Claims:The utility and scope of the invention is defined by the following claims:

Claims:
1. A method for identifying the unstable processes dynamics as time delay models includes the following steps as:
a) The closed-loop input and output data samples are used in training the CLRNN for estimating the equivalent lower-order time delay models.
b) The modeling approach is exact in terms of time delay estimation as both integer and fractional parts can be computed.
c) A self-correcting iterative procedure is used until the optimal model parameters are obtained. The unstable time-delay models are obtained through exact formulation of CLRNN weights.
2. On the basis of claim 1, closed-loop data-driven process identification can be done for unstable time-delay systems, which are not easy to be identified using open-loop experiments. The simple process models are directly obtained in terms of CLRNN weights
3. As per claims 1, the identified model are fixed in CLRNN structure and the PID parameters are updated by training the CLRNN with the given reference model data. , Description:Field of Invention
The present invention relates to the field of data-driven identification and controlling of process plants. The process plants generally involve time delays into their dynamics. Now-a-days the focus is shifting towards utilizing data-driven techniques for estimation and controlling the industrial systems. These data-driven methods commonly employ routine data and specifically designed signals for identification and controller tuning respectively, so that the actual process operation may not be interrupted.
Background of the invention
The industrial systems are in general operate under feedback control especially if the plant is having unstable dynamics to maintain its safety and economy. However, the system dynamics may change under different operating conditions therefore the controller which is tuned for a particulate operating condition may not give satisfactory result on different operating points. This problem can be solved by re-identifying the dynamics at current operating point. (S. Pandey & S. Majhi, [2019], IET Control Theory Applications, 13(15), pp. 2507–2519.). In this regard the closed-loop identification approach can be very useful where the closed-loop data can be directly used without requiring the loop to be broken. Hence the closed-loop identification does not affect the normal process operation. Also, these model parameters can be directly incorporates in computing or tuning the controllers. (U. M. Nath, C. Dey, & R. K. Mudi, [2021], IEEE Control Systems Letters, 5(4), pp. 1255–1260.)
A system modeling method is configured in (US10817801B2), where the disturbance rejection models are used to generate predicted system outputs. A method for automatic operation of industrial plants has been developed in (KR100532804B1) which utilizes the plant model obtained using neural network learning to capture the behavior of the actual physical system with the purpose to further analyze its dynamics for optimizing the performance. The Bayesian belief networks are used in (US6415276B1) for monitoring the health of processes by performing some fault detection, isolation and accommodation tasks on process elements and variables.
However, by going through the existing prior inventions, we came to know that the modeling of unstable process dynamics, which indeed needed to be performed in closed-loop for maintaining the safety and economy of the system. Also, in presence of communication and transportation time lags the existing methods may not be suitable.
In this invention, a data-driven Closed-loop Delayed Recurrent Neural Network Architecture is constructed, which can perform the process identification using closed-loop data with reference input and PID (Proportional Integral and Derivative) controller design using reference model’s input/output data. These tasks of identification and controlling can be done alternatively.

Summary of the invention
A single closed-loop time-delayed recurrent neural network architecture can do the tasks of process identification and PID controller tuning. All the process parameters and controller parameters are computed from trained neural network weights. This invention involves a fully data driven neural architecture, where the closed-loop data is used for model parameter estimation by keeping controller parameters fixed and when the PID controller is required to be updated the model parameters are kept fixed. In this invention both integer as well as fractional time-delays can be incorporated into the neural network architecture. Also, the process models can be estimated in discrete as well as in continuous time domains.
Brief description of Drawing
Figure 1 Closed-loop identification and controlling scheme using CLRNN
Figure 2 CLRNN architecture used for the closed-loop process identification - UFOPTD and USOPTD models
Figure 3 Complete systematic iterative connection architecture for the closed-loop time-delayed process identification using CLRNN
Detailed description of the invention
To set the weights in the second layer of the CLRNN, consider the parallel form of PID controller
C(z^(-1) )=K_p+(K_i T_s z^(-1))/(1-z^(-1) )+(K_d β(1-z^(-1) ))/(1-(1-βT_s ) z^(-1) ), (1)
where Kp, Ki, Kd, and β are the proportional, integral, derivative gains and derivative filter coefficient of the controller, respectively.
If the error signal e(n) is the input and u(n) is the output of the CLRNN's controller layer then according to (1), one can have the following difference equation representation as
u(n)=(2-βT_s )u(n-1)+(βT_s-1)u(n-2)+(K_p+K_d β)e(n)
+(K_i T_s-K_p (2-βT_s )-2K_d β)e(n-1)
+(K_d β+K_p (1-βT_s )-K_i T_s (1-βT_s ))e(n-2), (2)
where the weights of the controller layer of CLRNN are computed by using known controller parameter values in (2) as:
w_0^c=K_p+K_d β, (3)
w_1^c=K_i T_s-K_p (2-βT_s )-2K_d β, (4)
w_2^c=K_d β+K_p (1-βT_s )-K_i T_s (1-βT_s ), (5)
w_3^c=2-βT_s, (6)
w_4^c=βT_s-1. (7)
Therefore, for any combinations like P, PI, PD, or PID, the controller layer weights of the CLRNN can be calculated by using expressions from (3) to (7).
Now, Consider if the unstable process dynamics G(s) to be identified as the following UFOPTD process model as
G ̂(s)=(K ̂e^(-θ ̂s))/(τ ̂s-1), (8)
Where K ̂ is the gain, θ ̂ is the time-delay and τ ̂ is the time constant of the identified UFOPTD model.
Also, consider the case when an unknown unstable process dynamics G(s), identified as the following USOPTD process model given by:
G ̂(s)=(K ̂e^(-θ ̂s))/((τ_1 ) ̂s-1)((τ_2 ) ̂s+1) , (9)
where K ̂, θ ̂ and τ ̂_1 and τ ̂_2 represents the identified model’s gain, time-delay and time constants, respectively.
Now, to get the UFOPTD and USOPDT model, in terms of the trained CLRNN's process layer weights is written in the following expressions as:
The UFOPDT model parameters can be obtained using below formulation
Z[L^(-1) {((1-e^(-sT_s ) ))/s K ̂/((τ ̂s-1) ) e^(-s((θ_I ) ̂+(θ_NI ) ̂ ) T_s ) }];0≤|(θ_NI ) ̂ |<1, (10)
=(w_((θ_I ) ̂+1)^i z^(-1)+w_((θ_I ) ̂+2)^i z^(-2))/(1-w_1^l z^(-1) ) z^(-(θ_I ) ̂ ), (11)
K ̂=((w_((θ_I ) ̂+1)^i+w_((θ_I ) ̂+2)^i ))/((w_1^l-1) ), (12)
τ ̂=T_s/log_e⁡(w_1^l ) , (13)
(θ_NI ) ̂=1-log_e⁡((w_((θ_I ) ̂+2)^i+w_((θ_I ) ̂+1)^i w_1^l)/(w_((θ_I ) ̂+1)^i+w_((θ_I ) ̂+2)^i ))\/ log_e⁡(w_1^l ), (14)
θ ̂=((θ_I ) ̂+(θ_NI ) ̂ ) T_s. (15)
The USOPDT model parameters can be obtained using following formulation
[L^(-1) {((1-e^(-sT_s ) ))/s K ̂/((τ_1 ) ̂s-1)((τ_2 ) ̂s+1) e^(-s((θ_I ) ̂+(θ_NI ) ̂ ) T_s ) }];0≤|(θ_NI ) ̂ |<1, (16)
=(w_((θ_I ) ̂+1)^i z^(-1)+w_((θ_I ) ̂+2)^i z^(-2)+w_((θ_I ) ̂+3)^i z^(-3))/(1-α_1 z^(-1) )(1-α_2 z^(-1) ) z^(-(θ_I ) ̂ ), (17)
K ̂=(w_((θ_I ) ̂+1)^i+w_((θ_I ) ̂+2)^i+w_((θ_I ) ̂+3)^i)/(α_1-1)(1-α_2 ) , (18)
(τ_1 ) ̂=T_s \/ log_e⁡(α_1 ),(τ_2 ) ̂=-T_s \/ log_e⁡(α_2 ), (19)
(θ_NI ) ̂=(τ_1 ) ̂/T_s log_e⁡(((K(τ_1 ) ̂ ) ̂α_1 (α_2-α_1 ))/((τ_1 ) ̂+(τ_2 ) ̂ )[w_((θ_I ) ̂+3)^i-w_((θ_I ) ̂+1)^i α_1+K ̂α_1 (α_2-1)] ), (20)
θ ̂=((θ_I ) ̂+(θ_NI ) ̂ ) T_s. (21)
where the terms $\alpha_1$ and $\alpha_2$ in (\ref{33}) are defined as:
α_1=0.5(w_1^l+((w_1^l )^2+4w_2^l )^0.5 ), (22)
α_2=0.5(w_1^l-((w_1^l )^2+4w_2^l )^0.5 ). (23)
In Figure 1, the closed-loop identification scheme is shown, where it can be observed that the CLRNN mimics the complete closed-loop system. The CLRNN consists of three layers. The first layer referred to the error layer, which calculates the error between reference input and estimated output. The second layer is called the virtual controller layer, whose structure and weights are selected according to some knowledge of the stabilizing controller used with the actual unstable process for data generation. The last layer is referred to as the process model layer, which is responsible for capturing the unknown unstable delayed process dynamics in terms of its optimized weights.

In Figure 2, a more detailed CLRNN architecture, utilizing the parallel connection mode, has been shown, which includes three layers, each having a single neuron and corresponding activation functions. The CLRNN contains all the components of a typical closed-loop system, i.e., error computation part, controller part, and the process identifier part within its architecture. The Figure 3 shows the detailed iterative procedure used in this invention, where the parametric CLRNN is used to identify and model an unknown unstable delayed dynamics in the forms of UFOPTD and USOPTD models.
3 claims & 3 Figures