Teréz A. Várkonyi

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.

Fuzzy parameter tuning in the stabilization of an RFPT-based adaptive control for an underactuated system

In this paper a “Robust Fixed Point Transformation (RFPT)” based adaptive control of an underactuated physical system is stabilized by adaptively tuning only one parameter of a single fuzzy membership function. This approach serves as an alternative to Lyapunovs “direct” method that suffers from mathematical difficulties when a Lyapunov function candidate has to be found for the control of a dynamically singular or badly conditioned system as an underactuated cart plus double pendulum. In our case the reaction forces of the directly driven two rotary axles are used for controlling the linear motion of the cart within possible physical limits. As a modification of the common TORA (Translational Oscillations with an Eccentric Rotational Proof Mass Actuator) that has only one counterweight, the present solution applies two counterweights: one of them is actively used and the other one is kept in a “safe” position while the system is far from the dynamic singularity. When the singularity is approached the reserved axle takes the active role and the previously used weight is moved back to the nonsingular region. This session results in oscillatory motion that precisely has to be implemented by the controller. Instead developing complete and generally useful system model this approach extracts information on the recent behavior of the controlled system only in the given control situation by using only three adaptive control parameters. Two of them can be kept fixed but the third one may need fine tuning for stable control. Now a formerly proposed intricate tuning strategy is replaced by simple fuzzy tuning. It is illustrated by simulations that the controller can precisely track the prescribed trajectory even in the presence of considerable modeling errors and badly conditioned dynamics.

Robust Fixed Point Transformations in Chaos synchronization

Due to the technical difficulties related to the practical application of Lyapunovs 2nd or “direct” method in the adaptive control of nonlinear systems as an alternative approach the use of “Robust Fixed Point Transformations (RFPT)” were suggested on the basis of recent researches. Various application possibilities were revealed for the new controller and design for imprecisely and partially modeled fully and underactuated Classical Mechanical Systems, Electromechanical Systems by direct utilization and within the frames if the “Model Reference Controllers (MRAC)”. In the present paper a novel application, the synchronization of coupled, chaotic systems is considered. It is shown that besides the “traditional” problem tackling normally based on the use of Lyapunov functions the RFPT based approach can be successful, too. This statement is illustrated via simulation results for the synchronization of the Fitz-Hugh-Nagumo (FHN) neuron model.

Fuzzyfied Robust Fixed Point Transformations

Nowadays Fuzzy Logic Controllers (FLC) are getting more and more prevalent because of their friendly formalism and capability of using heuristic information. In many cases, traditional controllers are replaced with fuzzy techniques because they can handle systems with highly nonlinear or partly unknown models. The family of Robust Fixed Point Transformations (RFPT) has been partly developed to solve control tasks without knowing the exact parameters of the used model. This makes RFPT suitable to combine with Fuzzy Controllers resulting in the improvement of the performance of FLC. In this paper, a new RFPT-based Fuzzy Logic Controller is introduced on a cart-pendulum system. The simulations show that the more extreme situations we pick the more significantly the built-in RFPT can improve the Fuzzy Logic Controllers results.

Improved neural network control of inverted pendulums

Nowadays, neural network controllers (NNCs) are getting more and more prevalent because they are able to handle unknown systems by learning them and adapt to their changing behaviour. The family of robust fixed point transformations (RFPT) has been partly developed to solve control tasks without knowing the exact parameters of a controlled system. When disturbances effect a plant or the neural network controller is not trained properly RFPT integrated to the controller is suitable to reduce the problems caused by the model approximation and make the controller robust to the unknown external forces. In this paper, a novel combination of neural networks and robust fixed point transformations is introduced to balance an inverted pendulum on the top of a cart of changing nominal position. The results show that the inaccuracies caused by the disturbances can be reduced significantly when RFPT is used in the control process.

Survey on the control of time delay teleoperation systems

In the field of remotely controlled systems, stability is an issue researchers have to deal with. The reason is that usually, in such tasks, time delay occurs, which makes it challenging to design stable controllers. For this reason, more dedicated research has been started to determine the stability properties of time delay systems, particularly of bilateral teleoperation systems, and find stable control strategies. In this paper, authors show that the recent control solutions for time delay teleoperation systems open a new dimension for the interpretation of the basic concepts of controlling systems in general, and make the reevaluation of these concepts necessary. Traditional methods fail in many cases due to stability issues particularly when the time delay is varying or communication blackout occurs. The paper gives a brief overview of different techniques and discusses their applicability.

On the simulation of RFPT-based adaptive control of systems of 4 th order response

As an alternative of Lyapunov functions based design methods the “Robust Fixed Point Transformations (RFPT)”-based adaptive control design was developed in the past years. The traditional approaches emphasize the global stability of the controlled phenomena while leaving the details of the trajectory tracking develop as a not very clear consequence of the control settings the novel design directly concentrates on the observable response of the controlled system therefore it can concentrate on the tracking details as a primary design intent. Whenever a Classical Mechanical system that normally produces 2nd order response (i.e. acceleration) is forced through an elastic component its immediate response becomes 4th order one. Practical observation of the 4th order derivatives of a variable may suffer from measurement noises. Furthermore, when in simulation studies the higher order derivatives are numerically integrated and later numerically differentiated to provide the appropriate feedback signals the non-smooth jumps in the numerical integrator can destroy the simulation results. By the use of a simple 4th order model in this paper it is shown that the chained use of the built-in differentiators of the simulation package SCILAB is inappropriate for simulation purposes. It is also shown that by the use of a simple 4th order polynomial differentiator this problem can be solved. This statement is substantiated by simulation results.

Simple noise reduction in the adaptive synchronization of coupled neurons by Robust Fixed Point Transformation

To avoid the general mathematical difficulties of the application of Lyapunovs “direct” method in adaptive control in the present paper an alternative approach, the use of “Robust Fixed Point Transformation (RFPT)” is applied for the adaptive synchronization of two coupled, asymmetric, chaotically behaving, approximately known Fitz — Hugh — Nagumo (FHN) neurons. Since the RFPT scheme is based on the use of the “Expected — Realized Response Scheme” the noise in the observed quantities may influence the efficiency of the controller. For this purpose the use of a very simple, easily realizable technique is proposed that applies polynomial filtering coefficients in the time domain. Its efficiency is investigated and substantiated via extended simulation investigations.

Simple practical methodology of designing novel MRAC controllers for nonlinear plants

Besides realization of precise trajectory tracking a Model Reference Adaptive Controller (MRAC) has also provide the “external controller” with an illusion that instead of the actual system under control it deals with a “reference system” of quite different dynamic properties. The traditional MRAC approaches normally apply either analytical or universal approxi-mators based models and Lyapunovs 2nd method that can guarantee global (sometimes asymptotic) stability but leaves the question of kinematic and dynamic limitations open. Such details can be clarified by ample numerical computations used either for satisfying the conditions of stability itself or for optimizing the free parameters of the controllers by some Genetic Algorithm or other evolutionary methods. A recently introduced novel family of MRAC controllers the design of which drops Lyapunovs technique and directly concentrates on the kinematic and dynamic details is based on Robust Fixed Point Transformation (RFPT). It has only three adaptive parameters that can easily be set via only a few simulations. In this paper this simple and practical methodology is exemplified in the design of a new MRAC control for a strongly coupled two mass points - two nonlinear springs system in fully actuated and un-deractuated versions, too.

HSV color space based buoy detection module for autonomous underwater vehicles

In this paper, we describe the development and the testing process of an underwater buoy detection module (package) written for the Robot Operating System (ROS). We developed this module for the euRathlon 2015 challenge held in Piombino, Italy. Underwater conditions make it very difficult to use the RGB color space for object detection. Challenges include issues with underwater lighting, reflection and ray scattering. Initial testing was performed in a simulated environment using the UWSIM ROS package and live testing was primarily conducted at the competition on a Sparus II Autonomous Underwater Vehicle (AUV).