Paweł Olejnik

Mathematical model, computer aided design and programming of a multifunctional flying object

The quadrocopter, an unmanned aerial vehicle (UAV), is a type of aerodynamic object using thrust generated by the propellers revolving around the rotor mast. The main areas of focus for complete design and engineering research should be on its stabilization and realization of tasks to be performed during flight. To accomplish these tasks, it is necessary to consider the following stages: modeling of motion dynamics, computer-aided design, programming of the control unit, precise implementation, carefully selected motors and sensors, i.e. a gyroscope, accelerometer, camera, communication module, GPS module, and others. The presented results of research and experiments carried out at Lodz University of Technology in the Department of Automation and Biomechanics take into consideration most of these issues.

An Overview of ATmega AVR Microcontrollers Used in Scientific Research and Industrial Applications

Nowadays, microcontrollers are commonly used in many fields of industrial applications previously dominated by other devices. Their strengths such as: processing power, low cost, and small sizes enable them to become substitutes for industrial PLC controllers, analog electronic circuits, and many more. In first part of this article an overview of the Atmel AVR microprocessor family can be found, alongside with many scientific and industrial applications. Second part of this article contains a detailed description of two implementations of ATmega644PA microprocessor. First one is a controller with PID regulation that supports a DC motor driver. Second one is a differential equation solver with 4-th order Runge-Kutta method implemented. It is used for solving a torsion pendulum dynamics. Finally, some general conclusions regarding the two presented implementations are made.

Modeling And Parameter Identification Of Vibrations Of A Double Torsion Pendulum With Friction

Abstract The purpose of this paper is to investigate a double torsion pendulum with planar frictional contact. The single torsion pendulum with one-degree-of-freedom is an angular equivalent of the linear harmonic oscillator. The second degree of freedom has been obtained by adding a free body to the inverted single torsion pendulum. The free body’s angular displacement is caused by frictional forces appearing in the interface (contact zone) between the free body and the pendulum column’s head kinematically excited at its base by a mechanism with torsion spiral spring. An experimental station has been set up and run to find most unknown parameters of the pendulum from the time series of state variables taken as inputs to the Nelder-Mead method of identification. The obtained results proved significant usability of the identification method in the case of numerical simulation of the pendulum’s dynamical model. It has not been satisfactorily proved in the case of time characteristics coming from a real system that exhibits also some unrecognized physical effects.

Near the resonance behavior of a periodicaly forced partially dissipative three-degrees-of-freedom mechanical system

In this paper, a nonlinear three‐degrees‐of‐freedom dynamical system con‐ sisting of a variable‐length pendulum mass attached by a massless spring to the forced slider is investigated. Numerical solution is preceded by applica‐ tion of Euler‐Lagrange equation. Various techniques like time histories, phase planes, Poincaré maps and resonance plots are used to observe and identify the system responses. The results show that the variable‐length spring pendulum suspended from the periodically forced slider can exhibit quasi‐periodic, and in a resonance state, even chaotic motions. It was con‐ cluded that near the resonance the influence of coupling of bodies on the system dynamics can lead to unpredictable dynamical behavior.

Effectiveness of the Sliding Mode Control in a Two Coupled Discontinuous Dynamical Systems with Dry Friction

Numerical modeling and a tracking control of angular velocity of a rotor measured in the assumed sliding contact bearing subject to a discontinuous dynamical loading has been performed in this contribution. A contact interface in the direct current motor’s sleeve bearing has been treated as a dynamical system with dry friction, including a few sources of the stick-slip and creep-slip effects. The object of control is subject to an irregularly changing torque generated by another discontinuous dynamical system with friction. The loading comes from a block-on-belt model of a conveyer system with intensification of friction force, which has been elastically coupled with the direct current rotor’s shaft by means of the transmission belt. Therefore, the dynamic loading of the DC motor changes because of time-varying linear velocity of two belts. If such additional torque oscillates while the rotational velocity of the motor’s shaft is small due to a requirement, then it significantly affects the entire system’s dynamics producing stronger nonlinear response of the motor’s speed.

Impact of Varying Excitation Frequency on the Behaviour of 2-DoF Mechanical System with Stick-Slip Vibrations

Article shows the influence of varying excitation on dynamics of a 2-DoF mechanical system. The system consists of a vibrating block on a transmission belt driven by a DC motor. Stick-slip frictional effects between the block and the belt introduce significant varying of load affecting the operation of the driving system. Resultant unsteady rotational velocity of the DC motor acts as a time varying excitation for the vibrating system. Behaviour of the analysed system was investigated and compared with its response to a periodic excitation. Mathematical models of the block-on-belt system with normal force intensification mechanism and a DC motor driving system with worm gear have been developed and virtualized. Controlled changes of selected model parameters were made providing interesting results visible on the bifurcation diagrams.

Analog Electronic Test Board for an Estimation of Time Characteristics of the Basic Elements of Automatic Control Systems

This work presents the design and implementation of an analog electronic test board (AETB) for determining the time characteristics of basic elements of automatic control systems. Test signals are formed to study time responses of open and closed-loop basic control systems. In the practical part, a laboratory test board was designed and manufactured. Electronic components have been installed on a PCB prototype and the whole system has been enclosed in a polycarbonate box containing BNC junctions to connect it with an external oscilloscope. The device has been divided into functional blocks such as power supply, signal generator and a system containing basic elements of automation. Moreover, parameters of both the generator and the basic elements are tunable. By using the AETB test board, it is possible to analyze properties of the PID controllers as well as the first and second-order basic elements. In the preliminary stage of the design, numerical simulations allowed to choose proper values of most electronic components. Finally, a few waveforms were examined on the oscilloscope to make a comparison with the simulation results.

Programming and Computer Simulation of an Experimental Station for Automatic Launching of Badminton Shuttlecocks

The aim of this work is to construct and program an experimental station for an automatic launching of badminton shuttlecocks. The station should operate as a prototype device used to help badminton players improve their training, provide recurrence and precision of various badminton shots. It extends certain knowledge in the field of programming of microcontrollers. The system of automatic launching of shuttlecocks has been designed and started by running two speed-controlled DC motors driving a spinning aluminum rings. In order to build the appropriate system a stepper motor based gripper has been applied to pull out all shuttlecocks from a tube. The control system of the designed device is based on a C program that has been implemented on a microcontroller. The speed, scope and frequency of shots are adjustable regarding to the player’s requirements and abilities. In order to widen the station’s applicability, the additional remote control system was incorporated into the control unit. The investigations performed with the station were focused on numerical simulations and basic experimental verification of the expected trajectory.