In this research, our aim is to study the optimal control problem (OCP) for triple nonlinear elliptic boundary value problem (TNLEBVP). The Mint-Browder theorem is used to prove the existence and uniqueness theorem of the solution of the state vector for fixed control vector. The existence theorem for the triple continuous classical optimal control vector (TCCOCV) related to the TNLEBVP is also proved. After studying the existence of a unique solution for the triple adjoint equations (TAEqs) related to the triple of the state equations, we derive The Fréchet derivative (FD) of the cost function using Hamiltonian function. Then the theorems of necessity conditions and the sufficient condition for optimality of the constraints problem are proved
Experimental investigations have been carried out to investigate the pH-control problems of industrial electroplating wastewater treatment plants. The accurate and sensitive PID control system could treat most problem and disturbances in the normal operation of the water treatment. However, conventional treatment was replaced by proprietary treatment agent called a QUASIL which was found to be more effective for a wide range of pH.
In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.
Many of mechanical systems are exposed to undesired vibrations, so designing an active vibration control (AVC) system is important in engineering decisions to reduce this vibration. Smart structure technology is used for vibration reduction. Therefore, the cantilever beam is embedded by a piezoelectric (PZT) as an actuator. The optimal LQR controller is designed that reduce the vibration of the smart beam by using a PZT element.
In this study the main part is to change the length of the aluminum cantilever beam, so keep the control gains, the excitation, the actuation voltage, and mechanical properties of the aluminum beam for each length of the smart cantilever beam and observe the behavior and effec
... Show MoreModern automation robotics have replaced many human workers in industrial factories around the globe. The robotic arms are used for several manufacturing applications, and their responses required optimal control. In this paper, a robust approach of optimal position control for a DC motor in the robotic arm system is proposed. The general component of the automation system is first introduced. The mathematical model and the corresponding transfer functions of a DC motor in the robotic arm system are presented. The investigations of using DC motor in the robotic arm system without controller lead to poor system performance. Therefore, the analysis and design of a Proportional plus Integration plus Divertive (PID) controller is illustrated.
... Show MoreIn this time, most researchers toward about preparation of compounds according to green chemistry. This research describes the preparation of 2-fluoro-5-(substituted benzylideneamino) benzonitrile under reflux and microwave methods. Six azomethine compounds (B1-6) were synthesized by two methods under reflux and assisted microwave with the comparison between the two methods. Reflux method was prepared of azomethine (B1-6) by reaction of 5-amino-2-fluorobenzonitrile with some aldehyde derivatives with (50–100) mL of absolute ethanol and some quantity of GAA and time is limited between (2–5) hours with a yield between (60–70) percent with recrystallization for appropriate solvents. But the microwave-assisted method was synthesized of co
... Show MoreIn this paper, we study the convergence theorems of the Modified Ishikawa iterative sequence with mixed errors for the uniformly continuous mappings and solving nonlinear uniformly continuous mappings equation in arbitrary real Banach space.