CN102354115A - Order reduction and decoupling method of industrial control system - Google Patents

Abstract

The invention discloses an order reduction and decoupling method of an industrial control system. The industrial control system comprises a plurality of subsystems. The method comprises the following steps: A) establishing a nonlinear state space model of the industrial control system, wherein the nonlinear state space model comprises actuator dynamic which is coupled with the subsystems; B) designing expected closed-loop dynamic of the each reduced-order subsystem; C) selecting a sliding mode plane according to the expected closed-loop dynamic; D) designing a sliding mode controller so that the subsystems possess the expected closed-loop dynamic on the sliding mode plane, decoupling between the subsystems can be realized and the subsystems can guarantee to converge to the sliding mode plane in a limited time under the condition of errors caused by the actuator dynamic; E) using a saturation function which is similar to a switch function in the sliding mode controller, adjusting a key parameter so as to optimize closed-loop system performance. By using the method of the invention, system order can be reduced; the design of the controller can be simplified and the closed-loop system performance can be optimized.

Description

The depression of order and decoupling method of a kind of industrial control system

Technical field

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

Background technology

Actual industrial control system is generally made up of multiple subsystems that are mutually related, each subsystem is typically made up of actuator and object two parts, control system exports the deviation between setting value, the reference input of adjusting actuator according to object, so as to reach the purpose of control object output.In actual industrial control system frequently with conventional PID controllers, usual subsystems decentralised control, and do not consider Actuator dynamic.This control program has following two problems：

(1) Actuator dynamic can not be handled.Actuator in actual industrial system, such as hydraulic test, motor device, generally have complicated inner ring control system, to ensure its fast-response and pinpoint accuracy, but due to the non-ideal characteristic of device, actuator generally has time delay, whirl stagnant, dead band situations such as.If in Control System Design, this dynamic is not considered, control system performance will be deteriorated.But then, equation is write if arranging each actuator, and then designs controller, system dimension can be greatly increased again, controller design difficulty is increased at double.

(2) it can not be coupled between processing subsystem.Under normal circumstances, all there are various couplings between each subsystem of actual industrial system, for these couplings, if without processing, the precision to closed-loop control system will be impacted.But then, these are coupled, often simple in construction direct, using the flexibility of the decoupling control method of system, again meeting device design out of hand.

The content of the invention

In view of the drawbacks described above of prior art, the technical problems to be solved by the invention are to provide the depression of order and decoupling method of a kind of industrial control system, and method of the invention reduces systematic education, simplifies controller design, optimizes Performance of Closed Loop System.

To achieve the above object, the invention provides a kind of depression of order of industrial control system and decoupling method, the industrial control system includes multiple subsystems, it is characterised in that comprise the following steps：

A the Nonlinear state space model for the industrial control system for including being coupled between Actuator dynamic and the subsystem), is set up；

B the expectation closed-loop dynamic of the subsystem of each depression of order), is designed；

C), according to the expectation closed-loop dynamic, sliding-mode surface is selected；

D sliding mode controller), is designed, make the subsystem that there is the expectation closed-loop dynamic on the sliding-mode surface, decoupling between the subsystem is realized, and the subsystem is can guarantee that in the case where Actuator dynamic causes error, still in Finite-time convergence to the sliding-mode surface；

E), using the switch function in the approximate sliding mode controller of saturation function, and key parameter is adjusted, to optimize Performance of Closed Loop System.

Further, wherein the step A) the Nonlinear state space model be

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

The respectively integration of the key variables of each subsystem；

f₁..., f_nCoupling respectively between each described subsystem；

b₁..., b_nThe respectively non-linear gain of each subsystem, and b_i＞ 0；

u₁..., u_nThe respectively reference input of the actuator of each subsystem；

v₁..., v_nThe respectively output of the actuator of each subsystem；

T₁..., T_nThe time constant that respectively actuator of each subsystem is represented with first order inertial loop,

Wherein, n is the natural number more than 1, | | u₁(t)-v₁(t)||≤e₁..., | | u_n(t)-v_n(t)||≤e_n, wherein, e₁..., e_nThe upper bound of the error of actuator reference input value and actuator output valve for subsystem each described.

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

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

And ask

Take characteristic equation $(s-{\mathrm{\λ}}_1^1)(s-{\mathrm{\λ}}_2^1)=s^2+{\mathrm{\α}}_1^{1}s+{\mathrm{\α}}_0^1,$ Calculate

Step B2), sub-system n reduced order system

Take expectation closed-loop poleAnd ask for characteristic equation

Calculate

Wherein, n is the natural number more than 1.

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

Step C1), sub-system 1, take sliding-mode surface $s_1={\mathrm{\ξ}}_2^1\left(t\right)+{\mathrm{\α}}_0^1{\mathrm{\ξ}}_0^1\left(t\right)+{\mathrm{\α}}_1^1{\mathrm{\ξ}}_1^1\left(t\right)=0;$

Step C2), sub-system n, take sliding-mode surface $s_n={\mathrm{\ξ}}_1^n\left(t\right)+{\mathrm{\α}}_0^n{\mathrm{\ξ}}_0^n\left(t\right)=0.$

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

Step D1), sub-system 1, it is assumed that Non-linear coupling f₁(ξ¹..., ξⁿ) can survey, and measurement error

Wherein

For the upper bound of the nominal error of measurement apparatus, sliding mode controller is taken：

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

Wherein, ${\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000081145150000011.png,HDA0000081145150000012.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\&GreaterEqual;{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA0000081145150000011.png,HDA0000081145150000012.png"\; state="\{\{state\}\}">e</figure-callout>}}_1+\frac{1}{b_1}{\mathrm{<figure-callout\; id="1"\; label="e\; f"\; filenames="HDA0000081145150000011.png,HDA0000081145150000012.png"\; state="\{\{state\}\}">e</figure-callout>}}_{f_{}}+{\mathrm{\&delta;}}_1,$ δ₁＞ 0, k₁＞ 0；

Step D2), sub-system n, take 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, wherein the step E) the key parameter include：The expectation closed-loop pole of each subsystem

With saturation approximate function parameter εⁱ, wherein, 1≤i≤n, 1≤m_i≤n_i- 1, n_iFor the exponent number of i-th of subsystem.

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

The beneficial effects of the present invention are：

The method of the present invention utilizes the robust property of sliding mode technology, the output of processing actuator and the error of reference input, makes the coupling between system order reduction, and the method offseted using coupling terms, processing subsystem.The method of the present invention reduces systematic education, and simplified controller design, Performance of Closed Loop System is easy to adjust, and universality is good.

The technique effect of the design of the present invention, concrete structure and generation is described further below with reference to accompanying drawing, to be fully understood from the purpose of the present invention, feature and effect.

Brief description of the drawings

Fig. 1 is the curve map of saturation function.

Fig. 2 is the geometrized structure graph of kink dynamic control subsystem and tension force dynamic control subsystem.

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

Embodiment

The industrial control system of the present invention is by taking hot strip rolling control system as an example, to the Industry Control system of the present invention The depression of order of system is described in detail with decoupling method.But protection scope of the present invention not limited to this, the depression of order of industrial control system of the invention is adapted to conform with any industrial control system of Nonlinear state space model (including being coupled between Actuator dynamic and subsystem) with decoupling method.

The hot strip rolling control system includes kink dynamic control subsystem and tension force dynamic control subsystem.

As Figure 2-3, kink dynamic control subsystem includes PID, ATR (Automatic Torque Regulator, automatic torque adjuster) and kink dynamic module.Tension force dynamic control subsystem includes PI, ASR (Automatic Speed Regulator, automatic speed regulator) and tension force dynamic module.

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

Table 1

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

Kink mechanism dynamic model：

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

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

Wherein,

Kink rotating angular acceleration is represented, J represents total rotary inertia (including kink arm, loop back roll and counter-jib etc.) of the kink relative to axis of rotation, T_u(t) kinetic moment of kink, T are acted on for actuator_load(θ) is the loading moment of kink.

Kink loading moment T_load(θ) is generally made up of three parts, i.e.,

T_load(θ)=T_σ(θ)+T_s(θ)+T_L(θ)     (2.2)

Wherein, T_σ(θ) represents the loading moment that strip tension is acted on kink, T_sLoading moment of (θ) expression strip Action of Gravity Field on kink, and T_LThe loading moment that (θ) then produces for kink deadweight, their computational methods are as follows：

T_σ(θ)=σ hwR_l[sin (θ+β)-sin (θ-α)], (2.3)

T_L(θ)=gM_LR_GCos θ, (2.4)

T_s(θ)≈0.5gρLhwR_lCos θ, (2.5)

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

As shown in Fig. 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 mechanism dynamic model：

In the actual operation of rolling, the strip geometrical length between forward and backward milling train is typically larger than strip physical length, and strip is in extended state, and its tension force can be estimated that formula is as follows by strip level of stretch and strip Young's modulus：

$\mathrm{\&sigma;}\left(t\right)=E\left[\frac{L^{\&prime;}\left(\mathrm{\&theta;}\right)-(L+\mathrm{\&xi;}\left(t\right))}{L+\mathrm{\&xi;}\left(t\right)}\right],$ L ' (θ) ＞ (L+ ξ (t)) (2.8)

Wherein, E is strip Young's modulus, and L+ ξ (t) are front and back band steel physical length, and ξ (t) is accumulated by the difference of preceding rolling mill strip steel muzzle velocity and rear rolling mill strip steel entrance velocity, and calculation is as follows：

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

Wherein, the outlet of deformed area strip and entrance velocity, depending on operation roll of mill linear velocity

And occur the slide coefficient between strip and working roll.

Strip geometrical length L ' (θ between milling train_i) can then be calculated by Fig. 2 by method of geometry：

L ' (θ)=l₁(θ)+l₂(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, compared between milling train for L, strip actual accumulation amount ξ (t) very littles, thus ξ (t) can be omitted in the denominator of formula (2.8).But L ' (θ)-L and ξ (t) numerical value is in the same order of magnitude in the molecule, now ξ (t) can not then ignore.To formula (2.8) both sides derivation, the dynamical equation of strip tension can obtain：

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

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

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

System actuators dynamic, is made up of two parts：

Kink is generally driven by hydraulic test or high-speed electric expreess locomotive, and equips automatic torque regulating system (ATR), and its fast response time generally can be with first order inertial loop come approximate：

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

Wherein, T_TFor first order inertial loop time constant, T_u(t) it is the kinetic moment of kink, u_TFor control input.

Rolling mill roll is generally driven by heavy-duty motor, and is equipped with the auto-speed regulating system of complexity (ASR), generally can be with first order inertial loop come approximate, when carrying out network analysis：

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

Wherein, T_VFor first order inertial loop time constant, v (t) is milling train i roll linear velocity, u_vFor control input.

The depression of order and decoupling method of hot strip rolling control system are described in detail below, depression of order and the decoupling method of hot strip rolling control system comprise the following steps：

Step 1：The nonlinear control element state-space model for including coupling between Actuator dynamic and subsystem is set up, the integral term for introducing key variables causes system to have typical lower triangular structure, sets up the nonlinear system equation for including 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_vFor upper error.

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

To angle ring, it is assumed that angle ring expects that limit is：

Order $(s-{\mathrm{\&lambda;}}_{\mathrm{\&theta;}}^1)(s-{\mathrm{\&lambda;}}_{\mathrm{\&theta;}}^2)=s^2+{\mathrm{\&alpha;}}_{\mathrm{\&theta;}}^{1}s+{\mathrm{\&alpha;}}_{\mathrm{\&theta;}}^0$

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

To tension link, it is assumed that angle ring expects that limit is：

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

Step 3：According to expectation closed-loop dynamic selection sliding-mode surface；

It is for angle ring selection sliding-mode surface：

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

To tension link, selection sliding-mode surface is：

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

Step 4：Design sliding mode controller makes system have expectation closed-loop dynamic on sliding-mode surface, and causes system to can guarantee that Finite-time convergence to sliding-mode surface in the case where Actuator dynamic causes error, still.For angle ring, due to coupling terms T_load(t) it can survey, using measured value

Instead of, and measurement error $|T_{\mathrm{load}}\left(t\right)-{\hat{T}}_{\mathrm{load}}\left(t\right)|\&le;e_{\mathrm{load}},$ e_loadFor the measurement error upper bound.

Then for angle ring, 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, 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：Using the switch function in the approximate sliding mode controller of saturation function, and key parameter is adjusted, to optimize Performance of Closed Loop System.

Key parameter to be regulated is：Each subsystem expects closed-loop pole

With

Saturation approximate function parameter ε_θ, ε_σ(referring to Fig. 1).

Preferred embodiment of the invention described in detail above.It should be appreciated that one of ordinary skill in the art just can make many modifications and variations without creative work according to the design of the present invention.Therefore, all those skilled in the art, all should be in the protection domain being defined in the patent 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 (7)

1. the depression of order and decoupling method of a kind of industrial control system, the industrial control system include multiple subsystems, it is characterised in that comprise the following steps：

A the Nonlinear state space model for the industrial control system for including being coupled between Actuator dynamic and the subsystem), is set up；

B the expectation closed-loop dynamic of the subsystem of each depression of order), is designed；

C), according to the expectation closed-loop dynamic, sliding-mode surface is selected；

D sliding mode controller), is designed, make the subsystem that there is the expectation closed-loop dynamic on the sliding-mode surface, decoupling between the subsystem is realized, and the subsystem is can guarantee that in the case where Actuator dynamic causes error, still in Finite-time convergence to the sliding-mode surface；

E), using the switch function in the approximate sliding mode controller of saturation function, and key parameter is adjusted, to optimize Performance of Closed Loop System.

2. the depression of order and decoupling method of industrial control system as claimed in claim 1, wherein the step A) the Nonlinear state space model be

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

, wherein

The respectively integration of the key variables of each subsystem；

f₁..., f_nCoupling respectively between each described subsystem；

b₁..., b_nThe respectively non-linear gain of each subsystem, and b_i＞ 0；

u₁..., u_nThe respectively reference input of the actuator of each subsystem；

v₁..., v_nThe respectively output of the actuator of each subsystem；

T₁..., T_nThe time constant that respectively actuator of each subsystem is represented with first order inertial loop,

Wherein, n is the natural number more than 1, | | u₁(t)-v₁(t)||≤e₁..., | | u_n(t)-v_n(t)||≤e_n, wherein, e₁..., e_nThe upper bound of the error of actuator reference input value and actuator output valve for subsystem each described.

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

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

And ask for characteristic 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), sub-system n reduced order system

Take expectation closed-loop pole

And ask for characteristic equation

CalculateWherein, n is the natural number more than 1.

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

Step C1), sub-system 1, take 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), sub-system n, take sliding-mode surface $s_n={\mathrm{\&xi;}}_1^n\left(t\right)+{\mathrm{\&alpha;}}_0^n{\mathrm{\&xi;}}_0^n\left(t\right)=0.$

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

Step D1), sub-system 1, it is assumed that Non-linear coupling f₁(ξ¹..., ξⁿ) can survey, and measurement error

Wherein

For the upper bound of the nominal error of measurement apparatus, sliding mode controller is taken：

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

Wherein, $k_1\&GreaterEqual;e_1+\frac{1}{b_1}{e}_{f_1}+{\mathrm{\&delta;}}_1,$ δ₁＞ 0, k₁＞ 0；

Step D2), sub-system n, take 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.

6. power require 5 as described in industrial control system depression of order and decoupling method, wherein the step E) the key parameter include：The expectation closed-loop pole of each subsystem

With saturation approximate function parameter εⁱ, wherein, 1≤i≤n, 1≤m_i≤n_i- 1, n_iFor the exponent number of i-th of subsystem.

7. the depression of order and decoupling method of the industrial control system as described in power requires 1, the industrial control system are hot strip rolling control system, the hot strip rolling control system at least includes kink dynamic control subsystem and tension force dynamic control subsystem.

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