CN102354115B - Order reduction and decoupling method of industrial control system - Google Patents

Abstract

The invention discloses a method for reducing order and decoupling of an industrial control system. The industrial control system includes a plurality of subsystems, including the following steps: A), establishing an industrial control system including actuator dynamics and coupling between the subsystems The nonlinear state-space model of the system; B), the desired closed-loop dynamics of the described subsystems of each reduced order; C), according to the desired closed-loop dynamics, select the sliding mode surface; D), design the sliding mode controller, so that The subsystems have the desired closed-loop dynamics on the sliding surface, realizing decoupling between the subsystems, and making the subsystems still able to ensure that the dynamics of the actuators cause errors within a limited time Converge to the sliding mode surface; E), use a saturation function to approximate the switching function in the sliding mode controller, and adjust key parameters to optimize the performance of the closed-loop system. The method of the invention reduces the order of the system, simplifies the design of the controller, and optimizes the performance of the closed-loop system.

Description

A kind of depression of order of industrial control system and decoupling method

Technical field

The present invention relates to the method in a kind of industrial control technology field, specifically a kind of industrial control system depression of order and decoupling method based on sliding mode technology.

Background technology

The actual industrial control system is comprised of a plurality of subsystems that are mutually related usually, every sub-systems generally is made of actuator and object two parts, control system is according to the deviation between object output and setting value, the reference input of adjusting actuator, thus reach the purpose of control object output.The normal conventional PID controllers that adopts in the actual industrial control system, subsystems decentralised control usually, and do not consider Actuator dynamic.This control program has following two problems:

(1) can't the processing execution device dynamic.Actuator in the actual industrial system, as hydraulically operated equipment (HOE), motor device etc., usually has complicated interior ring control system, to guarantee its fast-response and pinpoint accuracy, but the situations such as due to the non-ideal characteristic of device, actuator has time delay usually, it is stagnant to whirl, dead band.If in Control System Design, do not consider that this is dynamic, will worsen the control system performance.But then, if being listed as, each actuator writes equation, so CONTROLLER DESIGN, can greatly increase system's dimension again, the controller design difficulty is strengthened at double.

(2) can't be coupled between processing subsystem.Generally, all there are various couplings between each subsystem of actual industrial system, for these couplings, if do not process, will impact the precision of closed-loop control system.But then, these couplings often simple in structurely directly adopt the decoupling control method of system, dirigibility that again can device design out of hand.

Summary of the invention

Because the defects of prior art, technical matters to be solved by this invention is to provide a kind of depression of order and decoupling method of industrial control system, and method of the present invention has reduced system's exponent number, has simplified the controller design, has optimized Performance of Closed Loop System.

For achieving the above object, the invention provides a kind of depression of order and decoupling method of industrial control system, described industrial control system comprises a plurality of subsystems, it is characterized in that, comprises the steps:

A), set up the Nonlinear state space model of the industrial control system that comprises Actuator dynamic and described subsystem coupling;

B), design the expectation closed-loop dynamic of the described subsystem of each depression of order;

C), according to described expectation closed-loop dynamic, select sliding-mode surface;

D), design sliding mode controller, make described subsystem have described expectation closed-loop dynamic on described sliding-mode surface, realize decoupling zero between described subsystem, and make described subsystem in the situation that Actuator dynamic causes error, still can guarantee to converge to described sliding-mode surface in finite time;

E), use the switch function in the approximate described sliding mode controller of saturation function, and regulate key parameter, to optimize Performance of Closed Loop System.

Further, described Nonlinear state space model wherein said steps A) is

$\left\{\begin{array}{c}{\stackrel{\·}{\mathrm{\ξ}}}_0^1={\mathrm{\ξ}}_1^1\\ {\stackrel{\·}{\mathrm{\ξ}}}_1^1={\mathrm{\ξ}}_2^1\\ {\stackrel{\·}{\mathrm{\ξ}}}_2^1=f_1({\mathrm{\ξ}}^1,...,{\mathrm{\ξ}}^n)+b_1({\mathrm{\ξ}}^1,...,{\mathrm{\ξ}}^n)v_1\left(t\right)\\ {\stackrel{\·}{v}}_1\left(t\right)=-\frac{1}{T_1}{v}_1\left(t\right)+\frac{1}{T_1}{u}_1\left(t\right)\\ .\\ .\\ .\\ {\stackrel{\·}{\mathrm{\ξ}}}_0^n={\mathrm{\ξ}}_1^n\\ {\stackrel{\·}{\mathrm{\ξ}}}_1^n=f_n({\mathrm{\ξ}}^1,...,{\mathrm{\ξ}}^n)+b_n({\mathrm{\ξ}}^1,...,{\mathrm{\ξ}}^n)v_n\left(t\right)\\ {\stackrel{\·}{v}}_n\left(t\right)=-\frac{1}{T_n}{v}_n\left(t\right)+\frac{1}{T_n}{u}_n\left(t\right)\end{array}\right.$ Wherein

Be respectively the integration of the key variables of each described subsystem;

f ₁..., f _nBe respectively the coupling between each described subsystem;

b ₁..., b _nBe respectively the non-linear gain of each described subsystem, and b _i＞0;

u ₁..., u _nBe respectively the reference input of the actuator of each described subsystem;

v ₁..., v _nBe respectively the output of the actuator of each described subsystem;

T ₁..., T _nThe actuator that is respectively each described subsystem is with the time constant of first order inertial loop representative,

Wherein, n is the natural number greater than 1, || u ₁(t)-v ₁(t) ||≤e ₁..., || u _n(t)-v _n(t) ||≤e _n, wherein, e ₁..., e _nThe upper bound for the error of the actuator reference input value of each described subsystem and actuator output valve.

Further, wherein said step B) comprise the following steps:

Step B1), to the reduced order system of subsystem 1 $\left\{\begin{array}{c}{\stackrel{\·}{\mathrm{\ξ}}}_0^1={\mathrm{\ξ}}_1^1\\ {\stackrel{\·}{\mathrm{\ξ}}}_1^1={\mathrm{\ξ}}_2^1\end{array}\right.$ Get the expectation closed-loop pole

And ask

Get secular equation $(s-{\mathrm{\&lambda;}}_1^1)(s-{\mathrm{\&lambda;}}_2^1)={\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000081145150000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+{\mathrm{\&alpha;}}_1^{1}s+{\mathrm{\&alpha;}}_0^1,$ Calculate

Step B2), to the reduced order system of subsystem n

Get the expectation closed-loop pole

And ask for secular equation

Calculate

Wherein, n is the natural number greater than 1.

Further, wherein said step C) comprise the following steps:

Step C1), to subsystem 1, get sliding-mode surface $s_1={\mathrm{\&xi;}}_2^1\left(t\right)+{\mathrm{\&alpha;}}_0^1{\mathrm{\&xi;}}_0^1\left(t\right)+{\mathrm{\&alpha;}}_1^1{\mathrm{\&xi;}}_1^1\left(t\right)=0;$

Step C2), to subsystem n, get sliding-mode surface $s_n={\mathrm{\&xi;}}_1^n\left(t\right)+{\mathrm{\&alpha;}}_0^n{\mathrm{\&xi;}}_0^n\left(t\right)=0.$

Further, wherein said step D) comprise the following steps:

Step D1), to subsystem 1, suppose Non-linear coupling item f ₁(ξ ¹..., ξ ⁿ) can survey, and measuring error

Wherein Be the upper bound of the nominal error of measurement mechanism, get sliding mode controller:

$u_1\left(t\right)=-\frac{1}{b_1({\mathrm{\&xi;}}^1,...,{\mathrm{\&xi;}}^n)}({\mathrm{\&alpha;}}_0^1{\mathrm{\&xi;}}_1^1\left(t\right)+{\mathrm{\&alpha;}}_1^1{\mathrm{\&xi;}}_2^1\left(t\right))-\frac{1}{b_1({\mathrm{\&xi;}}^1,...,{\mathrm{\&xi;}}^n)}{\hat{f}}_1({\mathrm{\&xi;}}^1,...,{\mathrm{\&xi;}}^n)-{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000081145150000011.png,HDA0000081145150000012.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\mathrm{sgn}\left(s_1\right),$

Wherein, ${\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000081145150000011.png,HDA0000081145150000012.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\&GreaterEqual;{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA0000081145150000011.png,HDA0000081145150000012.png"\; state="\{\{state\}\}">e</figure-callout>}}_1+\frac{1}{b_1}{\mathrm{<figure-callout\; id="1"\; label="e\; f"\; filenames="HDA0000081145150000011.png,HDA0000081145150000012.png"\; state="\{\{state\}\}">e</figure-callout>}}_{f_{}}+{\mathrm{\&delta;}}_1,$ δ ₁＞0，k ₁＞0；

Step D2), to subsystem n, get sliding mode controller:

$u_n\left(t\right)=-\frac{1}{b_n({\mathrm{\&xi;}}^1,...,{\mathrm{\&xi;}}^n)}\left({\mathrm{\&alpha;}}_0^n{\mathrm{\&xi;}}_1^n\left(t\right)\right)-\frac{1}{b_n({\mathrm{\&xi;}}^1,...,{\mathrm{\&xi;}}^n)}{f}_n({\mathrm{\&xi;}}^1,...,{\mathrm{\&xi;}}^n)-k_n\mathrm{sgn}\left(s_n\right),$

Wherein, k _n〉=e _n+ δ _n, δ _n＞0.

Further, described key parameter wherein said step e) comprises: the expectation closed-loop pole of each described subsystem

With saturated approximate function parameter ε ⁱ, wherein, 1≤i≤n, 1≤m _i≤ n _i-1, n _iIt is the exponent number of i sub-systems.

Further, described industrial control system is the hot strip rolling control system, and described hot strip rolling control system comprises the dynamic control subsystem of kink and the dynamic control subsystem of tension force at least.

Beneficial effect of the present invention is:

Method of the present invention is utilized the robust property of sliding mode technology, and the error of the output of processing execution device and reference input makes system order reduction, and the method for using coupling terms to offset, the coupling between processing subsystem.Method of the present invention has reduced system's exponent number, the controller design of simplification, and Performance of Closed Loop System is easy to adjust, and universality is good.

Be described further below with reference to the technique effect of accompanying drawing to design of the present invention, concrete structure and generation, to understand fully purpose of the present invention, feature and effect.

Description of drawings

Fig. 1 is the curve map of saturation function.

Fig. 2 is the geometry figure of the dynamic control subsystem of kink and the dynamic control subsystem of tension force.

Fig. 3 is the structural representation of the dynamic control subsystem of kink and the dynamic control subsystem of tension force.

Embodiment

Industrial control system of the present invention is take the hot strip rolling control system as example, and depression of order and the decoupling method of industrial control system of the present invention is elaborated.But protection scope of the present invention is not limited to this, and the depression of order of industrial control system of the present invention and decoupling method are applicable to meet Nonlinear state space model any industrial control system of (comprise between Actuator dynamic and subsystem and being coupled).

This hot strip rolling control system comprises the dynamic control subsystem of kink and the dynamic control subsystem of tension force.

As shown in Fig. 2-3, the dynamic control subsystem of kink comprises PID, ATR (Automatic Torque Regulator, moment regulator automatically) and kink dynamic module.The dynamic control subsystem of tension force comprises PI, ASR (Automatic Speed Regulator, automatic speed regulator) and tension force dynamic module.

In Fig. 2-3, the corresponding physical quantity of each symbol is as shown in the table:

Table 1

See also Fig. 2 and Fig. 3, the mechanism model of the dynamic control subsystem of kink and the dynamic control subsystem of tension force is as follows:

Kink Dynamic Mechanism model:

The kinetic model of kink can be obtained by the Newton's laws of motion of rotary rigid body, and concrete equation is as follows:

$J\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}\left(t\right)=T_u\left(t\right)-T_{\mathrm{load}}\left(\mathrm{\&theta;}\right)---\left(2.1\right)$

Wherein,

Expression kink rotating angular acceleration, J represents that kink is with respect to total moment of inertia (comprising the kink arm, loop back roll and balance arm etc.) of axis of rotation, T _u(t) act on the kinetic moment of kink, T for actuator _Load(θ) be the loading moment of kink.

Kink loading moment T _Load(θ) usually formed by three parts, namely

T _load(θ)＝T _σ(θ)+T _s(θ)+T _L(θ) (2.2)

Wherein, T _σ(θ) the expression strip tension acts on the loading moment on kink, T _s(θ) represent with the loading moment of steel Action of Gravity Field on kink, and T _LThe loading moment that (θ) produces for the kink deadweight, their computing method are as follows:

T _σ(θ)＝σhwR _l[sin(θ+β)-sin(θ-α)]， (2.3)

T _L(θ)＝gM _LR _Gcosθ， (2.4)

T _s(θ)≈0.5gρLhwR _lcosθ， (2.5)

Wherein, h is belt steel thickness, and w is strip width (other symbol physical meaning is referring to table 1).

As shown in Figure 2, α in formula, β can be calculated by geometric figure:

$\mathrm{\&alpha;}={\tan }^{-1}\left[\frac{R_l\sin \mathrm{\&theta;}-{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HDA0000081145150000011.png,HDA0000081145150000012.png"\; state="\{\{state\}\}">H</figure-callout>}}_1+{\mathrm{<figure-callout\; id="1"\; label="R\; r\; L"\; filenames="HDA0000081145150000011.png,HDA0000081145150000012.png"\; state="\{\{state\}\}">R</figure-callout>}}_r}{L_{}}\right],---\left(2.6\right)$

$\mathrm{\&beta;}={\tan }^{-1}\left[\frac{R_l\sin \mathrm{\&theta;}-{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HDA0000081145150000011.png,HDA0000081145150000012.png"\; state="\{\{state\}\}">H</figure-callout>}}_1+R_r}{L_4-R_l\cos \mathrm{\&theta;}}\right].---\left(2.7\right)$

Strip tension Dynamic Mechanism model:

In the actual operation of rolling, greater than band steel physical length, the band steel is in extended state to the band steel geometrical length between forward and backward milling train usually, and its tension force can and be with the steel Young modulus estimate by band steel level of stretch, and formula is as follows:

$\mathrm{\&sigma;}\left(t\right)=E\left[\frac{L^{\&prime;}\left(\mathrm{\&theta;}\right)-(L+\mathrm{\&xi;}\left(t\right))}{L+\mathrm{\&xi;}\left(t\right)}\right],$ L′(θ)＞(L+ξ(t)) (2.8)

Wherein, E is band steel Young modulus, and L+ ξ (t) is the front and back band steel physical length, and ξ (t) is by the difference accumulation of front rolling mill strip steel velocity of discharge and rear rolling mill strip steel inlet velocity, and account form is as follows:

$\stackrel{\&CenterDot;}{\mathrm{\&xi;}}\left(t\right)=\mathrm{\&upsi;}\left(t\right)---\left(2.9\right)$

Wherein, distorted area band steel exports and inlet velocity depend on the operation roll of mill linear velocity

And occur in the ratio of slip between steel and working roll.

Band steel geometrical length L ' (θ between milling train _i) can be calculated by method of geometry by Fig. 2:

L′(θ)＝l ₁(θ)+l ₂(θ)， (2.10)

$l_1\left(\mathrm{\&theta;}\right)=\sqrt{{({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HDA0000081145150000011.png,HDA0000081145150000012.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+R_l\cos \mathrm{\&theta;})}^2+{(R_l\sin \mathrm{\&theta;}+R_r-H_1)}^2},$

$l_2\left(\mathrm{\&theta;}\right)=\sqrt{{(L_4-R_l\cos \mathrm{\&theta;})}^2+{(R_l\sin \mathrm{\&theta;}+R_r-H_1)}^2}.$

In the actual operation of rolling, compare and milling train spacing L, band steel actual accumulation amount ξ (t) is very little, thereby can omit ξ (t) in the denominator of formula (2.8).But in molecule L ' (θ)-numerical value of L and ξ (t) is in the same order of magnitude, ξ this moment (t) can't ignore.To formula (2.8) both sides differentiate, can obtain the dynamic equation of strip tension:

$\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}\left(t\right)=\frac{E}{L}[\frac{d}{\mathrm{dt}}{L}^{\&prime;}\left(\mathrm{\&theta;}\right)-\stackrel{\&CenterDot;}{\mathrm{\&xi;}}\left(t\right)]$ (2.11)

$=\frac{E}{L}\left[R_l\right[\sin (\mathrm{\&theta;}+\mathrm{\&beta;})-\sin (\mathrm{\&theta;}-\mathrm{\&alpha;})]\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\left(t\right)-\mathrm{\&upsi;}\left(t\right)]$

α in formula, the same formula of β (2.6)-(2.7).

System's Actuator dynamic is comprised of two parts:

Kink is driven by hydraulically operated equipment (HOE) or high-speed electric expreess locomotive usually, and equips automatic moment regulating system (ATR), and its fast response time can be similar to first order inertial loop usually:

${\stackrel{\&CenterDot;}{T}}_u\left(t\right)=-\frac{1}{T_u}{T}_u\left(t\right)+\frac{1}{T_u}{u}_T---\left(2.12\right)$

Wherein, T _TBe first order inertial loop time constant, T _u(t) be the kinetic moment of kink, u _TBe control inputs.

Rolling mill roll is driven by heavy-duty motor usually, and is equipped with complicated auto-speed regulating system (ASR), when carrying out systematic analysis, usually can be similar to first order inertial loop:

$\stackrel{\&CenterDot;}{\mathrm{\&upsi;}}\left(t\right)=-\frac{1}{T_{\mathrm{\&upsi;}}}\mathrm{\&upsi;}\left(t\right)+\frac{1}{T_{\mathrm{\&upsi;}}}{u}_{\mathrm{\&upsi;}}\left(t\right)---\left(2.13\right)$

Wherein, T _VBe the first order inertial loop time constant, v (t) is the roll linear velocity of milling train i, u _vBe control inputs.

Below depression of order and the decoupling method of hot strip rolling control system described in detail, depression of order and the decoupling method of hot strip rolling control system comprise the steps:

Step 1: foundation comprises the nonlinear control element state-space model that is coupled between Actuator dynamic and subsystem, and the integration item of introducing key variables makes system have typical lower triangular structure, sets up the nonlinear system equation that comprises Actuator dynamic:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{I}}_{\mathrm{\&theta;}}\left(t\right)=\mathrm{\&theta;}\left(t\right)\\ \stackrel{\&CenterDot;}{\mathrm{\&theta;}}\left(t\right)=\mathrm{\&omega;}\left(t\right)\\ \stackrel{\&CenterDot;}{\mathrm{\&omega;}}\left(t\right)=-\frac{1}{J}{T}_{\mathrm{load}}\left(t\right)+\frac{1}{J}{T}_u\left(t\right)\\ {\stackrel{\&CenterDot;}{T}}_u\left(t\right)=-\frac{1}{T_T}{T}_u\left(t\right)+\frac{1}{T_T}{u}_T\left(t\right)\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{\&sigma;}}\left(t\right)=\mathrm{\&sigma;}\left(t\right)\\ \stackrel{\&CenterDot;}{\mathrm{\&sigma;}}\left(t\right)=\frac{E}{L}{F}_3\left(\mathrm{\&theta;}\right)\mathrm{\&omega;}\left(t\right)-\frac{E}{L}\mathrm{\&upsi;}\left(t\right)\\ \stackrel{\&CenterDot;}{\mathrm{\&upsi;}}\left(t\right)=-\frac{1}{T_{\mathrm{\&upsi;}}}\mathrm{\&upsi;}\left(t\right)+\frac{1}{T_{\mathrm{\&upsi;}}}{u}_{\mathrm{\&upsi;}}\left(t\right)\end{array}\right.$

The error of actuator reference input and actuator output valve is:

| T _u(t)-u _T(t) |≤e _T, | v (t)-u _v(t) |≤e _v, wherein, e _T, e _vBe upper error.

Step 2: the expectation closed-loop dynamic that designs each depression of order subsystem;

To angle ring, suppose that angle ring expectation limit is:

Order $(s-{\mathrm{\&lambda;}}_{\mathrm{\&theta;}}^1)(s-{\mathrm{\&lambda;}}_{\mathrm{\&theta;}}^2)={\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000081145150000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+{\mathrm{\&alpha;}}_{\mathrm{\&theta;}}^{1}s+{\mathrm{\&alpha;}}_{\mathrm{\&theta;}}^0$

The selection sliding-mode surface is: $s=\mathrm{\&omega;}\left(t\right)+{\mathrm{\&alpha;}}_{\mathrm{\&theta;}}^0{I}_{\mathrm{\&theta;}}\left(t\right)+{\mathrm{\&alpha;}}_{\mathrm{\&theta;}}^1\mathrm{\&theta;}\left(t\right)=0$

To tension link, suppose that angle ring expectation limit is:

Order $(s-{\mathrm{\&lambda;}}_{\mathrm{\&sigma;}}^1)=s+{\mathrm{\&alpha;}}_{\mathrm{\&sigma;}}^0$

Step 3: select sliding-mode surface according to the expectation closed-loop dynamic;

Select sliding-mode surface to be for angle ring:

$s_{\mathrm{\&theta;}}=\mathrm{\&omega;}\left(t\right)+{\mathrm{\&alpha;}}_{\mathrm{\&theta;}}^0{I}_{\mathrm{\&theta;}}\left(t\right)+{\mathrm{\&alpha;}}_{\mathrm{\&theta;}}^1\mathrm{\&theta;}\left(t\right)=0$

To tension link, select sliding-mode surface to be:

$s_{\mathrm{\&sigma;}}=\mathrm{\&sigma;}\left(t\right)+{\mathrm{\&alpha;}}_{\mathrm{\&sigma;}}^0{I}_{\mathrm{\&sigma;}}\left(t\right)=0$

Step 4: the design sliding mode controller makes system have the expectation closed-loop dynamic on sliding-mode surface, and makes system in the situation that Actuator dynamic causes error, still can guarantee to converge in finite time sliding-mode surface.For angle ring, due to coupling terms T _Load(t) can survey, adopt measured value Replace, and measuring error $|T_{\mathrm{load}}\left(t\right)-{\hat{T}}_{\mathrm{load}}\left(t\right)|\&le;e_{\mathrm{load}},$ e _LoadBe the measuring error upper bound.

For angle ring, the design sliding mode controller is:

$u_T\left(t\right)={\hat{T}}_{\mathrm{load}}\left(t\right)-J({\mathrm{\&alpha;}}_{\mathrm{\&theta;}}^0\mathrm{\&theta;}\left(t\right)+{\mathrm{\&alpha;}}_{\mathrm{\&theta;}}^1\mathrm{\&omega;}\left(t\right))-\mathrm{ksgn}\left(s\right)$

Wherein, k _θ〉=e _Load+ e _T+ δ _θ, δ _θ＞0.

For tension link, the design sliding mode controller is:

$u\left(T\right)=F_3\left(\mathrm{\&theta;}\right)\mathrm{\&omega;}\left(t\right)+\frac{L}{E}{\mathrm{\&alpha;}}_{\mathrm{\&sigma;}}^0\mathrm{\&sigma;}\left(t\right)+k_{\mathrm{\&sigma;}}\mathrm{sgn}\left(s\right)$

Wherein, k _σ〉=e _v+ δ _σ, δ _σ＞0.

Step 5: use the switch function in the approximate sliding mode controller of saturation function, and regulate key parameter, to optimize Performance of Closed Loop System.

Key parameter to be regulated is: each subsystem expectation closed-loop pole

With

Saturated approximate function parameter ε _θ, ε _σ(seeing also Fig. 1).

More than describe preferred embodiment of the present invention in detail.Should be appreciated that those of ordinary skill in the art need not creative work and just can design according to the present invention make many modifications and variations.Therefore, all those skilled in the art all should be in the determined protection domain by claims under this invention's idea on the basis of existing technology by the available technical scheme of logical analysis, reasoning, or a limited experiment.

Claims (6)

1. the depression of order of an industrial control system and decoupling method, described industrial control system comprises a plurality of subsystems, it is characterized in that, comprises the steps:

A), set up the Nonlinear state space model of the industrial control system that comprises Actuator dynamic and described subsystem coupling;

B), design the expectation closed-loop dynamic of the described subsystem of each depression of order;

C), according to described expectation closed-loop dynamic, select sliding-mode surface;

D), design sliding mode controller, make described subsystem have described expectation closed-loop dynamic on described sliding-mode surface, realize decoupling zero between described subsystem, and make described subsystem in the situation that Actuator dynamic causes error, still can guarantee to converge to described sliding-mode surface in finite time;

E), use saturated approximate function, and regulate key parameter, to optimize Performance of Closed Loop System.

Wherein, described Nonlinear state space model described steps A) is

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_0^1={\mathrm{\&xi;}}_1^1\\ {\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_1^1={\mathrm{\&xi;}}_2^1\\ {\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_2^1=f_1({\mathrm{\&xi;}}^1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&xi;}}^n)+b_1({\mathrm{\&xi;}}^1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&xi;}}^n)v_1\left(t\right)\\ {\stackrel{\&CenterDot;}{v}}_1\left(t\right)=-\frac{1}{T_1}{v}_1\left(t\right)+\frac{1}{T_1}{u}_1\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_0^n={\mathrm{\&xi;}}_1^n\\ {\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_1^n=f_n({\mathrm{\&xi;}}^1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&xi;}}^n)+b_n({\mathrm{\&xi;}}^1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&xi;}}^n)v_n\left(t\right)\\ {\stackrel{\&CenterDot;}{v}}_n\left(t\right)=-\frac{1}{T_n}{v}_n\left(t\right)+\frac{1}{T_n}{u}_n\left(t\right)\end{array}\right.,$ Wherein

Be respectively the integration of the key variables of each described subsystem;

f ₁..., f _nBe respectively the coupling between each described subsystem;

b ₁..., b _nBe respectively the non-linear gain of each described subsystem, and b _i0;

u ₁..., u _nBe respectively the reference input of the actuator of each described subsystem;

v ₁..., v _nBe respectively the output of the actuator of each described subsystem;

T ₁..., T _nThe actuator that is respectively each described subsystem is with the time constant of first order inertial loop representative,

Wherein, n is the natural number greater than 1, || u ₁(t)-v ₁(t) ||≤e ₁..., || u _n(t)-v _n(t) ||≤e _n, wherein, e ₁..., e _nThe upper bound for the error of the actuator reference input value of each described subsystem and actuator output valve.

2. the depression of order of industrial control system as claimed in claim 1 and decoupling method, wherein said step B) comprise the following steps:

Step B1), to the reduced order system of subsystem 1 $\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_0^1={\mathrm{\&xi;}}_1^1\\ {\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_1^1={\mathrm{\&xi;}}_2^1\end{array}\right.$ Get the expectation closed-loop pole

And ask for secular equation $(s-{\mathrm{\&lambda;}}_1^1)(s-{\mathrm{\&lambda;}}_2^1)=s^2+{\mathrm{\&alpha;}}_1^{1}s+{\mathrm{\&alpha;}}_0^1,$ Calculate

Step B2), to the reduced order system of subsystem n

Get the expectation closed-loop pole

And ask for secular equation

Calculate

Wherein, n is the natural number greater than 1.

3. the depression of order of industrial control system as claimed in claim 2 and decoupling method, wherein said step C) comprise the following steps:

Step C1), to subsystem 1, get sliding-mode surface

Step C2), to subsystem n, get sliding-mode surface

4. the depression of order of industrial control system as claimed in claim 3 and decoupling method, wherein said step D) comprise the following steps:

Step D1), to subsystem 1, suppose Non-linear coupling item f ₁(ξ ¹..., ξ ⁿ) can survey, and measuring error

Wherein

Be the upper bound of the nominal error of measurement mechanism, get sliding mode controller:

$u_1\left(t\right)=-\frac{1}{b_1({\mathrm{\&xi;}}^1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&xi;}}^n)}({\mathrm{\&alpha;}}_0^1{\mathrm{\&xi;}}_1^1\left(t\right)+{\mathrm{\&alpha;}}_1^1{\mathrm{\&xi;}}_2^1\left(t\right))-\frac{1}{b_1({\mathrm{\&xi;}}^1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&xi;}}^n)}{\hat{f}}_1({\mathrm{\&xi;}}^1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&xi;}}^n)-k_1\mathrm{sgn}\left(s_1\right),$

Wherein, $k_1\&GreaterEqual;e_1+\frac{1}{b_1}{e}_{f_1}+{\mathrm{\&delta;}}_1,$ δ ₁>0，k ₁>0；

Step D2), to subsystem n, get sliding mode controller:

$u_n\left(t\right)=-\frac{1}{b_n({\mathrm{\&xi;}}^1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&xi;}}^n)}\left({\mathrm{\&alpha;}}_0^n{\mathrm{\&xi;}}_1^n\left(t\right)\right)-\frac{1}{b_n({\mathrm{\&xi;}}^1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&xi;}}^n)}{f}_n({\mathrm{\&xi;}}^1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&xi;}}^n)-k_n\mathrm{sgn}\left(s_n\right),$

Wherein, k _n〉=e _n+ δ _n, δ _n0.

As power require depression of order and the decoupling method of 4 described industrial control systems, wherein said step e) described key parameter comprise: the expectation closed-loop pole of each described subsystem

With saturated approximate function parameter ε ⁱ, wherein, 1≤i≤n, 1≤m _i≤ n _i-1, n _iIt is the exponent number of i sub-systems.

6. require depression of order and the decoupling method of 1 described industrial control system as power, described industrial control system is the hot strip rolling control system, and described hot strip rolling control system comprises the dynamic control subsystem of kink and the dynamic control subsystem of tension force at least.

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