TAO Ping，XIAO Chao

1．DP Center，Chongqing Second Intermediate People’s Court，Chongqing 404020，China；2．College of Automation，Chongqing University，Chongqing 400044，China

Decoupling Control Algorithm of Online Self-tuning Based on DRNN

TAO Ping1*，XIAO Chao2

1．DP Center，Chongqing Second Intermediate People’s Court，Chongqing 404020，China；2．College of Automation，Chongqing University，Chongqing 400044，China

In order to solve the puzzle that the change of a loop circuit parameter results in operation parameters change of other loop circuit in the control system，the paper proposed a sort of decoup ling control algorithm of online self-tuning based on DRNN.In the paper，it took the temperature and hum idity controlof a certain controlled objectas an example，constructed the mathematic model，analyzed the coupling relationship among the system variable，designed the decoupling network.It transform s the multi-variable control system with coupling relationship as the independent single-variable control system so as to eliminate the effect among related control channels.Based on decoup ling algorithm of DRNN proposed in this paper，it made the research on system simulation experiment，and the response of system simulation demonstrated that it is very small to the effect of two channels of temperature and humidity control after through decoupling，and realized the decoupling among coupling variables.The results of simulation research show that the proposed decoupling controlalgorithm is feasible and reasonable.

self-tuning decoupling PID controller，diagonal recurrent neural network，parameter adjusting strategy，temperature and humidity decoup ling

1．Introduction

In the control engineering，the basic objective of decoupling system is to seek an appropriate control law，and which can make the multi-variable system of input and output correlation realize that each output is only controlled by a corresponding input，and different output is also controlled by different input. Neural network is a kind of operation model，due to owning itself strong capability in parallel processing，self-learning and nonlinearity processing etc，it has been widely applied to the control field of controller design，pattern recognition and fault diagnosis and so on［1－3］.Compared with the conventional feed-forward neural network，the recurrent neural network（RNN）has internal feedback，and therefore it can reflect the dynamic characteristic.In which，the diagonal recurrent neural network（DRNN）possesses stronger processing and presentation skill，by way of a simplification of RNN，it can bemore conveniently applied to control system to realize the decoupling control of multi-variable system［4－6］.

2．Structure and learning algorithm of DRNN

2．1．Structure of DRNN

DRNN is a three-layer network structure，namely the input layer，hidden layer and output layer.In which，the hidden layer is a recurrent layer，and the structure of DRNN is shown as in Fig.1.

In the DRNN，assume that the input vector is I＝[I1，I2，…，In] ．In which，Ii（k）is the inputof ithneuron in input layer，Xj（k）is outputof jthneuron in recurrent layer，f（·）is the S function，and O（k）is the output of DRNN.

Output of network output layer

Input of network recurrent layer

Output of network recurrent layer

In which，WIis the weight vector of network input layer，WDand WOis respectively the weight vector in recurrent and output layer of the network.

Fig.1 Structure of DRNN

The function of network identifier is used for identifying the controlled object online，and through training process online it can make output identification be able to approximate the actual output of the synchronous system，and the structure of network identifier is shown as in Fig.2.

Fig.2 Structure of network identifier

In which，u（k）and y（k）is respectively the input and output of controlled object.The input of DRNN is u（k）and y（k），and ym（k）is the output of identifier，and ym（k）＝O（k）．The identification error em（k）and the expression of identification index is respectively as below.

2．2．Learning algorithm of weight optimization of DRNN

The learning algorithm adopts the gradient descentmethod with themomentum factor.

The learning algorithm of input，recurrent and output layer weight is respectively as equation（1），equation（2）and equation（3）.

In which，the double S function is adopted in the recurrent layer neuron，namelyηI，ηD，ηOis respectively the learning rate of input，recurrent and output layer，andαis the inertia coefficient.

If the learning rate is enlarged then the convergence rate would be quicken，but it is easy to produce the oscillation and astaticism.If the learning rate is decreased then it can keep the algorithm stability，but the convergence ratewould be negative acceleration.Whetheweighted gradient is localized to the local extreme point.And if the inertial coefficient is adopted asmomentum factor then it can make weight correction depend on the both of the gradient and the weight change incremental of the last step at the same time.

3．Decoup ling model

For convenience to make the discussed puzzle be concretization，here it takes the decoupling between temperature and humidity of variable air volume（VAV）air-conditioning system as the example.In the conventional process of HVAC design，it always ignored the coupling among multi-loop without dealing with the coordinated control of multi-variable suchas temperature，and humidity etc，it only limited to study the control of indoor temperature.In fact，by means of decoupling control between temperature and humidity，it can createmore comfortable indoor environment.The coordinated control of temperature and humidity in the central air conditioning system generally is only used for operatingmode in winter.Fig.3 shows the object model of the indoor unit coupling in winter.According to the experience，if there is a rise in 1°Ctemperature，and then it would be roughly a drop of 2%relative humidity.

Fig.3 Objectmodel of unit coupling in winter

When the cold water inlet valve is closed the air temperature of heater outlet equals to the supply air temperatureθs，and considering the influence of valve Kvh，the transfer function of heater input u1and indoor temperatureθis as below.

When the initial indoor temperature does not be considered，but considering the influence of valve Kvh，the transfer function of humidifier adjusting valve u2and indoor temperatureθis as below.

The loop transfer function of heater input u1and indoor humidity d is as below.

When the input of heating valve is zero it can be considered as that the humidity of outlet air blowing equals to exhaust air humidity，and considering the influence of valve Kvc，the loop transfer function of humidifier adjusting valve u2and indoor humidity d is as below.

Combined with the above，the couplingmodel of temperature and humidity in VRV air-conditioning system can be expressed as below.

Therefore the couplingmodel of temperature and humidity is as the following.

If the time constant difference of two inertia nodes is rather large in the transfer function then the node of time constantbeing largewould play the leading role，at this time it can be equivalent as a firstorder system.

4．Im proved self-tuning decoup ling control based on DRNN

Fig.4 shows the structure of PID decoupling control for controlled object of two-variable，and its control algorithm is as equation（4）.

In which，T is the sampling time，error1（k）＝r1（k）－y1（k），error2（k）＝r2（k）－y2（k）．

Fig.4 Structure of PID decoupling control

Fig.5 Control system based on DRNN with self-tuning PID

By means of improved DRNN，it can make the optimization of PID decoupling control，and the structure of system based on DRNN is shown as in Fig.5.In which，DRNN1and DRNN2is respectivelyas the diagonal recurrentneural networks，and r，y is respectively the setting value and actual output value of the system.The following takes channel1of the controller as the example to explain the control algorithm.

The PID control parameter of proportion，integral and differential is tuned by DRNN.In the tuning process，the input is the PID control parameter of last time，the output is the PID control parameter of current time，and the process of parameter modification is shown as in Fig.6.

Fig.6 Structure of parameter modification node for PID

Generally，the evaluation is selected as

The adjusting method of PID controller is as equation（5），equation（6）and equation（7）.

The adjusting of kp1（k），ki1（k）and kd1（k）is related to each-self learning adjusting rate，and usually it takes a changeless constant.But the size of adjusting rate is related to the deviation amount and its change rate，therefore the learning adjusting rate of PID parameter in this paper is defined as

According to the above defined learning adjusting rate，it can follow the adjusting varied with system error and its change rate so as to obtain the optimal effect.And the principle of u2controller is the same as u1controller.

5．Simulation and its control effect analysis

In order to validate the effect of couplingmodel of temperature and humidity，it first transforms the following state equation as the difference equation form.

Firstly，assume the sampling period to be as1s，the response after decoupling could be obtained by PID.Fig.7 shows the decoupling response ofθand d when r1＝1 and r2＝0，and Fig.8 shows the decoupling response ofθand d when r1＝0 and r2＝1.

Fig.7 Response of PID decoupling

The following analyzes PID decoupling control of improved DRNN，assume the network structure is 3－7－1，the network input takes I＝｛u（k－1），y（k），1｝，the sampling period takes as5 s，the learning rate of input，recurrent and output layer takes as 0.4，αvalue of inertia system takes as0.04，and theinitial value of weight takes a random value over［－1，1］.It first considers the influence for temperature and humiditywhen the inlet air velocity of heater changes.Assume r1＝1（namely the input r1is the unit step）and r2＝0（namely the input r2cooling coil is zero），and the Jacobian value with time t is shown as in Fig.9.The value of PID control parameter after and before adjusting is shown as in Tab.1，and through decoupling the response is shown as in Fig.10.

Fig.8 Response of PID decoupling

Fig.9 Jacobian value of DRNN1

Tab.1 Parameters of PID control

From Fig.7，F(xiàn)ig.8 and Fig.10，it can be seen that when the input of system is unit step the PID decoupling control based on DRNN can obviously reduce the coupling effect of humidity loop，and the humidity effect can fast decay to zero within 100 s，and the rising rime is shorten to 15 s.In like manner，when the cold water valve opening changes（namely the input r2is unit step）and r1is zero，the value of PID control parameter after and before adjusting is shown as in Tab.1 and the Jacobian value with time t is shown as in Fig.11.Through decoupling the response is shown as in Fig.12.

Fig.10 Response of PID control decoupling

Fig.11 Jacobian value of DRNN2

Fig.12 Response of PID control decoupling

From Fig.12，it can be seen that when the cooling coil input is unit step signal the output of system can track the unit step signal without no steady error within 200 s，and the coupling phenomenon of humidity is obviously weaken.It can fast decay within 50 s.

From the simulation result，it can be seen that it can obtain better control effect to adopt the algorithm of self-tuning PID decoupling control for temperature and humidity decoupling of air conditioning room.

6．Conclusions

Based on mathematical modeling of related temperature-humidity segment，by means of unique ad-vantages of recurrent neural network，the above designed a sort of improved self-tuning PID decoupling controller based on diagonal recurrent neural network.Through the experiment simulation under Matlab environment，it validated that the proposed improved algorithm is feasible and reasonable.

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摘要：摩擦式限滑差速器用于保證驅(qū)動橋兩側(cè)車輪在行程不等時能以不同轉(zhuǎn)速旋轉(zhuǎn)，并根據(jù)路面情況自動改變驅(qū)動輪間轉(zhuǎn)矩的分配，提高汽車的通過能力。基于載重汽車某進口驅(qū)動橋新型摩擦式限滑差速器，對其殼體在不同工況下進行結(jié)構強度的有限元分析。分析結(jié)果表明：該差速器殼體的結(jié)構強度符合要求。為差速器殼體的改進設計和結(jié)構優(yōu)化提供了一定的理論依據(jù)。

關鍵詞：摩擦式；限滑差速器；有限元；結(jié)構強度

中圖分類號：TH12

基于對角遞歸神經(jīng)網(wǎng)絡的在線自整定解耦控制算法

陶 平1*，肖 超2
1.重慶第二中級人民法院數(shù)據(jù)處理中心，重慶 404020；
2.重慶大學自動化學院，重慶 400044

為了解決控制系統(tǒng)中一個回路參數(shù)變化導致其他回路的運行參數(shù)改變，提出了一種基于DRNN的在線自整定解耦控制算法。以某被控對象溫濕度控制為例構建了數(shù)學模型，分析了系統(tǒng)變量之間的耦合關系，設計了解耦網(wǎng)絡。將存在耦合關系的多變量控制系統(tǒng)變換為獨立的單變量控制系統(tǒng)，以消除相關控制通道之間的影響?；谒岢龅膶沁f歸神經(jīng)網(wǎng)絡解耦算法進行了系統(tǒng)仿真實驗。系統(tǒng)仿真響應顯示：經(jīng)過解耦后的溫濕控制2個通道相互之間影響很小，實現(xiàn)了耦合變量的解耦。仿真研究結(jié)果表明：提出的解耦控制算法是可行與合理的。

自整定解耦PID控制器；對角遞歸神經(jīng)網(wǎng)絡；參數(shù)整定策略；溫濕度解耦

TP273

新型摩擦式限滑差速器殼體有限元分析

黃 霞*，丁 軍，喬慧麗
重慶理工大學，重慶 400054

10.3969／j.issn.1001－3881.2013.12.026

2013－02－15

*TAO Ping，Senior Engineer.E-mail：wztaocq＠126.com