Smart Systems for Industrial Applications. Группа авторов

difficult to control. Classical PID control does not provide the better accuracy of the system for various external disturbances.

      Next, the neural network control combined with PID for pneumatic system was analyzed. Based on the learning rule, the system results are compared with the classical PID controller. Survey on neural network gives improved performances than PID control. It has fast response, adaptability, robustness, and reliability. Neural network + PID control performs better based on optimization of system response compare with conventional PID. It comprises inherent aspects as neurons, topological structure, and knowledge-based learning rule for improving system operation. Due to lack of control in pneumatic servo system, it is tough to adopt with conventional method. Literature research shows neural network control of pneumatic servo system has fast response, suitable static and dynamic control, robustness, and good adaptability. Neural network control can be used a system with complex, nonlinear, and uncertainty that has extensive challenging applications. It is used to tuning of FOPID control with particle swarm optimization (PSO) technique which gives strong stochastic optimizing output. It depicts the movement of swarm particles around search space to solve the problem. Comparison of SNPID, neural + PID, and optimization of FOPID using PSO techniques was analyzed.

      The proposed approach defines the position control of pneumatic system using FOPID optimized with GA. The following parameters to be tuned up for optimum response. It consists of proportional, integral, and derivative gain, fractional-order integrator, and fractional-order differentiator. The approach defines the implementation of the system with fast tuning optimum parameters. Optimized FOPID-based [20] pneumatic servo system influences the improved performance of the system. In last decades, fractional-order dynamic system and various types of controllers have been studied in engineering. FOPID techniques were enhanced by Podulbny. He demonstrated the system output which compared with the classical PID controllers. PSO uses number of swarm particles that searching the optimal solution. Using fitness function, the system parameters can be optimized with fewer numbers of iterations. In PSO simulation, results show the better results than other methods. The proposed method can apply in practical system for their précised control of high power to weight ratio. The techniques give efficient results in optimal design controllers. Pneumatic servo system is used in automatic control industries. It requires high accuracy of control due to their compressibility of gas and friction. The rods less cylinder with two chambers are used. The controllers are not required any pressure sensors and reference value before connecting with the system. It has no preceding idea and uncertainty of the system. Based on the results, the proposed method achieves superior mechanism over sliding mode controllers (SMCs). The controllers track three reference signals with better précised output compare with SMCs.

Proposed linear model pneumatic system controller has main topologies: first, designing of adaptive back stepping controller without having any knowledge about actual model of the system; second, the model can able to design a controller without having previous model information of reference signal; and third, system can design a controller without expensive of pressure sensors and it has better practical application prospects. The control parameters of power factor correction (PFC) is designed by a small signal model. The output of PFC converter gives nonlinear response. GA is used to optimize the parameters of PFC converter for desired operation. From the assigned fitness function the quasi optimal control parameters are obtained. The fitness function of individual parameters of PFC converter is executed in MATLAB M-file. GA is used to get optimal parameters around search space through numbers of iteration. Simulation results shows the transient response of the system by optimizing the parameters. The control parameters of PFC converter are optimized using GA. MATLAB coding is established to calculate the performance of the PFC converter for various control parameters. After optimizing, the response of the system has reduced overshoot, settling time, better transient and steady state response. The proposed method is used to optimize the even topology of the converter and provides suitable approach for evaluating power electronic circuits.

      Drawbacks:

       The accuracy of integer order PID controller is low.

       The existing system using integer order PID controller requires high power consumption.

       The control performance of IPID controller with improved control parameters derived by GA can is poor in the sensor accuracy and energy consumption.

       The robustness of the system is poor.

2.4 Proposed Controller and Its Modeling

      The system we proposed uses FOPID controller instead of IPID controller for position control of pneumatic position servo system. It provides a better efficiency of the system by using FOPID controller. This system provides more accurate output compare to that of IPID controller. The power consumption of this system using FOPID controller is much lesser than the previously existing system. The robustness of this system is better than previously existing system using traditional IPID controller.

      2.4.1 Modeling of Fractional-Order PID Controller

       2.4.1.1 Fractional-Order Calculus

      Fractional-order operator, is defined

      (2.1)

      where t₁ and t₂ are the upper and lower time limits for the operator.

      The term λe is the fractional order. It is an arbitrary complex number. Real(λe) is the real part of λe.

      The Grnwald-Letniknov (GL) fractional-order derivative of the function f(t) is defined

      (2.2)

      where −1 is the rounding operation, c is the calculation step, and is the binomial coefficients defined as ϵ⁰.

      Integration and differential denoted by a uniform expression.

      (2.3)

      The fractional-order operator can be done by using the following equation [8]:

      (2.4)

      where

      (2.5)

      (2.6)

      By ignoring the very old data, an approximate fractional-order approximation is obtained by

      (2.7)

      where and L is the memory length.

       2.4.1.2 Fractional-Order PID Controller

      The equation of the IPID controller is

      (2.8)

      where K_pi, K_jj