Decoupling Control Algorithm of Online Self-tuning Based on DRNN

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

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 be more 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 input of ithneuron in input layer，Xj(k)is output of 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 descent method with the momentum 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，and α is 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 rate would be negative acceleration．When，the weighted gradient is localized to the local extreme point．And if the inertial coefficient is adopted as momentum 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.Decoupling 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 such as 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 create more comfortable indoor environment．The coordinated control of temperature and humidity in the central air conditioning system generally is only used for operating mode 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 Object model of unit coupling in winter

When the cold water inlet valve is closed the air temperature of heater outlet equals to the supply air temperature θs， and considering the influence of valve Kvh，the transfer function of heater input u1and indoor temperature θ is 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 temperature θ is 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 coupling model of temperature and humidity in VRV air-conditioning system can be expressed as below．

Therefore the coupling model 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 constant being large would play the leading role，at this time it can be equivalent as a firstorder system．

4.Improved self-tuning decoupling 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 respectively as the diagonal recurrent neural 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 coupling model of temperature and humidity，it first transforms the following state equation as the difference equation form．

Firstly，assume the sampling period to be as 1s，the response after decoupling could be obtained by PID．Fig．7 shows the decoupling response of θ and d when r1=1 and r2=0，and Fig．8 shows the decoupling response of θ and 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 as 5 s，the learning rate of input，recurrent and output layer takes as 0．4，α value of inertia system takes as 0．04，and the initial value of weight takes a random value over［－1，1］．It first considers the influence for temperature and humidity when 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，Fig．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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