Ibrahim Eksin

A new optimization method: Big Bang-Big Crunch

Nature is the principal source for proposing new optimization methods such as genetic algorithms (GA) and simulated annealing (SA) methods. All traditional evolutionary algorithms are heuristic population-based search procedures that incorporate random variation and selection. The main contribution of this study is that it proposes a novel optimization method that relies on one of the theories of the evolution of the universe; namely, the Big Bang and Big Crunch Theory. In the Big Bang phase, energy dissipation produces disorder and randomness is the main feature of this phase; whereas, in the Big Crunch phase, randomly distributed particles are drawn into an order. Inspired by this theory, an optimization algorithm is constructed, which will be called the Big Bang-Big Crunch (BB-BC) method that generates random points in the Big Bang phase and shrinks those points to a single representative point via a center of mass or minimal cost approach in the Big Crunch phase. It is shown that the performance of the new (BB-BC) method demonstrates superiority over an improved and enhanced genetic search algorithm also developed by the authors of this study, and outperforms the classical genetic algorithm (GA) for many benchmark test functions.

Self tuning fuzzy PID type load and frequency controller

In this paper, a self tuning fuzzy PID type controller is proposed for solving the load frequency control (LFC) problem. The fuzzy PID type controller is constructed as a set of control rules, and the control signal is directly deduced from the knowledge base and the fuzzy inference. Moreover, there exists a self tuning mechanism that adjusts the input scaling factor corresponding to the derivative coefficient and the output scaling factor corresponding to the integral coefficient of the PID type fuzzy logic controller in an on-line manner. The self tuning mechanism depends on the peak observer idea, and this idea is modified and adapted to the LFC problem. A two area interconnected system is assumed for demonstrations. The proposed self tuning fuzzy PID type controller has been compared with the fuzzy PID type controller without a self tuning mechanism and the conventional integral controller through some performance indices.

Self-tuning of PID-type fuzzy logic controller coefficients via relative rate observer

Abstract In this study, a new method is proposed for tuning the coefficients of PID-type fuzzy logic controllers (FLCs). The new method adjusts the input scaling factor corresponding to the derivative coefficient and the output scaling factor corresponding to the integral coefficient of the PID-type FLC using a fuzzy inference mechanism in an on-line manner. The fuzzy inference mechanism that adjusts the related coefficients has two inputs, one of which is called “normalized acceleration” and the other one is the classical “error”. The “normalized acceleration” gives the “relative rate” information about the fastness or slowness of the system response. An appropriate rule-base is generated for the adaptation of the derivative coefficient of the PID-type FLC using these two input variables. The integral coefficient is then updated as the reciprocal of the derivative coefficient. The robustness and effectiveness of the new self-tuning algorithm have been compared with the other related tuning methods proposed in the literature through simulations. The simulations are done on a second-order system with varying parameters and time delay.

Design of a sliding mode controller with a nonlinear time-varying sliding surface

In this study, a new sliding surface design approach for second-order systems is proposed that varies the sliding surface in a nonlinear and time-varying fashion. The control law is reformulated by using the new surface that is defined in the new co-ordinate axis. The nonlinear surface is then moved in a proper direction by using a time-varying function. Simulations are performed on a second-order nonlinear model of a two-link planar manipulator system. The results of the new design methodology are compared with a classical sliding mode controller and a sliding mode controller possessing a discretely moving sliding surface. It has been shown that the proposed method has improved the system performance in terms of a decrease in the reaching time, robustness to disturbances and smoother phase plane trajectory. The decrease obtained in the reaching time is quite valuable, as it improves the robustness of the controlled system to external disturbances and parameter variations.

Type-2 fuzzy model based controller design for neutralization processes.

In this study, an inverse controller based on a type-2 fuzzy model control design strategy is introduced and this main controller is embedded within an internal model control structure. Then, the overall proposed control structure is implemented in a pH neutralization experimental setup. The inverse fuzzy control signal generation is handled as an optimization problem and solved at each sampling time in an online manner. Although, inverse fuzzy model controllers may produce perfect control in perfect model match case and/or non-existence of disturbances, this open loop control would not be sufficient in the case of modeling mismatches or disturbances. Therefore, an internal model control structure is proposed to compensate these errors in order to overcome this deficiency where the basic controller is an inverse type-2 fuzzy model. This feature improves the closed-loop performance to disturbance rejection as shown through the real-time control of the pH neutralization process. Experimental results demonstrate the superiority of the inverse type-2 fuzzy model controller structure compared to the inverse type-1 fuzzy model controller and conventional control structures.

An Intelligent Hybrid Fuzzy Pid Controller

In this study, a design methodology is introduced that blends the classical PID and the fuzzy controllers in an intelligent way and thus a new intelligent hybrid controller has been achieved. Basically, in this design methodology, the classical PID and fuzzy controller have been combined by a blending mechanism that depends on a certain function of actuating error. Moreover, an intelligent switching scheme is induced on the blending mechanism that makes a decision upon the priority of the two controller parts; namely, the classical PID and the fuzzy constituents. The simulations done on various processes using the new hybrid fuzzy PID controller provides ‘better’ system responses in terms of transient and steady-state performances when compared to the pure classical PID or the pure fuzzy controller applications. The controller parameters are all tuned by the aid of genetic search algorithm.

A stochastic neighborhood search approach for airport gate assignment problem

An appropriate and efficient gate assignment is of great importance in airports since it plays a major role in the revenue obtained from the airport operations. In this study, we have focused mainly on maximum gate employment, or in other words minimize the total duration of un-gated flights. Here, we propose a method that combines the benefits of heuristic approaches with some stochastic approach instead of using a purely probabilistic approach to top-down solution of the problem. The heuristic approaches are usually used in order to provide a fast solution of the problem and later stochastic searches are used in order to ameliorate the previous results of the heuristic approach whenever possible. The proposed method generates an assignment order for the whole planes that corresponds to assignment priority. The ordering process is followed by the allocation step. Since, in practice, each airport has its own physical architecture, there have been arisen many constraints mainly concerning airplane types and parking lots in this step. Sequentially handling the plane ordering and allocation phases provides us great modularity in handling the constraints. The effectiveness of the proposed methodology has been tried to be illustrated firstly on fictively generated flight schedule data and secondly on the real world data obtained from a real world application developed for Istanbul Ataturk Airport.

Inverse fuzzy Model Control with online adaptation via Big Bang-Big Crunch optimization

Fuzzy logic modeling is a powerful tool in representing nonlinear systems. Moreover, inverse fuzzy model can be used as a controller in an open loop fashion to produce perfect control. However, in the case of modeling mismatches and disturbances that might occur on the system, open loop control would not be sufficient. In that case, the modeling errors and disturbances could be compensated by internal model control (IMC) with an on-line model adaptation scheme. The on-line adaptation is usually accomplished via recursive least square algorithm. In this study, big bang-big crunch (BB-BC) optimization method, which has a low computational time and high convergence speed, has been used as an on-line adaptation scheme. The inverse fuzzy model based IMC and the BB-BC optimization method based adaptation have been implemented and tested on a real time heating process system.

A new design method for sliding mode controllers using a linear time-varying sliding surface

Abstract The main objective of this study is to present a time-varying sliding surface using a new design method to improve the performance of a classical sliding mode controller that has a constant linear sliding surface. In the proposed method, the sliding surface is defined on new coordinate axes: one of the coordinates is the original sliding surface and the other one is naturally chosen as perpendicular to this axis. An important property of the proposed method is that it has a simple geometric interpretation and provides continuous movement of the sliding surface. A comparison of the proposed method against both the classical sliding mode controller and sliding mode controller with a discretely rotating sliding surface is made through simulations. Simulations are first performed on a typical second-order linear system without any disturbances and parameter variations. Next, bounded external disturbance and parameter variations are inserted into the system simulations. Results have shown that the proposed method improved the system performance, providing decreases in the reaching and settling times, and the proposed method has demonstrated more robustness to disturbances and parameter variations compared to its counterparts.

Big Bang Big Crunch Optimization Method Based Fuzzy Model Inversion

The inverse fuzzy model can be used as a controller in an open loop fashion to produce perfect control if there does not exist any disturbance or parameter variation in the system. In this paper, a new fuzzy model inversion technique that is based on an evolutionary search algorithm called Big Bang Big Crunch (BB-BC) optimization is introduced. Even though various fuzzy inversion methods can be found in literature, these methods are only applicable under certain conditions or limitations. On the other hand, there does not exist any limitation or condition for the new methodology presented here. In this new technique, the inverse fuzzy model control signal is generated iteratively as a consequence of an optimization operation. Since the BB-BC optimization algorithm has a high convergence speed and low computational time, the optimal inverse fuzzy model control signal is generated within each sampling time. The beneficial sides of the open loop control approach based on the proposed fuzzy model inversion technique are illustrated through two simulation studies.