Adrienn Dineva

Adaptive control of underactuated mechanical systems using improved "Sigmoid Generated Fixed Point Transformation" and scheduling strategy

With the aim of evading the difficulties of the Lyapunov function-based techniques in the control of nonlinear systems recently the Sigmoid Generated Fixed Point Transformation (SGFPT) has been introduced. This systematic method has been presented for the generation of whole families of Fixed Point Transformations that can be used in nonlinear adaptive control of Single Input Single Output (SISO) as well as Multiple Input Multiple Output (MIMO) systems. This paper proposes a new control strategy based on the combination of the adaptive and optimal control by applying time-sharing in the SGFPT method. The scheduling strategy supports error containment by cyclic control of the different variables. Further, this paper introduces new improvements on SGFPT technique by introducing Stretched Sigmoid Functions. The efficiency of the presented control solution has been applied in the adaptive control of an underactuated mechanical system. Simulation results validate that the proposed scheme is far promising.

Sigmoid generated fixed point transformation control scheme for stabilization of Kapitza's pendulum system

In adaptive nonlinear control Lyapunovs 2nd or Direct method became a fundamental tool in control design. Recently the application of the “Sigmoid Generated Fixed Point Transformation (SGFPT)” has been introduced for replacing the Lyapunov technique. This systematic method has been presented for the generation of whole families of Fixed Point Transformations and has been extended from Single Input Single Output (SISO) to Multiple Input Multiple Output (MIMO) systems. Furthermore, the Stretched Sigmoid Functions have been introduced. In this paper a new function of this family have been investigated in order to obtain a more precise positioning of the function in the vicinity of the solution of the control task. The applicability and effectiveness of the proposed control method have been confirmed by the adaptive control of the inverted pendulum with vertical vibration of the pivot, i.e. the so-called Kapitzas pendulum. Results of numerical simulations have revealed that the proposed control design ensures performance enhancement.

Combination of RFPT-based adaptive control and classical model identification

The traditional approach in the design of adaptive controllers for nonlinear dynamic systems normally applies Lyapunovs “direct” method that has the main characteristic features as follows: a) it yields satisfactory conditions for the stability, b) instead focusing on the primary design intent (e.g. the precise prescription of the trajectory tracking error relaxation) it concentrates on proving “global stability” that often is “too much” for common practical applications, c) in the identification of the model parameters of the controlled system it provides a tuning algorithm that contains certain components of the Lyapunov functions therefore it works with a large number of arbitrary adaptive control parameters; d) the parameter identification process in certain cases is vulnerable if unknown external perturbations can disturb the system under control. In order to replace this technique by a simpler approach concentrating on the primary design intent the “Robust Fixed Point Transformation (RFPT)”-based technique was suggested that - at the cost of sacrificing the need for global stability - applied iteratively deformed control signal sequences that on the basis of Banach Fixed Point Theorem converged to the appropriate control signal only within a bounded basin of attraction. This method was found to be applicable for a wide class of systems to be controlled, it was robust against the unknown external disturbances, used only three adaptive control parameters and later was completed by fine tuning of only one of these control parameters to keep the system in the region of convergence. In the present paper theoretical and simulations based considerations are presented revealing that the two methods can be combined in the control of certain physical systems.

Increased cycle time achieved by fractional derivatives in the adaptive control of the Brusselator model

In the control of chemical reactions the goal is to stabilize the control and take care of the design that has to integrate engineering aspects, as restrictions concerning the control signals, and the phenomenological limits that are not necessarily expressed by the reaction kinetic equations (e.g. no negative concentrations can be physically interpreted, and the reactants at the side of ingress cannot be purely extracted from the stirring tank reactor). In this paper the Robust Fixed Point Transformation (RFPT)-based adaptive approach was chosen for the control of an approximately modeled Brusselator reaction. The main reason of that was the fact that this methodology concentrates on the primary design goals as precise realization of the prescribed concentrations while the more conventional design methods that apply some Lyapunov function mainly concentrate on guaranteeing global stability without providing quasi-optimal solutions for the primary goals. Though the RFPT-based design has only local stability, its region of stability may be quite satisfactory for several practical applications. For controlling chemical reactions Continues Stirring Tank Reactors (CSTR) are widely used engines. The Busselator model will be represented in a CSTR in the simulations. In the present example two different reactants can be injected into the tank and the mixture is taken out in a single outlet. The necessary sampling frequency is a practically important design factor. It is shown that by the use of fractional order derivatives in the prescribed error relaxation considerably increases the necessary sampling time so it decreases the sampling frequency. This statement is substantiated by simulation results.

Replacement of parameter tuning with simple calculation in adaptive control using “Sigmoid generated fixed point transformation”

Lately a systematic method was presented for the generation of whole families of Fixed Point Transformations that can be used in nonlinear adaptive control of Single Input - Single Output (SISO) as well as Multiple Input - Multiple Output (MIMO) systems as alternatives of Lyapunovs direct method. This transformation was called Sigmoid Generated Fixed Point Transformation (SGFPT). This paper introduces new improvements on this alternative approach. It is shown that in contrast to the original Robust Fixed Point Transformation (RFPT), for guaranteeing the global stability of the control, instead of tuning, a simple estimation can be done for one of the adaptive control parameters. The novel method is demonstrated by the adaptive control of a 2 Degree of Freedom (DoF) TORA system. Simulation results validate that the suggested approach is beneficial and ensures satisfactory performance.

Improved Denoising with Robust Fitting in the Wavelet Transform Domain

In this paper we present a new method for thresholding the coefficients in the wavelet transform domain based on the robust local polynomial regression technique. It is proven that the robust locally-weighted smoother excellently removes the outliers or extreme values by performing iterative reweighting. The proposed method combines the main advantages of multiresolution analysis and robust fitting. Simulation results show efficient denoising at low resolution levels. Besides, it provides simultaneously high density impulse noise removal in contrast to other adaptive shrinkage procedures. Performance has been determined by using quantitative measures, such as signal to noise ratio and root mean square error.

Fuzzy expert system for automatic wavelet shrinkage procedure selection for noise suppression

Signal processing is an indispensable issue of several technical areas. Wavelet shrinkage, i.e. thresholding in the wavelet coefficient domain, has been successfully used for signal and image noise removal problems. Although, the selection of the suitable wavelet threshold procedure is still a challenging task, because the applied method has significant impact on the result. Furthermore, the specific choice of wavelet, decomposition level and threshold rule, etc., allows a wide variability of the shrinkage method. This paper presents a new supervisory fuzzy expert system for automatic wavelet shrinkage method selection for noise suppression of unknown signals. Simulation results show efficient performance of the system.

Non-conventional Control Design by Sigmoid Generated Fixed Point Transformation Using Fuzzy Approximation

Lyapunov’s 2nd or Direct method is recognized as being the primary tool of adaptive control of nonlinear dynamic systems. The great majority of the adaptive nonlinear control design rest on Lyapunov’s stability theorem. Recent findings have revealed that the Robust Fixed Point Transformation-based method can succesfully replace the Lyapunov technique. Later the “Sigmoid Generated Fixed Point Transformation (SGFPT)” has been introduced. This systematic method has been proposed for the generation of whole families of Fixed Point Transformations. Its extension from Single Input Single Output (SISO) to Multiple Input Multiple Output (MIMO) systems has also been given. In recent times, the great majority of model building issues are replaced by “Soft Computing” techniques. In contrast to the classical mathematical methods the intelligent methodologies are able to cope with ill-defined systems, disturbances and missing information by an efficient and robust way. Especially fuzzy logic has become to be used to model complex systems. This contribution makes an attempt to utilize the advantages of fuzzy approximation in the SGFPT control design. The theoretical investigations are validated by the adaptive control of the inverted pendulum. Comparative analysis have been carried out between the “affine” and the “soft computing-based” models. Results of numerical simulations confirm the applicability and efficiency of the proposed method.

Robot control in ispace by applying weighted likelihood function

Recently the intelligent space applications have become increasingly beneficial considering robot control. In this paper the visual controlling concept is presented in the iSpace framework. The positions of the end-effector of the robot manipulator are presented by the 3D spatial coordinates extracted from image pairs. The exact image Jacobian matrix of the mapping from Cartesian space to image space is given, the task space controllers can be directly extended to image-space controllers. The Jacobian matrix poses uncertainty if modeling and calibration errors are present. Despite the fact that much progress has been presented in the literature of visual servoing, there are only a few results obtained for the stability analysis in presence of the uncertain camera parameters. This research aims developing a new method for the control of the manipulator in Cartesian space, using the vision information of the environment obtained by cameras using the OptiTrack framework. The robotic manipulator is mounted on a mobile tank. The control scheme allows the end effector to transit smoothly from Cartesian-space feedback to vision-space feedback when the target is inside the vicinity of the camera. Key points on the manipulator are marked which are detected by the camera system. The framework calculates the coordinates of the markers, and thus estimate the state of each joint of the manipulator within a margin of error. In order to achieve the most precise estimation each camera image is weighted during the evaluation. The weights are determined using data set of images. After, a likelihood function is assigned for each joint that is used for defining the position and designing the motion. During the experiments the proposed control concept has proven to be reliable.

Performance enhancement of fuzzy logic controller using robust fixed point transformation

Despite its excellent performance as a controller for linear and non-linear systems, the fuzzy logic controller has certain limitations. For instance, large-scale complex fuzzy systems like multi-input, single-output, or multi-output systems are used in various applications with large number of rules. Furthermore, the results also depend on the selected membership functions, etc. This paper presents a novel framework that instead of reducing the number of rules for a fuzzy logic controller, combines it with a fixed point transformation based adaptive control. The adopted approach is based on the Mamdani-type fuzzy controller and enhanced by the Sigmoid Generated Fixed Point Transformation control strategy to cope with modeling inaccuracies and external disturbances that can arise. The general procedure is applied to a nonlinear Kapitza pendulum. Numerical simulations are validating the applicability of the proposed scheme and demonstrating the controller’s performance.