Andrzej Koszewnik

The parrot UAV controlled by PID controllers

Abstract The paper presents the process of modeling and designing control laws for four-rotor type of the Parrot UAV. The state space model is obtained by using several phenomena like gyroscopic effects for rigid bodies, propellers and rotors. The obtained model has been used to design PID control laws for roll, pitch, yaw angle and altitude, respectively. The numerical simulations of the closed loop model are shown that system in satisfy way stabilize flight of the quadro-rotor in all considered directions.

Modeling of Beam as Control Plane for a Vibration Control System

An active vibration damping system with the use of piezoelements fixed to the structure is presented in the paper. The optimal location of the piezo-stripes on the structure is calculated for given cost functions. Coefficient correlations between control forces, strains, mode shapes, frequency changes, modal masses and modal stiffness are analyzed in order to find simpler method for calculation of the quasi-optimal localization of piezo-sensors and piezo-actuators. Reduced model of the open-loop system was identified and the simulations were carried out in order to find the best controller to reduce the amplitude of vibrations. The correctness of the selection of the controller was verified and investigated experimentally.

Reduction Methods of Structure Models for Control System Purposes

To design vibration control system for flexible structures their mathematical model should be reduced. In the paper we consider the influence of the model reduction on the dynamics of the real closed-loop system. A simply cantilever beam is an object of consideration since we are able to formulate the exact analytical model of such structure. As a result of reduction the model with low frequency resonances is usually separated from the high frequency dynamics because high frequency part of the model is naturally strong damped. In order to estimate dynamical system for control purposes in the paper we applied a few orthogonal methods such as: modal, Rayleigh-Ritz and Schur decompositions. As it is shown all methods well calculate resonances frequencies but generate different anti-resonances frequencies. From control strategy in point of view of the flexible structures these anti-resonances have significantly influence on the stability and dynamics of the closed-loop systems.

Frequency Domain Identification of the Active Beam Model for the Vibration Control System

An identification procedure of the active vibration damping system with the piezo-elements glued to the structure is presented in the paper. Such identification can be carried out in analytical way (Guyan reduction) by using of low-band pass amplifiers. First, we have identified the open loop system in the frequency domain by using experimental setup with real amplifier and beam equipped in piezo-strips working as actuators and sensor, respectively. For the frequency range 1 Hz to 400 Hz we have obtained Bode plots with helped of Dynamic Signal Analyzer which were base to further calculations. Second, mathematical model have been adjusted to the experimental results by the least square sum approach and also by the consideration of a system which was modeled by finite elements. A three first resonance frequencies and three first anti-resonance frequencies have obtained.

Desiginig of active vibration control system for smart structure 2-D with non-collocated piezo-elements

To design vibration control system for flexible structures their mathematical model should be reduced. In the paper we consider the influence of the model reduction on the dynamics of the real closed-loop system. A SFSF smart plate as a TITO system is an object of consideration since we are able to formulate the exact analytical model of such structure. As a result of reduction the model with low frequency resonances is usually separated from the high frequency dynamics because high frequency part of the model is naturally strong damped. In order to estimate dynamical system for control purposes in the paper we applied a few orthogonal methods such as: modal and Schur decompositions. As it is shown all methods well calculate resonances frequencies but generate different anti-resonances frequencies. From control strategy in point of view of the flexible structures these anti-resonances have significantly influence on the stability and dynamics of the closed-loop systems.

The active vibration control of the plate structure by using LQG controller and piezo-stripes

The active vibration control of SFSF (Simply Supported-Free-Simply Supported-Free) smart plate by using linear quadratic Gaussian (LQG) controller is described in the paper. In order to design proper optimal control law two pairs of PZT actuators and sensors oriented in two perpendicular directions X and Y are glued to the plate. The aforementioned locations and orientations of PZT elements allow to decouple the TITO system onto two SISO subsystem for separately control odd and even modes. The process of design LQG controller is performed in two stages. In the first stage with using Matlab software the parameters of controllers are determined based on the simulations results in time and frequency domains. On the other hand, in the second step the designed controllers are verified on the lab stand by implemented control laws to real time processor (Dspace).

Modelling and testing of the piezoelectric beam as energy harvesting system

Abstract The paper describes modelling and testing of the piezoelectric beam as energy harvesting system. The cantilever beam with two piezo-elements glued onto its surface is considered in the paper. As result of carried out modal analysis of the beam the natural frequencies and modes shapes are determined. The obtained results in the way mentioned above allow to estimate such location of the piezo-actuator on the beam where the piezo generates maximal values of modal control forces. Experimental investigations carried out in the laboratory allow to verify results of natural frequencies obtained during simulation and also testing of the beam in order to obtain voltage from vibration with help of the piezo-harvester. The obtained values of voltage stored on the capacitor C0 shown that the best results are achieved for the beam excited to vibration with third natural frequency, but the worst results for the beam oscillating with the first natural frequency.

PID CONTROLLERS DESIGN APPLIED TO POSITIONING OF BALL ON THE STEWART PLATFORM

Abstract The paper presents the design and practical implementation of PID controllers for a Stewart platform. The platform uses a resistance touch panel as a sensor and servo motors as actuators. The complete control system stabilizing the ball on the platform is realized with the Arduino microcontroller and the Matlab/Simulink software. Two processes required to acquire measurement signals from the touch panel in two perpendicular directions X and Y, are discussed. The first process includes the calibration of the touch panel, and the second process - the filtering of measurement signals with the low pass Butterworth filter. The obtained signals are used to design the algorithm of the ball stabilization by decoupling the global system into two local subsystems. The algorithm is implemented in a soft real time system. The parameters of both PID controllers (PIDx and PIDy) are tuned by the trial-error method and implemented in the microcontroller. Finally, the complete control system is tested at the laboratory stand.

Active Vibration Control Method for Space Mechanical Structure with Piezostacks

Mechanical structures are spatial, three-dimensional (3D) systems of distributed parameters. They present quite complicated plants, if methods of control systems theory are applied. The design process of the vibration control system for such plants is extremely difficult and requires an extensive heuristic knowledge. The subject of the control system is to eliminate the vibrations of the free end at the plane parallel to the foundation Similar problems are met, when the stabilization of robot arms, antennas, satellite solar batteries or slender skyscrapers is considered. In the paper we have presented the 3D bar structure with sticked parallel two piezo-stacks into bars. Recall piezo-elements are actuators, but sensors are two eddy-current sensors located in near free end the structure in perpendicular directions X and Y. Thus the whole structure is TITO (Two Input Two Output) system. For such system the control law was designed with used LQR controller. Above controller was designed for coupled and decoupled system also. In both case a correct damp and very short period of the vibration were criteria to choose the controller parameters. All investigations were carried out in two steps. In the first step control laws were designed in computer simulation. In the second step these control laws were verified experimentally on the laboratory stand by using DSP. Finally, desired control laws were compared.