pushes system state variables towards the sliding line. A chattering measure is introduced. The integral of the sliding measure, and performance indicators, including the rise time, error integral and steady state error, are used to define a fitness function in a step reference scenario. The method is tested on the model of a 2-DoF DD (Direct Drive) SCARA type robot, via simulations. The GA-tuned SMC, however, is obtained for a fixed reference signal and fixed payload. Different references and payload values may lead to chattering effects and performance degradation. The second SMC parametertuning method proposed in the thesis employs a fuzzylogic system to enlarge the operation range of the controller. The chattering measure and the sliding variable are used as the inputs of this system. The fuzzylogic system tunes the controller output smoothing mechanism on-line, which opposes the off-line GA technique. Again, simulations carried out with the Direct-Drive robot model are employed to test the control and the tuning method. The variable sliding control gain and the introduction of a “Smoothing Function” tuned by a GA and a FuzzyLogic System are novel contributions.
This work aims to develop a controller based on interval type-2 fuzzylogic to simulate an automatic voltage regulator (AVR) in transient stability power system analysis. It was simulated a one machine control to check if the interval type-2 fuzzylogiccontroller (IT2FLC) implementation was possible. After which results were compared to the results obtained with the AVR itself. The traditional type-1 FuzzyLogicController (FLC) using precise type-1 fuzzy sets cannot fully handle such uncertainties. A type-2 FLC using type-2 fuzzy sets can handle such uncertainties to produce a better performance. However, manually designing the type-2 Membership Functions (MFs) for an interval type-2 FLC is a difficult task. This paper will present a Genetic Algorithm (GA) based architecture to evolve the type-2 MFs of interval type-2 FLCs used for transient stability power system analysis.
Young et al. have presented a comprehensive framework to slidingmode control design solutions . Slidingmode control methodology has been very widely applied in applications like electric drives, position control of DC motor, isothermal chemical process reactors, autonomous under water vehicles [2, 3, 4, 5]. Esfahani et al. have introduced improved slidingmodecontroller for nonlinear quadruple tank system. In order to reduce chattering effect in conventional slidingmodecontroller, discontinuous term is replaced by adaptive proportional-differential term and satisfactory results are obtained . Verma et al. have proposed a comparative analysis of control performance of boiler drum level using various classical approaches like cascaded control, internal model control (IMC), feedback- feedforward control and fuzzylogic control (FLC). Results have shown that FLC has better performance versus other approaches . Lingda Kong et al. proposed a control algorithm based on cloud model to adjust PID parameters and the method has realized fast and accurate control for drum water level . A fuzzylogic based feedback controller is proposed to control non-linear dynamic systems like water bath temperature control system to achieve desired response . Dimeo et al. have proposed control system design of boiler-turbine unit using geneticalgorithms. The ability of geneticalgorithms to develop state feedback controller and proportional-integral (PI) for non linear multi-input and multi-output plant model is explored . Liu Sheng et al. have presented a slidingmodecontroller with adaptive genetic algorithm (AGA) to control the drum water level of the ship boiler system and have shown that slidingmodecontroller with AGA leads to better performance than the conventional PID controller .
where J is the objective function value; e(t) is the error of position signal. Normally m = 2, b = 0, 1 and 2 represents three different optimum criterion Integral square error (ISE), Integral square time weighted error (ISTE) and Integral square time-squared weighted error (IST 2 E) respectively. The same Eq. (4) can be used to derive Integral absolute time error (IATE) by taking m = 1 and b = 1. Mean square of tracking error can be arbitrarily small by choosing appropriate design parameters (Ayoubi and Tai, 2012). In optimal control design the controller parameters are obtained by minimizing certain predefined performance indices. These performance indices can be ISE, ISTE, IATE, IST 2 E or any user defined function as is taken in case of linear quadratic regulator (LQR). Usually conventional local search algorithm such as gradient decent, conjugate gradient decent etc. are used to minimize the given predefined performance indices. However, the convergence of this gradient based algorithms highly dependent on initial search point at the same time there is a chance that the solution may get trapped by a local minimum, especially for a multi performance index. These limitations of conventional local search can be addressed by the use of global search algorithms such as evolutionary computation (EC), genetic algorithm (GA), particle swarm optimization (PSO) or any other derivative free algorithms. In this paper PSO is taken into consideration to minimize the objective function. PSO is used to find the parameters such as PID parameters (K p , K i , K d ) and sliding control parameters (K w , λ, φ) of different controllers discussed in the
important issue and causes an extremely high estimation of the bounds. To solve this problem, the selection of a desired sliding surface and 𝑠𝑖𝑔𝑛 function play a vital role and if the dynamics of the PUMA arm are derived from the sliding surface then the linearisation and decoupling through the use of feedback, not gears, can be realised. In this state, the derivative of the sliding surface can help to decouple and linearise the closed-loop PUMA arm that would be expected in CTC. Linearisation and decoupling by the above method can be obtained in spite of the lack of quality of the PUMA arm dynamic model, which is in contrast to the CTC that requires an exact dynamic model of the system. It is a well-known fact that the uncertainties can be very well compensated by an on-line tuning PID-like FLC and sliding surface slope tuning. To compensate for the uncertainties fuzzylogic theory is a good candidate, but the design of a FLC with perfect dynamic compensation in the presence of uncertainty is not trivial. Therefore, in this research, uncertainties are estimated by discontinuous feedback control and the linear part controller is added to eliminate the chatter. To increase the bounds of uncertainty, fuzzy gains and sliding surface slope coefficients will be tuned by an on-line tuning method. The above discussion gives the rational for selecting the proposed methodology in this research.
The ever-growing use of various vehicles for transportation, on the one hand, and the statistics of soaring road accidents resulting from human error, on the other hand, reminds us of the necessity to conduct more extensive research on the design, manufacturing and control of driver-less intelligent vehicles. For the automatic control of an autonomous vehicle, we need its dynamic model, which, due to the existing uncertainties, the un-modeled dynamics and the performed simplifications, is impossible to determine exactly. Add to this, the external disturbances that exist on the movement path. In this paper, two adaptive controllers have been proposed for tracking the trajectory of a car-like robot. The first controller includes an indirect radial-basis-function neural network whose parameters are updated online via gradient descent. The second controller is adaptively updated online by means of fuzzylogic. The proposed controller includes a nonlinear robust section that uses the slidingmode method and a fuzzylogic section that updates some of the nonlinear control parameters online. The fuzzylogic system has been designed to deal with the chattering problem in the controller of car-like robot. In both controllers, the parameters have been determined by means of genetic algorithm. The obtained results indicate that even with the consideration of un-ideal effects such as uncertainties and external disturbances, the proposed controller has been able to perform successfully.
In order to make the spherical underwater robot better finish the task of underwater operation, the good control system and control method are essential. Researchers have proposed a variety of motion control methods, and the control algorithms of underwater which have been applied: PID control, improved PID control, fuzzy control, adaptive control, slidingmode control, neural network control, robust control, and some combination of these control algorithms. Slidingmode control (SMC), which is robust to model uncertainty and to parameter variations, and it has good disturbance rejection features. There have been a wide variety of applications of it [4,5,6,7,8,9,10,11] . However, it inherits a discontinuous control action and hence chattering phenomena will take place when the system operates near the sliding surface. Sometimes this discontinuous control action can even cause the system performance to be unstable. Fuzzy Control (FC) has supplanted conventional technologies in many applications. One major property of fuzzylogic is its ability to express the amount of ambiguity in human thinking. Therefore, when the mathematical model of the process does not exist, or exists but with uncertainties, FC is an alternative way to deal with the unknown process. However, the huge number of fuzzy rules for high-order systems makes the analysis complex [12,13,14,15] . The system used in this paper is a combination of fuzzy control and the slidingmode control.
Spong , derived a simple adaptive nonlinear control law for n-link robot manipulators. Passivity-based approach is used and the stability of the uncertain system is guaranteed based on the Lyapunov theory. This methodology has some advantages about both robustness and design. Er and Gao  designed a robust adaptive fuzzy neural controller for multilink manipulators. Asymptotic stability of the control system is established using the Lyapunov theory. This study shows that tracking errors and handled external disturbances are compensated by this new controller. Tayebi  represents adaptive iterative learning control for rigid robot manipulators. This model includes unknown parameters. This control was designed based on a proportional-derrivative feedback control. The simulation results show the effectiveness of the proposed controller. An integration of kinematic controller and a torque controller was presented by Fukao, Nakagawa and Adachi . First a new adaptive control law was introduced than a torque adaptive controller derived by using this new adaptive kinematic controller. The controller was applied to a nonholonomic mobile robot. The results show that for proposed controller was effective at values of angular velocity approaching zero. Fateh and Farhangfard  discussed the uncertainties of the Jacobian matrix in the control system. The trajectory tracking error in the task space was improved by using the new controller. Feedback linearization is the main part of this control method. Massoud, Elmaraghy and Lahdhiri  used a feedback linearization, a slidingmode technique, and a LQE methodology together. The controller takes advantages of these control methods and the new control method was applied to flexible joint manipulator. The results showed that the developed controller was successful in end-point position control.
fuzzyslidingmodecontroller and slidingmode control with PID tuning method for a class of uncertain system is presented. The goal is to achieve system robustness against parameter variations and external disturbances. A Fuzzylogiccontroller using simple approach & smaller rule set is proposed. Suitable PID control gain parameters can be systematically on-line computed according to the developed adaptive law. To reduce the high frequency chattering in the switching part of the controller, a boundary layer technique is utilized. The proposed method controller is applied to a brushless DC motor control system.
fore, an adequate control law is presented in this paper and this one is based on Global Terminal SlidingMode (GTSM) with fuzzy control. This control law aims to guarantee the avoidance of the kinematic disturbances which are injected in the angular and linear velocities, respectively. Moreover, the dynamic model based on exponential reaching law is presented to avoid the un- certainties. The control law provides the asymptotic stability by taking into account the fuzzy rules and Lya- punov theory. Thus, the chattering phenomenon should be avoided. The simulation works prove the robustness of the proposed control law by considering the distur- bances function and the robot can follow the desired trajectories.
Intelligent, robust and effective control of mobile robots is one of the challenging tasks of researchers and scientists across the globe. Mobile robots get so much attention in 21 st century research due to their versatility and huge application potential for commercial usage in households, industry etc. Mobile robots can be used to perform critical surgeries, look for mines and oil deep beneath the sea bed, extensively used in space exploration, can be used instead of human workers on an industry‟s assembly line, drive cars, record valuable data in places impossible for humans to go etc. So, due to these wide ranges of applications, mobile robots have become one of the focal points of modern day research. Study of mobile robots combines researchers from diverse fields and backgrounds like electronics, mechanics, computer science, material sciences etc. A fully autonomous robot in the real world must possess abilities to:
origin of the phase plane. Since a RBFNN is used to approximate the non-linear mapping between the sliding variable and the control law, the weightings of the RBFNN should be regulated based on the reaching condition, s s $ < 0 . An adaptive rule is used to adjust the weightings for searching the optimal weighting values and obtaining the stable converge property. The adaptive rule is derived from the steep descent rule to minimize the value of
Every chromosome defines a way of representing the meaning of input temperature control variables ‘et’ and ‘cet’ with specific range values. GeneticTuning Algorithm is being included in the program routine for FIS. The temperature controlling knowledge is represented with rule set shown in table III. The input variables ‘et’ and ‘cet’ forms the chromosome, while the output variable ‘cc’ is fixed and is allowed to hand tune by the FIS designer before running the tuning algorithm. When the GeneticTuning Algorithm is executed the FIS is made to run that generates the value of output variable ‘cc’. The desirable value of ‘cc’ is almost tending towards zero. Accordingly the GeneticTuning Algorithm goes through interactions. The iterations are terminated when fitness functions checks the value of ‘cc’ and expected value of ‘cc’ being achieved. As many as FIS versions are generated equal to the number of iterations. The designer has flexibility to select any FIS
This paper proposes the implementation of a fuzzy based robust sliding model control design to obtain voltage regulation in a boost converter with high dc gain. The proposed controller has an inner loop based on sliding- mode control whose sliding surface is defined for the input inductor current. The current reference value of the sliding surface is modified by a fuzzylogiccontroller in an outer loop that operates over the output voltage error.Robustness is analyzed in depth taking into account the parameter variation related with the operation of the converter in different equilibrium points. Simulations and experimental results are presented to validate the approach for a 20–100-W boost converter stepping-up a low dc voltage (15–25-V dc) to a 400-V dc level.
Fig 5: Configuration of the fuzzycontroller Defining 5 linguistic values denoted as NB (Negative Big), NM (Negative Medium), NS (Negative Small), Z (Zero), PS (Positive Small), PM (Positive Medium) và PB (Positive Big) for input and output variables. The linguistic values are qualified by piece-wise membership functions defined in the universe of discourse of [-1, 1] as shown in Fig 6,7,8.
The block diagram of the system is shown in Figure 4. A circuit is designed to isolate the digital in- put-output. Simple filters are emplaced to eliminate wrong measures because of cable length that connect the systems. Experiments were executed at three axis of the robot. DAQ Card is 16 Bits, 299kS/s and has 8 Digital I/O, 2 Analog output 2, 24 bit counter/timers.
The maximum error of six legs for the proposed controller is about 1mm, in other words, the position tracking results of our method are relatively crude but still sufficient in the practical applications. However, although the classical FSMC controller can satisfy the trajectory tracking performance of the 6-DOF parallel robot, the velocity control results (as in Fig. 11(b)) cannot meet the requirement of robotics for medical purpose, since the chattering is distinct especially in high speed situations. The reason why velocity tracking performance is so concerned in this rehabilitation practice is conducted as follows. Lower limb rehabilitation robots have to be manipulated within a wide range of speeds. In practical implementations, velocity chattering is highly undesirable because it may impact the plant dynamics and thus result in unforeseen instabilities, which is especially destructive in the training process. However, among researches on fuzzyslidingmode control, only a few considered the chattering characteristics of the velocity tracking control. In papers (36-38), the systems all realized trajectory tracking in simulation or practical environment. A cascade-control algorithm based on slidingmode was proposed in Ref. 27 to realize the trajectory tracking control of a parallel robot. However, the system lacked direct measurements of the velocity signal, and the velocity observer was designed using the position error, which may introduce severe noises.
The proposed FuzzyLogicController is compared with conventional controllers like the PI and the PID controller for evaluating the validity of the FuzzyLogicController developed. Figure 8.1 shows the response of the system when a PI controller is used. Figure 8.2 shows the response when a PID controller is used. Figure 8.3 shows the response when the proposed FuzzyLogicController is used.
Adaptive Controllers can be effective for time varying and nonlinear systems, but they have limitations when such systems operate with drastic and/or modal changes. A GASL has been developed and presented for the control of such systems and to enhance the performance of the adaptive controllers in the STR framework. . The GASL is designed to tune the adaptive STR identification model and controller parameters to maintain desirable dynamic performance. The addition of the GASL to the PID STR expands the STR ability to maintain control of nonlinear systems under large and quick shifts in system modes and/or disturbances compared to the basic STR. The developed GASL has been applied to a nonlinear adaptive suspension system for assessment. Simulation investigation results have been presented to show the effectiveness of utilizing the developed supervisory loop technique within the adaptive STR framework as it maintained system desirable performance under repeated disturbance and modality change conditions.
2.9. Recent Work on Type-2 Fuzzy Sets and Systems 75 The first application of a type-2 fuzzylogiccontroller to an autonomous mobile robot was implemented by Hagras , who demonstrated that it outperformed a type-1 FLC. The architecture of the controller was based upon interval type-2 fuzzylogic controllers which were used to implement the basic navigation behaviours, and also the coordination of them to produce a type-2 hierarchical FLC. Experiments were carried out in a labora- tory environment and also outdoors. The environments were challenging, dynamic and unstructured in nature. Numerous experiments were carried out including night time op- eration. It was shown that the type-2 controllers dealt in real-time with the uncertainties of the environments. The results obtained showed very good real-time control responses, which had outperformed the equivalent type-1 FLCs and HFLCs. There was about a 64% reduction in the number of rules for the type-2 FLCs and HFLCs to those used in the equivalent type-1 configuration system. The first instance of an industrial DSP embed- ded platform, with a real time type-2 FLC, used to control a marine diesel engine was by Lynch et al , . They found that the type-2 FLCs dealt with the uncertainties in real-time and produced a robust control response. This demonstrated that the embedded type-2 FLCs outperformed the PID and type-1 FLCs previously used to control the ma- rine engine whilst using smaller rule bases. Coupland has shown that the use of geometric methods can resolve the computational overhead required in general type-2 fuzzylogic, and so allow it to be applied to time critical control problems . This was demonstrated in , where a general type-2 FLC outperformed both an interval type-2 and a type-1 FLC, all executing the same tasks. Studies comparing type-2 and type-1 FLC perfor- mance have shown that the best results are given by the type-2 controllers , . In the realm of robot soccer games Figueroa et al.  explored how the type-2 fuzzylogiccontroller overcome the uncertainty in the control loop without increasing the com- putational cost of the application. Hagras recently described a method to develop a type-2 FLC through embedded type-1 FLCs demonstrating that the type-2 FLC outperforms the type-1 FLCs that it was based on .