Development of sliding mode control based on diagonal recurrent neural network for coupled tank system

Neural Computing and Applications https://doi.org/10.1007/s00521-024-09849-x (0123456789().,-volV)(0123456789().,-volV) ORIGINAL ARTICLE Development of sliding mode control based on diagonal recurrent neural network for coupled tank system Ahmad M. El-Nagar1 • Mohamed I. Abdo1 Received: 6 May 2023 / Accepted: 12 April 2024 Ó The Author(s) 2024 Abstract This study presents the development of sliding mode control (SMC) using the diagonal recurrent neural network (DRNN) for nonlinear systems. Firstly, the SMC for linear systems is developed for nonlinear coupled tank system. Second, the DRNN is used to design the equivalent part of the SMC law, which is performed to approximate the dynamics of a controlled process. Third, the sliding surface for the switching control is developed using the DRNN. The DRNN parameters are tuned using Lyapunov function to achieve the controlled process stability. For the developed scheme, discontinuous signum function is used to compensate the chattering phenomenon. The developed scheme is applied for controlling the uncertain nonlinear coupled tank system. The simulation results indicate that the developed scheme can respond to the effects of system uncertainties compared to other existing schemes. Keywords Sliding mode control  Diagonal recurrent neural network  Sliding surface  Coupled tank system  Lyapunov function 1 Introduction Most practical dynamic systems have uncertain effects such as parameter uncertainties, external disturbances, model nonlinearities and structure uncertainties. These challenging problems cannot be covered using linear and conventional controllers. Subsequently, it is essential to develop robust control schemes for solving such problems and to obtain certain performance requirements [1–3]. In recent years, robust adaptive schemes based on trajectory tracking have attracted great attention for nonlinear systems such as adaptive probabilistic Takagi–Sugeno–Kang (TSK) fuzzy controller [4], adaptive interval type-2 TSK fuzzy controller [5], adaptive sliding mode control (SMC) [6] and SMC based on proportional-integral-derivative & Ahmad M. El-Nagar Mohamed I. Abdo 1 Department of Industrial Electronics and Control Engineering, Faculty of Electronic Engineering, Menoufia University, Menof 32852, Egypt (PID) and proportional-integral (PI) sliding surface, respectively [7, 8]. SMC approach is a class of the variable structure control schemes, which is a nonlinear robust controller that is able to respond insensitivity to structure uncertainties, rejection of an external disturbance, fast and good transient response, and stable control system [9]. SMC contains a switching control law that moves the states of the plant from any initial value on the sliding surface, which is set by the user in the switching surface and to preserve the system states on a desired sliding surface [10, 11]. However, the SMC includes the following problems: (1) it is necessary to obtain the precise mathematical model for the controlled process to design the SMC [9]. This problem decreases the performance of the controller in some control applications. (2) chattering phenomenon, which is an inherent problem in the design of SMC [10]. This problem also decreases the SMC performance. (3) uncertainty bounds, which are required for designing the switching control law of SMC [11]. To avoid such problems, several researchers proposed several approaches for solving the chattering problems such as approximating the discontinuous switching control law by using saturation function [12], using low pass filter [13], using variable structure adaptive control [14] and 123 Neural Computing and Applications using adaptive intelligent technique [15]. On the other hand, some researchers used the adaptive control schemes using Lyapunov theory such as genetic algorithm [16], event-triggering dissipative control [17] and other schemes for complex industrial systems [18] to handle the problem of knowing the perfect mathematical model of the controlled process. In [19], SMC with a bound estimation was introduced for controlling robot manipulator to solve the problem of the uncertainty bounds. In recent years, several researchers have integrated the SMC with intelligent techniques such as fuzzy logic systems (FLSs) [20] and neural networks (NNs) [9, 11, 21–29]. In [10], the fuzzy SMC with PI sliding surface for linear system was introduced. SMC law requires a precise knowledge about the controlled process. Moreover, the FLS was proposed to compensate the chattering phenomenon. In [9], an adaptive radial basis function NN (RBFNN)-based SMC for nonlinear plants was introduced. RBFNN was performed to approximate the unknown parameters of the controlled process. Also, the problem of chattering is solved based on a smooth continuous control action. In [11], a NN-based SMC for rotating stall and surge in axial compressors was introduced. The adaptive NN was used to avoid the problem of obtaining a precise mathematical model for the controlled process. In [25], a recurrent NN (RNN) based fuzzy SMC was introduced for 4-degree freedom remotely operated vehicle. The model uncertainties were compensated and estimated using RNN. On the other hand, the chattering phenomenon was handled using FLS as a switching term. In [29], NN was proposed to approximate the unknown continuous uncertainties and disturbance for an autonomous surface vehicle where the uncertainty bounds for the sliding surface was compensated using Lyapunov theory. Destination tank area In this paper, SMC based on diagonal RNN (DRNN) is introduced for uncertain nonlinear systems. The developed controller is motivated from the previous published works in [9–11, 21–29] to cover the disadvantages of the work in [10]. First, the SMC in [10], which was designed to linear systems is developed to uncertain nonlinear system (coupled tank system as a benchmark in this paper). Second, the NN in [9, 11, 21–29], which was used to approximate the unknown controlled system is developed to DRNN as the first time that used with SMC based on the authors’ best knowledge. DRNN is a type of NN, which belongs to the partially connected RNNs [30]. DRNN was introduced to identify nonlinear systems, which have a superior modeling accuracy compared with other NN techniques [31]. In this paper, the SMC is designed based on the DRNN. The SMC law consists of two terms; the first one is the equivalent control law, which is performed based on the DRNN. The nonlinear controlled system is approximated using DRNN. The second part is the switching control signal, which is dependent on the sliding surface. The sliding surface is performed based on DRNN. For the proposed controller, the discontinuous signum function is used to compensate the chattering problem. The updating weights of DRNN are obtained using Lyapunov function to guarantee the controlled system stability. The proposed scheme is designed for controlling uncertain (...truncated)