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In this paper, a robust nonlinear approach for control of liquid levels in a quadruple tank system (QTS) is developed based on the design of an integrator backstepping super-twisting controller, which implements a multivariable sliding surface, where the error trajectories converge to the origin at any operating point of the system. Since the backstepping algorithm is dependent on the derivatives of the state variables, and it is sensitive to measurement noise, integral transformations of the backstepping virtual controls are performed via the modulating functions technique, rendering the algorithm derivative-free and immune to noise. The simulations based on the dynamics of the QTS located at the Advanced Control Systems Laboratory of the Pontificia Universidad Católica del Perú (PUCP) showed a good performance of the designed controller and therefore the robustness of the proposed approach.

Accurate regulation of the liquid level in a quadruple tank system (QTS) is not easy and imposes higher requirements on control strategies, so the design of controllers in these systems is challenging due to the difficulty of dynamic analysis of its nonlinear characteristics and parametric uncertainties. To overcome these problems in liquid level regulation and increase the robustness to the pump coefficients, this article proposes and investigates the use of an optimal hybrid fractional-order type-2 fuzzy-PID (OH-FO-T2F-PID) regulator using a combination of two bio-inspired evolutionary optimizers, namely augmented grey wolf optimizer and cuckoo search optimizer, which gives rise to the new hybrid A-GWOCS algorithm. This control mechanism was chosen to facilitate the convergence of the water liquids in the two tanks as quickly as possible to the corresponding required values. In addition, a collaborative optimization technique with several objectives is used to adjust the regulator parameters. The capability and efficiency of the suggested regulator is first investigated through computer simulation results and then confirmed by real-time control experimental results on the QTS based on dSPACE 1104 computation engine. The findings showed that the suggested OH-FO-T2F-PID regulator significantly outperformed both the optimized ADRC and the OH-FO-T1F-PID regulators. Specifically, it reduced the rising time by 17.02% and 95.21%, respectively, and the settling time by 25.13% and 74.28%. Additionally, the designed OH-FO-T2F-PID regulator successfully eliminated the steady-state error and overshoot, enabling precise regulation of the QTS, and maintenance the liquid level at the desired set point under a wide range of working situations. The robustness of the recommended regulator is also studied by considering − 50% disturbance in the QTS parameters, and the findings showed that the OH-FO-T2F-PID regulator is less susceptible to variations in parameters.

The multivariable process plays a significant role in industrial applications, and designing a controller for the Multi-Input Multi-Output process is challenging due to dynamic process changes and interactions between system variables. Traditionally, the PI family of controllers has been used for its simple design, easy tuning, and quick deployment. However, these processes require complex control actions due to multiple loops in process plants. Thus, this paper proposes an Iterative Learning Controller Dead-time compensating PI, which utilizes the newly developed hybrid Simulated Annealing-Ant Lion Optimization algorithm for Single-Input Single-Output process simulation and real-time experimentation on the Quadruple Tank System. To validate the effectiveness of the developed controller, Machine Learning techniques such as regression and ensemble trees are used to accurately predict the actual system response using error values from respective processes. The simulation and experimental results demonstrate that the proposed controller achieved better performance. The regression and ensemble tree algorithm models effectively predicted the actual response. The obtained data shows that the proposed controller improved system stability and robustness by minimizing nearly half of the overshoot and improving settling time, with an average of 29.9596% faster than the other controller in the SISO process and 14.6116% in the MIMO process.

A quadruple tank system using a new anti-disturbance technique called Modified Active Disturbance Rejection Control (MADRC) is introduced in this paper, along with a detailed examination of its design and hardware (H/W) implementation. To maintain the water levels in the quadruple system at predefined targets while minimizing the impact of external disturbances, the proposed scheme employs two advanced nonlinear controllers, enhanced tracking differentiator schemes, and newly developed nonlinear extended state observers (NNLESO). The proposed modified ADRC method outperforms the alternatives, according to the experimental data. With an improved ability to reject disturbances, the STC-ADRC approach reduced the output response oscillation to 3.33% of the equilibrium value. The NLPD-ADRC method, on the other hand, effectively managed system dynamics under disturbance conditions, as evidenced by a 4.666% oscillation. Additionally, disturbances had a significant impact on the S-fal-ADRC scheme, highlighting how distinct the proposed control mechanisms were in terms of performance. This work represents a significant advancement in the control of interconnected non-linear quadruple tank systems and proves that the MADRC method is effective in enhancing system stability and disturbance attenuation.

Model predictive control (MPC) is one of the important techniques for control of nonlinear and multivariable systems within constraints. Though the MPC ensures superior performance, it demands high computational resources to solve online optimization problems. With the advent of sophisticated deep learning methods, neural networks can be employed to improve the computational efficiency of the MPC. In the present study, recurrent neural network (RNN) is used to approximate the MPC control law and tested on the benchmark multivariable quadruple tank (QT) system which consists of four interconnected tanks which demonstrate nonlinear and non-minimum phase characteristics. Modern variants of RNN, namely long short-term memory and gated recurrent unit, are used in this study to mimic the nonlinear MPC (NMPC) by learning the closed-loop simulation data. The optimum network architecture is chosen by altering the number of hidden nodes and layers till the required control performance on test dataset is reached. In order to test the efficacy of RNN as MPC controller, its performance is compared with the performance of linear MPC (LMPC). The automatic control and dynamic optimization (ACADO) toolkit is used in the optimization step of the NMPC computations. The servo and regulatory responses of the RNN-based MPC are compared with LMPC and evaluated in terms of standard control performance metrics such as integral squared error (ISE) and control effort (CE).

The quadruple-tank system (QTS) is a popular educational resource in universities for studying multivariable control systems. It enables the analysis of the interaction between variables and the limitations imposed by multivariable non-minimum phase zeros, as well as the evaluation of new multivariable control methodologies. The works utilizing this system present a theoretical model that may be too idealistic and based on erroneous assumptions in real-world implementations, such as the linear behavior of the actuators. In other cases, an identified linear model is directly provided. This study outlines the practical grey-box modeling procedure conducted for the QTS at the University of Cordoba and provides guidance for its implementation. A configurable nonlinear model was developed and controlled in a closed loop using different controllers. Specifically, decentralized control, static decoupling control, and simplified decoupling control were compared. The simulation designs were experimentally validated with high accuracy, demonstrating that the conclusions reached with the developed model can be extrapolated to the real system. The comparison of these three control designs illustrates the advantages and disadvantages of decoupling in certain situations, especially in the presence of non-minimum phase zeros.

The dynamics of a quadruple tank system (QTS) represent an extensive class of multivariate nonlinear uncertain systems found in the industry. It has been established that changes in split fractions affect the transmission zero location, thereby altering the operating conditions between the minimum and non-minimum phase regions. The latter is difficult to control as more fluid flows into the two upper tanks than into the two bottom tanks, resulting in competing effects between the initial and final system responses. This attribute, alongside nonlinearity, uncertainties, constraints, and a multivariate nature, can degrade closed-loop system performance, leading to instability. In this study, we addressed the aforementioned challenges by designing controllers for the regulation of the water flow in the two bottom tanks of the QTS. For comparative analysis, three controller algorithms—a nonlinear model predictive controller (NMPC), NMPC augmented with an extended Kalman filter (i.e., NMPC-EKF) and linear model predictive controller (LMPC)—were considered in the analysis and design of the control mechanism for the quadruple water level system in a non-minimum phase condition via the Matrix Laboratory (MATLAB) simulation package environment. The simulated and real-time results in the closed loop were analyzed, and the controller performances were considered based on faster setpoint responses, less oscillation, settling time, overshoot, and smaller integral absolute error (IAE) and integral square error (ISE) under various operational conditions. The study showed that the NMPC, when augmented with an EKF, is effective for the control of a QTS in the non-minimum phase and could be designed for more complex, nonlinear, and multivariable dynamics systems, even in the presence of constraints.

Nonlinear systems with uncertainty and disturbance are very difficult to model using mathematic approach. Therefore, a black-box modeling approach without any prior knowledge is necessary. There are some modeling approaches have been used to develop a black box model such as fuzzy logic, neural network, and evolution algorithms. In this paper, an evolutionary neural network by combining a neural network and a modified differential evolution algorithm is applied to model a nonlinear system. The feasibility and effectiveness of the proposed modeling are tested on a piezoelectric actuator SISO system and an experimental quadruple tank MIMO system.

This paper proposes a fresh state error feedback linearization control method with disturbance observer (DOB) and L2 gain for a quadruple-tank liquid-level system. Firstly, in terms of the highly nonlinear and strong coupling characteristics of the quadruple-tank system, a state error feedback linearization technique is employed to design the controller to achieve liquid-level position control and tracking control. Secondly, DOB is purposed to estimate uncertain exogenous disturbances and applied to compensation control. Moreover, an L2-gain disturbance attenuation technology is designed to resolve one class of disturbance problem by uncertain parameter perturbation existing in the quadruple-tank liquid-level system. Finally, compared with the classical proportion integration differentiation (PID) and sliding mode control (SMC) methods, the extensive experimental results validate that the proposed strategy has good position control, tracking control, and disturbance rejection performances.

The optimal management of multi-purpose water reservoir networks is a challenging control problem, because of the simultaneous presence of multiple objectives, the uncertainties associated with the inflow processes and the several interactions between the subsystems. For such systems, model predictive control (MPC) is an attractive control strategy that can be implemented in both centralized and decentralized configurations. The latter is easy to implement and is characterized by reduced computational requirements, but its performance is sub-optimum. However, individual decentralized controllers can be coordinated and driven towards the performance of a centralized configuration. Coordination can be achieved through the communication of information between the subsystems, and the modification of the local control problems to ensure cooperation between the controllers. In this work the applicability of coordination algorithms for the operation of water reservoir networks is evaluated. The performance of the algorithms is evaluated through numerical simulation experiments on a quadruple tank system and a two reservoir water network. The analysis also includes a numerical study of the trade-off between the algorithms' computational burden and the different levels of cooperation. The results show the potential of the proposed approach, which could provide a viable alternative to traditional control methods in real-world applications.