 4, the stable region is maximum when λ is 0.3.

Then, the K is further determined by_dThe order μ is a variable with a constant value of 1, and different stability domains are obtained by changing the value of the order μ, where μ is 0.8 and the stability domain is maximum.

Finally, the values of the order λ, μ are considered together, when λ is 0.3 and μ is 0_.The maximum stable region is obtained at 8. Thus determining the parameter values: λ 0.3, μ 0.8, K_d＝1_。

Finally, the stable region Φ of the system at this time is determined as shown in fig. 4.

Next, according to the method described in step S103, under the constraint of the regional pole index D (0, pi/3), K is equal to 0.8, 0.3, μ is equal to 0.3 for the given parameter λ_d1. According to the equation (13), when the frequency ω is changed from 0 to ∞, the fractional order PI under the constraint of the regional pole index can be obtained^λD^μController parameter solution set Q_θAs shown in fig. 5.

Finally, according to the method described in step S104, Q_θAnd the parameters represented by the intersection of phi and phi are the finally designed parameter solution set of the fractional order PID controller meeting the regional pole index. And is in Q_θAnd three groups of numbers are randomly selected from the intersection of phi and phi, wherein the first group is as follows: k is a radical of_p＝1.2457,k_i0.1027, the second set of parameters is: k is a radical of_p＝5.2289,k_i1.1512, the third set of parameters is: k is a radical of_p＝7.5845,k_iAt 0.5214, the set speed stabilizes at 60, i.e., the input r (t) is 60. By fractional order PI meeting regional pole index^λD^μThe controller controls the speedThe obtained several degree change curve is shown in fig. 8. As can be seen from the figure, the final speed of the unmanned intelligent automobile can be stabilized at 60, and the controller can meet the requirement.

Aiming at the unmanned intelligent automobile shown in the formula (15), an integral-order PI is designed^λD^μController for comparison, i.e. λ 1, μ 1, K_dFinding the integral order PI at this time when 1^λD^μThe controller satisfies the set of controller parameters under the regional pole index constraint, as shown in fig. 6. As can be seen by comparing FIGS. 5 and 6, PI of integer order^λD^μFractional order PI to controller^λD^μThe solution set domain of the controller satisfying the parameters of the regional pole index is much larger, so that the fractional order PI satisfying the regional pole index^λD^μThe controller can meet more parameter sets of expected performance indexes, and can enable the unmanned intelligent automobile to meet the expected performance requirements, so that parameter setting is more convenient.

The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention.

Claims (5)

1. PI of unmanned intelligent automobile^λD^μMethod for parameter optimization of a controller, wherein the speed control of the unmanned smart car is based on using a fractional order PI^λD^μThe controller realizes stable control, and is characterized by comprising:

s101: transfer function according to speed control process of unmanned intelligent automobileAnd fractional order PI^λD^μController transfer functionEstablishing unmanned intelligent automobile closed-loop systemAnd establishing a fractional order PI according to the stability of the unmanned intelligent automobile closed loop system^λD^μController parameter space (k)_p,k_i,k_dλ, μ), the transfer function of the vehicle speed control process of the unmanned intelligent vehicle takes the speed v(s) of the unmanned intelligent vehicle as a controlled variable, takes the rotating speed RPM(s) of the direct current motor as a manipulated variable, and v(s) ═ G(s) RPM(s);

s102: performing fractional order PI according to D division principle^λD^μController parameter space (k)_p,k_i,k_dλ, μ) to obtain (k)_p,k_i) The parameter stability domain of (1);

s103: according to a preset regional pole index, carrying out fractional order PI^λD^μController parameter space (k)_p,k_i,k_dLambda, mu) to obtain a first parameter solution set Q satisfying the regional pole index_θ；

S104: according to the parameter stable domain phi and the first parameter solution set Q_θThe intersection of the two sets of the partial order PI meets the regional pole index^λD^μA second parameter solution set of the controller, the second parameter solution set being a fractional order PI satisfying a speed control optimization of the unmanned smart car^λD^μA controller parameter solution set.

2. The method according to claim 1, wherein said step S104 is followed by step S105: optionally, a parameter (k) is solution-set from the second parameter_p,k_i) Substituting into the fractional order PI_λD_μAnd a controller.

3. The method of claim 1, wherein the regional pole metric constraint range is an angular region D (α, θ);

wherein α is a decay rate (or a decay coefficient), θ is a regional pole index angle, and a region determined by α and θ is D (α, θ) to represent the regional pole index.

4. The method of claim 3, wherein the first parameter solution set is: a system pole is arranged in an area D (alpha, theta) restricted by an area pole index, and the value range [ omega ] of the preset frequency omega_min,ω_max]And obtaining a first parameter solution set meeting the regional pole index.

5. A method according to claim 1, wherein (K) in step 102 is found from the characteristic equation 1+ G (j ω) C (j ω) 0 of the control system_P,K_i) The parameter stability domain of (2).