Zadeh originally proposed the fuzzy logic and the fuzzy set theory [1,2] . Fuzzysystems are knowledge-based or rule-based systems formed via human knowledge and heuristics. They have been applied for a wide range of researching ﬁelds, such as control, communi- cation, medicine, management, business, psychology, etc. The most signiﬁcant applications and studies about fuzzysystems have con- centrated on the control area [3–10] . The development of fuzzy- PIDcontrollers for various engineering problems has been a major research activity in recent years. Duan et al. proposed an inherent saturation of the fuzzy-PID controller revealed due to the ﬁnite fuzzy rules  . Karasakal et al. applied fuzzyPIDcontrollers based on an online tuning method and rule weighing in  . Boubertakh et al. proposed new auto-tuning fuzzy PD and PI controllers using reinforcement-learning algorithm for single-input single-output and two-input two-output systems  . In this way, the heuristic pa- rameters of fuzzy-PIDcontrollers have to be determined via an appropriate approach. A very effective way to choose these param- eters is the use of evolutionary algorithms  , such as the Genetic Algorithm (GA)  and particle swarm optimization (PSO)  ,
2. 2. Adaptive Fuzzy P-PID controller The graphical view of the proposed adaptive fuzzy P-PID damping controller with a global signal Δf is shown in Fig. 5. The membership functions are used to specify a set of rules, called the rule base which developed based on the optimization procedure. Rules are developed based on two inputs and three linguistic terms. In an inference model, all the rules are compared to the inputs to decide which rules are relevant in the current condition. After the corresponding process, the necessary rules are extracted and the controlled output is specified for the different input conditions. The de-fuzzification mechanism pro- duces the final crisp output of FLC with regard to the fuzzified input. In Fig. 5, the tracking Δf is the input of the fuzzy inference system. The membership functions for Δf and , and the output kfuzzy are of the conventional tri- angular kind. In practice, most of the physical systems have inherent tractable characteristics such as high-order and nonlinearity. Therefore, the PIDcontrollers are added to meet the performance demand and multiobjective CGSA method is used to optimize the fuzzy P-PID pa- rameter. In other words, the proposed controller consists of the fuzzy P and the conventional PID with low-pass fil- ter. The component fuzzy P tend to make a system faster. The derivative part of PID is used to reduce the rapid
Metered et al. (2015) had implemented particle swarm optimization (PSO) algorithm to tune the PID controller implemented on a semi-active quarter car suspension sys- tem. A 2DoF model with MR damper is simulated in a Matlab/Simulink environment with bump and random road inputs. The system was tested in time and frequency domain. It was observed that POS tuned PID controller improves ride comfort and vehicle stability. Kesarkar and Selvaganesan (2015) designed fractional orderPID con- troller using artificial bee colony algorithm with objective functions such as integral absolute error, integral square error, and integral time absolute error implemented to a multi-modal complex optimization problem. The authors observed that the results were promising as compared to the conventional PID method. Niu (2014) had imple- mented GA-based optimization method to tune PID pa- rameters of the active suspension system. Absolute error control is used as an objective function to tune the PID parameters. It was observed that the GA-based optimizedPID controller improves the dynamic performance of the active suspension system and improves stability. Gad et al. (2017) implemented a fractional orderPID controller to a semi-active seat suspension. PID parameters are tuned using multi-objective GA for a seat suspension system using the 6-DoF human body. It is observed that GA-based PID controller improved SEAT value, VDV ra- tio, and crest factor as compared to the passive system and classical PID controller. Results are obtained in time as well as frequency domain. Tammam et al. (2013)
It is fact that the single objective optimization with (12) has been carried out only with set-point changes and additionally we have shown the load-disturbance characteristics of such optimum set-point tracking based FO fuzzyPIDcontrollers. Since, modulating the maximum magnitude of sensitivity function to control the load disturbance characteristics like that in  are difficult and more mathematically involved for highly nonlinearcontrollers as in our case, we restricted our study on various performance comparison with the family of FO fuzzyPIDcontrollers for optimum set-point based tuning only. The variation in control signal or manipulated variable has also been taken into consideration for unit set-point change only in the optimization based controller tuning process. The summary of the comparative performances of the family of fuzzy FOPID controllers are presented in Table 6 for three classes of oscillatory fractional order processes with various levels of relative dead-time. The proposed family of FO hybrid fuzzyPID controller structure is believed to dominate future process control industries over present day’s fuzzyPIDcontrollers, if the hardware implementation issues can be circumvented for both the fuzzy  and fractional differ- integral modules -. In addition to the recommended structure, it is interesting to see the achievable design trade-offs for different controller structure which requires multi- objective formulation of the controller tuning problem using different conflicting objectives (13) and (14).
Extremal optimization (EO) [33, 34] is a novel meta-heuristics optimization algorithm originally inspired by far-from-equilibrium dynamics of self- organized criticality (SOC) [35, 36]. Unlike traditional evolutionary algorithms, it merely selects against the bad instead of favoring the good randomly or according to a power-law probability distribution, and the mechanism of EO can be characterized from the perspectives of statistical physics, biological co- evolution and ecosystem . The original EO algorithm and its modified versions have been successfully applied to a variety of benchmark and real-world engineering optimization problems, such as graph partitioning , graph coloring , travelling salesman problem [40, 41], maximum satisfiability (MAX-SAT) problem [42, 43], numerical optimization problems and multi-objective optimization problems [44, 45], community detection in complex network , steel production scheduling , design of heat pipe , and unit commitment problem for power systems . The more comprehensive introduction concerning EO is referred to the surveys [50, 51].
Conventional multi-objective optimisation methods (such as the weighted sum method (Hwang and Masud, 1979) and the goal attainment method (Gembicki, 1974)) often struggle to satisfy these requirements in the optimi- sation of real-world engineering problems as they can ﬁnd only a single point from the approximation set rather than a diverse distribution of potential solutions. This means that a decision maker cannot fully understand the shape of the trade-oﬀ space (and thus know whether the a priori trade-oﬀs they have chosen are appropriate) without run- ning the optimisation routine many times. However, since evolutionary algorithms search a population of candidate solutions in parallel, they are able to ﬁnd multiple non- dominated solutions from this approximation set. This provides the decision maker with a set of potential solu- tions to choose from, rather than a single solution that may not meet the required performance criteria.
paper with optimal selection of weighting matrices for handling FO process with time delay, in a compact NIOPTD template. The optimal choice of the weighting matrices along with the FO differ- integrals of the PI λ D µ controller have been obtained through multi-objective NSGA-II algorithm, based on simultaneous minimization of two conflicting time domain integral performance indices – ITSE and ISDCO. Thus, the proposed method preserves the state optimality of LQR and at the same time gives a low error index in the closed loop time response while also ensuring stability and efficiently handling the time delay terms of FO process. These improvements enable the control designer to obtain satisfactory closed loop response while also enjoying the benefits of LQR in the optimal PI λ D µ controller tuning. The MOO results in a range of controller parameters lying on the Pareto front as opposed to a single controller obtained by commonly adopting single-objective optimization framework, by satisfying different conflicting time domain objectives. It is shown that there exists a trade-off between the two time domain objectives and an improvement in one performance index would invariably result in a deterioration of the other. Thus the designer can choose a controller according to the specific requirements of his control problem. Our simulation results show that the proposed techniques works well even for a highly oscillatory and a highly sluggish FO system with time delay yielding a range of solutions on the Pareto front. For delay dominant plants our simulation shows He’s method and for balanced lag and delay plants Cai’s method perform better, whereas for lag-dominant systems the solutions are comparable. Tuning rules for the five optimal LQR-FOPID knobs have been provided as a function of process parameter – delay to lag ratio (L/T) and fractional exponent of the process (α). Future scope of work may include multi-objective LQR based FOPID controller tuning for unstable and integrating fractional ordersystems with time delay and extending the concept of FO-LQR to noisy processes using FO Kalman filter and Linear Quadratic Gaussian (LQG) technique.
Remark 4.1 In Example 4.1 and Example 4.2 of , the systems (4.1) and (4.2) with con- ditions f (t, 0) ≡ 0 and g(t, 0) ≡ 0 are considered. However, in Example 4.1 of this paper, f (t, y) = 2t + 28(t – 1 2 ) 2 , g(t, y) = t 2 + 100(t – 1 2 ) 2 , we can easily see that f (t, 0) ≡ 0 and g(t, 0) ≡ 0. Thus, it is clear that one cannot deal with the system (3) of this paper by the method presented .
The grid-enabled framework for multi-objective optimisa- tion described in this paper is best suited to computation- ally expensive evaluation functions such as the robust con- troller design problem presented in section 4. This is due to the communication overheads involved in the distribution and management of the evaluation function jobs across multiple diverse resources. For some computationally triv- ial evaluation functions this distribution and management may result in a degradation in performance compared with a sequential MOEA on a single machine. Whilst further work is planned to determine the scale of problems for which this framework is most effective, it is expected that research and development in the field of grid-middleware, job submission services and job management services will result in a reduction in these communication overheads. This will allow our framework to provide increased perfor- mance for less computationally expensive problems. How- ever, our framework is not intended to replace sequential MOEAs in cases where the performance of the sequential MOEA is satisfactory.
Abstract: Fuzzy Logic Controller (FLC) performance is greatly dependent on its inference rules. In most cases, the more rules being applied to a FLC, the accuracy of the control action is enhanced. Nevertheless, a large set of rules requires more computation time. As a result, FLC implementation requires fast and high performance processors. In this paper, it is shown that the inference rule table of a two-input FLCs for Higher Order System can be reduced to form a Single Input Fuzzy Logic Controller (SIFLC), which can be easily implemented using a lookup table. Simulated results are presented to demonstrate the better dynamic performance of higher order system using SIFLC compared to the conventional FLC (CFLC) and classical PID.
The Fuzzy logic is widely used in processes where system dynamics is either very complex or exhibit a highly nonlinear character. The first fuzzylogic control algorithm implemented by Mamdani was constructed to synthesize the linguistic control protocol of a skilled human operator.
ABSTRACT: this paper presents two efficient methods for speed control of a separately excited D.C motor using PID control and fuzzy logic control. The motor was modelled and converted to a subsystem in SIMULINK. The simulation development of the PID controller with the mathematical model of DC motor is done using Ziegler- Nichols method and trial and error method. The PID parameter is tested with MATLAB/SIMULINK program. (FLC) the fuzzy logic controller is designed according to fuzzy rules so that the systems are fundamentally robust. There are 25 fuzzy rules. The FLC has two inputs. One is the motor speed error between the reference and actual speed and the second is change in speed error (speed error derivative).For comparison purpose, PID and Fuzzycontrollers have been tested using MATLAB/SIMULINK program for speed under load and no load conditions. The result shows that the Fuzzy controller is the best controller than PID controller. In addition fuzzy logic controller Demonstrates good performance, faster design and work well for high-order and nonlinear and shows the efficiency over the PID controller.
In the last few years there has been an increasing interest in the study of oscillatory and asymptotic behavior of solutions of diﬀerence equations. Compared to second-order diﬀerence equations, the study of higher-order equations, and in particular fourth-order equations (see, e.g., [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]), has received consider- ably less attention. An important special case of fourth-order diﬀerence equations is the discrete version of the Schr¨odinger equation.
In this paper we consider a nonlinear boundary value problem generated by a fourthorder diﬀerential equation on the semi-inﬁnite interval in which the lim-4 case holds for fourthorder diﬀerential expression at inﬁnity. Using the well-known Banach and Schauder ﬁxed point theorems we prove the existence and uniqueness theorems for the nonlinear boundary value problem.
Abstract-- This paper studies control of load frequency in single area power system with PID controller. In this study, PID parameters are improved using the multi- objective genetic algorithm technique. The proposed controller compared with a conventional PIDcontrollers tuned by Ziegler-Nicholas technique, Particle Swarm Optimization (PSO). The effectiveness of the anticipated scheme is confirmed throw the comparison of steady state response characteristics. For this study, MATLAB- Simulink software is used.
In Networked Control System (NCS), the communication network is used to exchange the information between sensors, actuators and controllers. The NCS increases the system agility and ease to maintenance. The Fig1 derives the structure of NCS. The sensor generates the control signal to the controller. The controller generates the error signal to actuator. The NCS is effected by delay called the Network induced delay ( ) which is given by equation.1
The expected temperature range in a living room in a house is 45 to 90 Fahrenheit. The fan speed would be in the range 0 to 100 rpm. We would like to build a fuzzy estimation for the fan speed in such away to get the speed set according to the current temperature value. Depending on the degree of fuzziness, the number of membership functions is to be selected. For example, the temperature range could be subdivided into a number of sub ranges; each range is covered by certain membership function. The number of those membership functions is decided by the designer and has no specific limit. The higher the number of the membership functions, the higher the degree of selectivity possible. It is fact an application dependent decision. In this example, we can build a system with two membership functions in the input side. One represents the cold range (45-67 Fahrenheit) and one for the hot range (68 to 90 Fahrenheit) and other two membership functions in the output side. One represents the slow speed (0 to 50 rpm) and the other represents the fast speed (51 to 100 rpm). We can see that the resulting system would be less vigilant to temperature variations and the response to these changes is less selective. Now let us increase the selectivity by dividing the room temperature range into five sub ranges, namely; ‘cold’, ‘cool’, ‘just right’, ‘warm’, and ‘hot’. We can also divide the fan speed into five regions: ‘stop’, ‘slow’, ‘medium’, ‘fast’, and ‘blast’. One can easily tell that the latter is way better than the former when it comes to selectivity comparison. However, increasing the number of membership functions does not improve the performance of
a are calculated by the equation (23). The corresponding numerical solution of (11) is computed by fourthorder Runge-Kutta method. The approximate analytic solutions and numerical solutions are plotted in the figure Fig.1 and Fig. 2. From the figures we observe that the analytical solution and the numerical solution are in nice coincidence.
This project proposes a WECS with battery storage for isolated load applications. A complete MATLAB/SIMULINK simulation is done for the proposed system. Thesimulation is validated for different wind speeds. Perturbation and observation method is implemented to track MPP. The system operates MPPT by varying boost converter duty ratio. Control of load power is accomplished with the help of bidirectional buck boost converter connected to battery bank. The excess power generated is used to charge the battery and it discharges when there is a shortage of power. Simulation is carried out for different wind speeds. Here in this project I have replaced PI Controllers with fuzzy logic controllers in order to obtain accurate results.
The control objective is to steer the yaw angle to zero in order to suppress the shimmy when the landing gear system is subjected to uncertainties, which are varying taxiing veloc- ity, and wheel caster length during landing; also, torsional spring stiffness is considered as the probabilistic uncertain parameter. Therefore, both time-varying and probabilistic un- certain parameters are considered in this study. The performance of the designed controller is verified by simulation results, which shows that the proposed RMPC using the LMI ap- proach leads to finding a solution at each sample time with guaranteed closed-loop stability, high computational efficiency and strong disturbance rejection ability. Compared with the designed RMPC dealing with only one time-varying parameter (taxiing velocity) , the proposed RMPC can handle two time-varying parameters, i.e. caster length, taxiing velocity and one probabilistic uncertain parameter, i.e. spring stiffness.