How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach

This article presents a qualitative mathematical model to simulate the relationship between supplied water and plant growth. A novel aspect of the construction of this phenomenological model is the consideration of a structure of three phases: (1) The soil water availability, (2) the available water inside the plant for its growth, and (3) the plant size or amount of dry matter. From these phases and their interactions, a model based on a three-dimensional nonlinear dynamic system was proposed. The results obtained showed the existence of a single equilibrium point, global and exponentially stable. Additionally, considering the framework of the perturbation theory, this model was perturbed by incorporating irrigation to the available soil water, obtaining some stability results under different assumptions. Later through the control theory, it was demonstrated that the proposed system was controllable. Finally, a numerical simulation of the proposed model was carried out, to depict the soil water content and plant growth dynamic and its agreement with the results of the mathematical analysis. In addition, a specific calibration for field data from an experiment with wheat was considered, and these parameters were then used to test the proposed model, obtaining an error of about 6% in the soil water content estimation.

Real-time implementation of Fuzzy Logic Controller based on chicken swarm optimization for the ball and plate system

The ball and Plate (BaP) system is the typical example of the nonlinear dynamic system that is used in a wide range of engineering applications. So, many researchers in the control field are using the Bap system to check robust controllers under several points that challenge it, such as internal and external disturbances. Our manuscript proposed a position control intelligent technique with two directions (2D) for the BaP system by optimized multi Fuzzy Logic Controllers (FLC’s) with Chicken Swarm Optimization (CSO) for each one. The gains and rules of the FLC’s can tune based on the CSO. This proposal utilizes the ability of the FLC’s to observe the position of the ball. At our work, the BaP system that belonged to Control Laboratory/Systems and Control Engineering department is used for real-time proposal implementation. The results have been showing a very good percentage enhancement in settling time, rise time, and overshoot, of the X-axis and Y-axis, respectively.

Orbital stability analysis of trajectories of highly nonlinear dynamic systems with feedback coupling

Orbital stability and qualitative study of the oscillations of a highly nonlinear dynamic system with feedback coupling are considered. For a highly nonlinear dynamic system with feedback coupling that satisfies Liénard’s theorem (on the existence and uniqueness of a periodic solution), a complete study of the phase pattern of the system is conducted. Applying the Poincaré criterion, the conditions for the existence of limit cycles and their Lyapunov stability are determined. The diagrams of phase trajectories are constructed numerically using the Mathcad 15 software package. Limit cycles are established, which are consistent with the limit cycles obtained by the Poincaré method. The behavior of trajectories outside the limit cycles is investigated. Recurrent homogeneous Pfaff equations are obtained, which determine the behavior of the systems “at infinity”. It was determined that the infinitely distant point of the horizontal axis is the only singular point for these equations. Linear approximations of recurrent homogeneous equations are obtained, which make it possible to determine the nature of the singular points. It was found that the trajectories then wind like a spiral on the limit cycles. Images of trajectories on the phase plane outside the limit cycles for the cases of degrees of nonlinearity under consideration are constructed.

Applications of Approximate Optimal Control to Nonlinear Systems of Tracked Vehicle Suspensions

Technique of approximate optimal vibration control and simulation for vehicle active suspension systems are developed. Considered the nonlinear damping of springs, mechanical model and a nonlinear dynamic system for a class of tracked vehicle suspension vibration control are established and the corresponding system of state space form is described. To prolong the working life of suspension system and improve ride comfort, based on the active suspension vibration control devices and using optimal control approach, an approximate optimal vibration controller is designed, and an algorithm is presented for the vibration controller. Numerical simulation results illustrate the effectiveness of the proposed technique.