Non-minimum phase Multi-input Multi-Ouput (MIMO) systems are known to be difficult to control. Model Predictive Control (MPC) algorithms are powerful control design methods widely applied to industrial processes. The handling of various input constraints in the MPC problem of ARIMAX non-minimum phase MIMO systems is considered. This approach is applied for control of industrial quadruple tanks. However, there is no easy way to solve the problem of constraints. The methods based on the quadratic programming (QP) technique are used to solve the constrained optimization problem. A comparative study of unconstrained and constrained control system behavior is given. Some illustrative simulation results for a considered system are presented and discussed. Encouraging results are obtained that motivate for further investigations.

In this paper, the Adaptive Generalized Predictive Control is designed to control a heat exchanger pilot plant. The standard Generalized Predictive Control (GPC) algorithm is presented. The Adaptive Generalized Predictive Control is then applied to achieve set point tracking of the output of the plant. A Single Input Single Output (SISO) model is used for control purposes. The model parameters are estimated on-line using an identification algorithm based on Recursive Least Squares (RLS) method. The performance of the proposed controller is illustrated by a simulation example of a heat exchanger pilot plant. Obtained results demonstrate the effectiveness and superiority of the proposed algorithm.

Model Predictive Control (MPC) is an advanced method of controllers, explicitly uses of model to obtain control signal. MPC is popular in industry and academia because it is capable to deals with non-minimum phase, unstable, dead time and multivariable processes, and solves the problem of constraints. MPC with integral action method is used in this study for the quadruple tank system by taking the lower two tanks into account. The objective of this work is to design and study the MPC method for controlling the level of tanks in a quadruple tank process depending on type of constrained problems. However, to solve the problem of constraints is not easy way. The methods based on the quadratic programming function and ‘if-else’ technique are presented to solve the problem of the process constraints in MPC. A comparative study is performed with the quadratic programming function and ‘if-else’ technique. The performance of the proposed method is tested for reference tracking and disturbance rejection behavior. Simulation results are presented and discussed to show the performance of the controller.

Liquid storage tanks are widely used in sectors such as water treatment, oil and gas, food processing, and chemical manufacturing. Knowing the exact amount of liquid in a tank is essential for ensuring safety, preventing spills, and optimizing process control; therefore, the liquid level in a tank must be maintained at a precise reference point. This is where liquid level control for tanks becomes crucial and constitutes a fundamental problem in the industrial sector due to nonlinearities, multivariable coupling, and stochastic disturbances. Given the drawbacks of available control methods, such as classical Model Predictive Control (MPC), which are highly dependent on model accuracy and struggle to reject complex stochastic noise, predicting random disturbances represents a major technological challenge. A new approach is proposed to specifically address the problem and challenge of the four-tank system, where water levels in two lower tanks must be controlled by two pumps, often with varying delays and significant parameter disturbances. To establish a relationship between expected performance and MPC parameters, this approach uses a novel hybrid nonlinear MPC, Extended State Observer, and Physics-Informed Neural State Estimation (NMPC-ESO-PINSE) architecture. A Physics-Informed Neural State Estimation (PINSE) layer, chosen for its learning capacity, is designed to filter sensor noise by applying Bernoulli’s physical laws, while an Extended State Observer (ESO) is integrated to capture and compensate for unmodeled uncertainties in the process. Finally, a proposed hybrid (NMPC-ESO-PINSE) strategy leverages these clean, physically consistent state estimations to solve a non-convex optimization problem via Sequential Quadratic Programming (SQP), computing optimal pump voltages. Extensive numerical simulations demonstrate the superior resilience of this decoupled framework against parametric drifts and continuous noise sequences, yielding a $+27.36\%$ reduction in global Root Mean Square Error (RMSE) compared to standard NMPC, accelerating the closed-loop settling time to $15.2 \mathrm{s}$, and restricting transient overshoot to just $0.18\%$.

Small hydro power is one of the most important renewable energy in the world. It does not encounter the problem of population displacement and is not as expensive as solar or wind energy. However, small hydro electrical generating units are usually isolated from the grid network; thus, they require control to maintain of constant the power for any working conditions. This paper presents a flow control approach for the speed control of hydro turbines. Power can be controlled by controlling the amount volume of water running into turbine. In this study, the adaptive predictive control is designed to control a flow for the automatic control of small hydro power plants. The standard Generalized Predictive Control (GPC) algorithm is presented. The Adaptive Generalized Predictive Control is then applied to achieve set point tracking of the output of the plant. A Single Input Single Output (SISO) model is used for control purposes. The model parameters are estimated on-line using an identification algorithm based on Recursive Least Squares (RLS) method. The performance of the proposed controller is illustrated by a simulation example of Small hydro power plant. Obtained results have shown better characteristics concerning both set point tracking and disturbance robustness for adaptive predictive control.