József K. Tar

Fuzzy Control System Performance Enhancement by Iterative Learning Control

This paper suggests low-cost fuzzy control solutions that ensure the improvement of control system (CS) performance indices by merging the benefits of fuzzy control and iterative learning control (ILC). The solutions are expressed in terms of three fuzzy CS (FCS) structures that employ ILC algorithms and a unified design method focused on Takagi-Sugeno proportional-integral fuzzy controllers (PI-FCs). The PI-FCs are dedicated to a class of servo systems with linear/linearized controlled plants characterized by second-order dynamics and integral type. The invariant set theorem by Krasovskii and LaSalle with quadratic Lyapunov function candidates is applied to guarantee the convergence of the ILC algorithms and enable proper setting of the PI-FC parameters. The linear PI controller parameters tuned by the extended symmetrical optimum method are mapped onto the PI-FC ones by the modal equivalence principle. Real-time experimental results for a dc-based servo speed CS are included.

Generic two-degree-of-freedom linear and fuzzy controllers for integral processes

Abstract This paper presents a new framework for the design of generic two-degree-of-freedom (2-DOF), linear and fuzzy, controllers dedicated to a class of integral processes specific to servo systems. The first part of the paper presents four 2-DOF linear PI controller structures that are designed using the Extended Symmetrical Optimum method to ensure the desired overshoot and settling time. The second part of the paper presents an original design method for 2-DOF Takagi–Sugeno PI-fuzzy controllers based on the stability analysis theorem. Experimental results for the speed control of a servo system with variable load illustrate the performance of the new generic control structures.

Replacement of Lyapunov's direct method in Model Reference Adaptive Control with Robust Fixed Point Transformations

The “Model Reference Adaptive Control (MRAC)” is a popular and efficient controller that normally is designed by the use of Lyapunovs 2nd (“direct”) method guaranteeing global asymptotic stability. However, the use of Lyapunov function can entail a relatively complicated tuning that may have disadvantages whenever very fast applications are needed. In this paper an alternative background, the application of “Robust Fixed Point Transformations (RFPT)” working with local basin of attraction of convergence is recommended to simplify this task. As a potential application example the adaptive control of an “Electrostatic Micro-actuator (EμA)” is considered that contains considerable non-linearities. The conclusions of the paper are substantiated by simulation results.

Fixed point transformations-based approach in adaptive control of smooth systems

The mathematical foundations of the modern Soft Computing (SC) techniques go back to Kolmogorov’s approximation theorem stating that each multi-variable continuous function on a compact domain can be approximated with arbitrary accuracy by the composition of single-variable continuous functions [1]. Since the late eighties several authors have proved that different types of neural networks possess the universal approximation property (e.g. [2]). Similar results have been published since the early nineties in fuzzy theory claiming that different fuzzy reasoning methods are related to universal approximators (e.g. in [3]). Due to the fact that Kolmogorov’s theorem aims at the approximation of the very wide class of continuous functions, the functions to be constructed are often very complicated and highly non-smooth, therefore their construction is difficult. As is well known, continuity allows very extreme behavior even in the case of single-variable functions. The first example of a function that is everywhere continuous but nowhere differentiable was given by Weierstras in 1872 [4]. At that time mathematicians believed that such functions are only rare extreme examples, but nowadays it has become clear that the great majority of the continuous functions have extreme properties. The seemingly antagonistic contradiction between the complicated nature of the universal approximators and their successful practical applications makes one arrive at the conclusion that if we restrict our models to the far better behaving “everywhere differentiable” functions, these problems ab ovo can be evaded or at least reduced.

Group theoretical approach in using canonical transformations and symplectic geometry in the control of approximately modelled mechanical systems interacting with an unmodelled environment

In spite of its simpler structure than that of the Euler-Lagrange equations-based model, the Hamiltonian formulation of Classical Mechanics (CM) gained only limited application in the Computed Torque Control (CTC) of the rather conventional robots. A possible reason for this situation may be, that while the independent variables of the Lagrangian model are directly measurable by common industrial sensors and encoders, the Hamiltonian canonical coordinates are not measurable and can also not be computed in the lack of detailed information on the dynamics of the system under control. As a consequence, transparent and lucid mathematical methods bound to the Hamiltonian model utilizing the special properties of such concepts as Canonical Transformations, Symplectic Geometry, Symplectic Group, Symplectizing Algorithm, etc. remain out of the reach of Dynamic Control approaches based on the Lagrangian model. In this paper the preliminary results of certain recent investigations aiming at the introduction of these methods in dynamic control are summarized and illustrated by simulation results. The proposed application of the Hamiltonian model makes it possible to achieve a rigorous deductive analytical treatment up to a well defined point exactly valid for a quite wide range of many different mechanical systems. From this point on it reveals such an ample assortment of possible non-deductive, intuitive developments and approaches even within the investigations aiming at a particular paradigm that publication of these very preliminary and early results seems to have definite reason, too.

A Survey of Technologies for Climbing Robots Adhesion to Surfaces

Climbing robots are being developed for applications ranging from cleaning to inspection of difficult to reach constructions. These machines should be capable of travelling on different types of surfaces (such as floors, walls, ceilings) and to walk between such surfaces. Furthermore, these machines should adapt and reconfigure for various environment conditions and should be self-contained. Regarding the adhesion to the surface, they should be able to produce a secure gripping force using a light-weight mechanism. Bearing these facts in mind, this paper presents a survey of different technologies used for climbing robots adhesion to surfaces.

Dynamics of the fractional-order Van der Pol oscillator

In this paper we propose a modified version of the classical unforced Van der Pol oscillator that occurs when introducing a fractional-order time derivative in the state space equations that describes its dynamics. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, for several values of orders fractional derivative and, consequently, of the total system order. It is shown that the system can exhibit different output behavior depending on the total system order. Several numerical simulations and performance indices illustrate the fractional dynamics

Chaos formation and reduction in robust fixed point transformations based adaptive control

In the design of adaptive controllers for roughly modeled nonlinear dynamic plants the most popular prevalent fundamental mathematical tool is Lypunovs “direct” method. Though normally it guarantees global stability several controller performance parameters of practical engineering significance cannot directly be addressed in this manner. In general simulation investigations or GA-based parameter optimization is needed for refining the controller. A possible alternative of the Lyapunov function technique is the application of Robust Fixed Point Transformation (RFPT) that has only local region of convergence but directly addresses practical needs as error relaxation. In this paper the details of quitting the region of convergence and its consequences are investigated. In the control of a 2 Degree Of Freedom (DOF) paradigm it will be shown that though this process has chaotic features it does not has drastic consequences in the control quality. Furthermore, it also is shown that by a simple smoothing trick this chaos can be refined and reduced to a limited amplitude of chattering that much probably is tolerable in many practical applications.

VS-type stabilization of MRAC controllers using robust fixed point transformations

Nowadays, control of dynamical systems with uncertainties is a common problem. Many sulutions can be found in the literature, one of these methods is the family of Robust Fixed Point Transformations (RFPT) with local basin of attraction. The method is based on the idea that if someone has to use an approximate model in a control task, there is a function which, locally converging to the right solution, can reduce the disadvantages of the approximation. In this paper, authors show that though RFPT can loose its local convergensity, it can still improve a simple controllers results and this improvement makes the controllers behavior very similar to that of a sliding mode controller. The similarity includes the so called chattering effect, but a simple smoothing algorithm is also introuced to minimize the fluctuation of the control signal.

Linear and fuzzy control solutions for a laboratory Anti-lock Braking System

Three slip controllers are designed and implemented on an anti-lock braking system (ABS), a PI controller, one SISO fuzzy controller without dynamics and a PI-fuzzy one. The system is highly nonlinear. The design approaches are based on system modeling and identification and knowledge from experiments. The controllers are based on the local linearization of the controlled plant and the use of fuzzy control in terms of the modal equivalence principle. The simplicity of design and implementation is highlighted by real-time experiments.