Fuzzy-GA PID controller with incomplete derivation and its application to intelligent bionic artificial leg

This paper proposes a novel method to graphically compute all feasible gain and phase margin specifications-oriented robust and optimal fractional PID controllers to stabilize time delay processes (TD) of any order. The gain-phase margin tester method is utilized to guarantee the concerned systems certain robust safety margins and test the constant gain margin boundary, constant phase margin boundary, and stability boundary in the parameter plane. The overlapping region of these plotted boundaries, which represents all feasible robust stabilizing PID controllers and allows the considered TD processes to retain pre-specified safety margins, is graphically determined as the gain and phase margin specifications-oriented region (GPMSOR). The variations of the GPMSOR and the stability region with respect to the variations of the noninteger orders of the integral and derivative terms have been investigated. According this, it is possible to slightly enlarge the GPMSOR by altering the noninterger order of the integral and derivative terms. This modifications in GPMSOR through altering the noninteger orders of the integral and derivative terms allows us to find the robust and optimal PID controller gain set for the considered TD systems. In other words, the selected fractional order PID controllers from the GPMSOR not only retain the prescribed GM and PM specifications but minimize the integral of the absolute error (IAE) or the integral of the squared error (ISE) performance criterion. Finally, an illustrative example cited from the literature with computer simulations is provided to demonstrate the effectiveness and confirm the validity of the proposed methodology.

Different industrial applications frequently use overhead cranes for moving and lifting huge loads. It applies to civil construction, metallurgical production, rivers, and seaports. The primary purpose of this paper is to control the motion/position of the overhead crane using a PID controller using Genetic Algorithms (GA) and Bee Algorithms (BA) as optimization tools. Moreover, Fuzzy Logic modified PID Controller is applied to obtain better controller parameters. The mathematical model uses an analytical method, and the PID model employs Simulink in MATLAB. The paper presents the PID parameters determination with a different approach. The development of membership functions, fuzzy rules employ the Fuzzy Logic toolbox. Both inputs and outputs use triangular membership functions. The result shows that the optimized value of the PID controller with the Ziegler-Nichols approach is time-consuming and will provide only the initial parameters. However, PID parameters obtained with the optimization method using GA and BA reached the target values. The results obtained with the fuzzy logic controller (0.227% overshoot) show improvement in overshoot than the conventional PID controller (0.271% overshoot).

An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems

Based on the ant colony system (ACS) algorithm and fuzzy logic control, a new design method for optimal fuzzy PID controller was proposed. In this method, the ACS algorithm was used to optimize the input/output scaling factors of fuzzy PID controller to generate the optimal fuzzy control rules and optimal real-time control action on a given controlled object. The designed controller, called the Fuzzy-ACS PID controller, was used to control the CIP-I intelligent leg. The simulation experiments demonstrate that this controller has good control performance. Compared with other three optimal PID controllers designed respectively by using the differential evolution algorithm, the real-coded genetic algorithm, and the simulated annealing, it was verified that the Fuzzy-ACS PID controller has better control performance. Furthermore, the simulation results also verify that the proposed ACS algorithm has quick convergence speed, small solution variation, good dynamic convergence behavior, and high computation efficiency in searching for the optimal input/output scaling factors.

APPLICATION OF OPTIMAL-TUNING PID CONTROL TO INDUSTRIAL HYDRAULIC SYSTEMS

In power system any unpredictable variations of consumption load will cause fluctuation in frequency and the transferred power between the lines. Load frequency control is one of the main problems in the power system which synchronizes with automatic generation control. Checking the different factors that cause unbalance in power system is necessary and one of the important factors of them is the load that randomly varies. In this paper, a three area power system in deregulated environments with participation of synchronized generation of wind with Doubly Fed Induction Generator (DFIG), hydro and thermal power plants are studied. The load in this power system is considered as a random variable which periodically and randomly has frequency of 0.25 around nominal amount. Fluctuations are caused due to considering load as a random variable and using wind-powered turbine with DFIG in power system. To improve the response of power system, the optimal fuzzy logic, PID controller and FACTS devices will be used. Imperialist Competitive Algorithm (ICA) has been used for optimizing the parameters of a fuzzy logic controller. PID Controller parameters have been optimized with three intelligent algorithms, ICA, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) Algorithm and the results will be compared with each other. With comparison the result it is observed that in the case of using optimal fuzzy logic controller (OFLC) we have the fastest response with the minimum over shoot and under shoot, also in this case the transferred power between the areas is settled in the lowest value. The results show a significant reduction in losses in transmission lines.

A novel optimal PID control design is proposed in this paper. The methodology of linear quadratic regulator is utilized to search the optimal parameters of the PID controller. The augmented state vector of performance measure involves output signals only. The weighting functions are determined through poles assignment. The existence criteria of the optimal PID controller are derived. The new PID tuning algorithm is applied to the speed control of BLDC motors. Computer simulations and experimental results show that the performance of the optimal PID controller is better than that of the traditional PID controller.

This thesis focuses on the development and analysis of general methods for the design of optimal discrete PID control strategies for multivariable glass furnace processes, where standard genetic algorithms (SGAs) are applied to optimise specially formulated objective functions. Furthermore, a strong emphasis is given on the realistic model parameters identi cation method, which is illustrated to be applicable to a wide range of higher order model parameters identi cation problems. A complete, realistic and continuous excess oxygen model with nonlinearity effect was developed and the model parameters were identified. The developed excess oxygen model consisted of three sub-models to characterise the real plant response. The developed excess oxygen model was evaluated and compared with real plant dynamic response data, which illustrated the high degree of accuracy of the developed model. A new technique named predetermined time constant approximation was proposed to make an assumption on the initial value of a predetermined time constant, whose motive is to facilitate the SGAs to explore and exploit an optimal value for higher order of continuous model's parameters identi cation. Also, the proposed predetermined time constant approximation technique demonstrated that the population diversity is well sustained while exploring the feasible search region and exploiting to an optimal value. In general, the proposed method improves the SGAs convergence rate towards the global optimum and illustrated the effectiveness. An automatic tuning of decentralised discrete PID controllers for multivariable processes, based on SGAs, was proposed. The main improvement of the proposed technique is the ability to enhance the control robustness and to optimise discrete PID parameters by compensating the loop interaction of a multivariable process. This is attained by adding the individually optimised objective function of glass temperature and excess oxygen processes as one objective function, to include the total effect of the loop interaction by applying step inputs on both set points, temperature and excess oxygen, at two different time periods in one simulation. The effectiveness of the proposed tuning technique was supported by a number of simulation results using two other SGAs conventional tuning techniques with 1st and 2nd order control oriented models. It was illustrated that, in all cases, the resulting discrete PID control parameters completely satisfied all performance specifications. A new technique to minimise the fuel consumption for glass furnace processes while sustaining the glass temperature is proposed. This proposed technique is achieved by reducing the excess oxygen within the optimum thermal efficiency region within 1.7% to 3.2%, which is approximately equal to about 10% to 20% of excess air. Therefore, by reducing the excess oxygen set point within the optimum region, 2.45% to 2%, the fuel consumption is minimised from 0:002942kg/sec to 0:002868kg/sec while the thermal efficiency of the glass temperature is sustained at the desired set point (1550K). In addition, a reduction in excess oxygen within methane combustion guidelines will assure that undesirable emissions are in control throughout the combustion process. The efficiencies of the proposed technique were supported by a number of simulation results applying the three SGAs controller tuning techniques. It was illustrated that, in all cases, the fraction of excess oxygen reduction results in a great minimisation of fuel consumption over long plant operating periods.

Studies by simulation on the model of a multistage flash (MSF) desalination plant have shown certain features of the model developed, on the basis of physical laws and correlations. The most important of these is nonlinearity which relates to the changing of the process characteristics with the operating conditions. It is shown that a fixed PID controller cannot be optimal, if the operating point changes from the one at which the optimal controller was designed. In this paper, the parameter variations in the linearised plant model have been modelled over the operating region of interest, and these are mapped into the parameter space of the optimal PID controller. The resulting algorithm is a parameter scheduling scheme for the MSF plant for optimal PID control with a choice among four criteria (ISE, IAE, ISTE, and IATE). The scheme illustrated is with reference to the top brine temperature control of an actual 18 stage MSF desalination plant.

The control performance of a fixed parameters PID controller in a dynamic system will be reduced. To solve this problem, an optimized nonlinear PID controller with fuzzy inference system is proposed. The first order plus dead time (FOPDT) is a high dynamic system. This paper introduces the development and implementation of the optimal fuzzy PID controller for the FOPDT system to improve the control performance. The control process of temperature is a FOPDT model, and the approximate mathematical model is constructed according to the analysis of the step response curve without close-loop control. The design of fuzzy PID controller and the implementation of the control software are carried out by using MATLAB\Simulink. The experimental results show that, compared with the traditional PID controller, the optimized fuzzy PID controller can greatly improve the control performance for the FOPDT system.

This paper addresses a control frequency scheme of the microgrid system using a fractional order PID controller. The proposed Microgrid system is consisted of a Photovoltaic System, Wind Turbine Generator, Diesel Engine Generator, Fuel Cell, and different storage systems like Battery Energy Storage Systems, and Flywheel Energy Storage Systems. The principal objective of the present paper is to limit the frequency and power deviations by the application of the proposed controller which has five parameters to be determined through optimization techniques. Krill Herd algorithm is used for determining the optimum fractional order PID controller parameters using the Integral of Squared Error. A comparison between the Genetic Algorithm and Krill Herd is done, and the obtained simulation results presents that the investigated controller-based Krill Herd outperforms the Genetic Algorithm in terms of fewer fluctuations in power and frequency deviation.

The acronym PID stands for Proportion-Integral-Differential control. Each of these, the P, the I and the D are terms in a control algorithm, and each has a special purpose. Conventional PID controller has a simple structure and can provide satisfactory performance for many control problems. For process control systems, in particular, more than 95% of the controllers used are of PID type (Ogata, 2002). This is because it is easily applicable to field use, and also easily adjustable. The process of stabilization or improving the performance of the system is achieved by attaching a controller or compensator to the closed loop system. There are different types and structures of controllers. However, the controller cannot deal fully with nonlinear and/or time varying systems. In the design of a PID controller, the main difficulty has been how the control gains should be selected for good control performance, especially where the process to be controlled is of high order with complex nonlinear dynamics. This problem is made more difficult by the need to keep these gains tuned, during operations, to ensure robust performance in the face of plant parameter variations, load or environment disturbances and measurement noise. Genetic algorithms (GAs) are one of the efficient tools that are employed in solving optimization problems (Rothlauf, 2006). Because of the simplicity and robustness, PID controllers are frequently the used controllers in industries (Almeida et al., 2005). Parameters adjustment of PID controllers is an old challenge in the field of control system design. Some of methods have been proposed to select the PID coefficients, but they are not completely systematic methods and result in a poorly tuned controller that needs some trail and error. So far, finding new methods to automatically select PID parameters was interest of researches (Ho, 2003), (Almeida et al., 2005), (Nasri et al., 2007), and (Mansour, 2011). However in this chapter, the selection of optimal PID controller coefficients are introduced and applied based on genetic algorithms technique. Therefore it is possible to find genetically the optimal controller coefficients, Kp, Ki, and Kd with the constraint of minimizing absolute or square error signal to achieve system stability and to enhance system performance. However in feedback control systems the most important requirement is the stability of the whole system (Bartoszewicz, 2011). Another requirement is the speed, i.e. in the case of a changing reference value or a disturbance; the control error should be eliminated as soon as possible. Finally, simulation results will be implemented using MATLAB/SIMULINK to test system performance and stability. Due to the fact that in the last two decades MATLAB became the standard computing environment for engineers from different fields of science, a

In this paper, a decentralized PID controller in PI mode is tuned using Biggest-Log Modulus (BLT) tuning method and a stochastic optimization method i.e. Duelist Algorithm (DA) for multivariable system. A TITO system with FOPDT model is considered to examine the performance of the controller using those two different methods. In BLT method, the PID controller tuning parameters were first designed by using Ziegler-Nichols (ZN) method from S-curve, then the biggest log modulus is obtained to find the F factor and detuned the ZN value using the factor of BLT method. In DA method, the Integral Absolute Error (IAE) was utilized as objective function to determine optimal PID controller settings. The two PID controllers are simultaneously being optimized to find the optimal PID parameters. The performances of the control system are observed for both the changes of set point and disturbance value. The performance showed by the system using DA method is better than BLT method. DA method did improve the stability of the system towards the step changes and has a lower IAE value.

We present in this paper a novel method (called PID design through numerical optimization) for the design of adaptive fuzzy PID controllers to achieve optimal control performance. By applying the numerical optimization, the fuzzy PID design problem is transferred to a numerical optimization problem. First, a fuzzy parameter tuner is built to generate initial PID parameters, including positions and shapes of fuzzy membership functions and scaling factors. Then the gradient-based Sequential Quadratic programming (SQP) algorithm is employed to iteratively minimize the cost function by iterating the parameters. Unlike conventional PID design, this method is capable of reaching the desired control performance, such as minimum overshoot or long term stability. Another unique feature is that the optimized adaptive PID controller is applicable to a wide variety of time-varying and nonlinear systems. The proposed method is applied to the induction motor control problem and the experimental results are presented to demonstrate its effectiveness and performance.

AnnotationThere are given the results for the analytical synthesis of optimal control algorithm in a closed circuit for the third-order dynamical system, describing by two different groups of state variables. For improvement the quality of time optimal control system is offered to use the predictive output value, expected through the object’s dead-time. A comparative analysis of quality and sensitivity control systems with the time optimal and linear PID or PI controllers is done. Calculations were carried out on the example of the automatic control system of superheated steam temperature of strait-flow boiler TPP-210.