OP Conference Series: aterials Science and Engineering PAPER OPEN ACCESS A Two-Wheeled, Self-Balancing Electric Vehicle Used As an Environentally Friendly ndividual eans of Transport To cite this article: D Bdziuch and W Grzegoek 6 OP Conf. Ser.: ater. Sci. Eng. 48 3 Related content - Deterination of the Optial Position of Pendulus of an Active Self-balancing Device G R Ziyakaev, O A Kazakova, V V Yankov et al. - A theristor theroeter with digital display P T Priestley - A tie arking device for electronic teperature recorders L ichalski View the article online for updates and enhanceents. This content was downloaded fro P address 46.3.7.46 on //8 at 8:4
Scientific Conference on Autootive Vehicles and Cobustion Engines KONOT 6 OP Publishing OP Conf. Series: aterials Science and Engineering 48 6 3 doi:.88/757-899x/48//3 A Two-Wheeled, Self-Balancing Electric Vehicle Used As an Environentally Friendly ndividual eans of Transport D Bździuch and W Grzegożek nstitute of Transport, Cobustion Engines and Ecology, Lublin University of Technology, Poland nstitute of otor Vehicles and Cobustion Engines, Cracow University of Technology, Poland E-ail: witek@ech.pk.edu.pl Abstract: This paper shows a concept of a odel of a two-wheeled self-balancing vehicle with an electric otor drive as an environentally-friendly personal transporter. The principle of work, odelling of construction and perforing a siulation are presented and discussed. The visualization of the designed vehicle was ade thanks to using Solid Works a coputer-aided design progra. The vehicle was odelled as an inverted pendulu. The stability of the echanis in the equilibriu position was studied. An eeplary steering syste was also subjected to the analysis that copared two controllers: PD and LQR which enabled to onitor the balance of the vehicle when the required conditions were fulfilled. odelling of work of the controllers and the evaluation of the obtained results in required conditions were perfored in the ATLAB environent.. ntroduction Rapid technology developent and progress in civilization akes the nuber of cars grow constantly. These are ainly vehicles powered by cobustion, whose efficiency is relatively sall in coparison to efficiency of the electric engine - 3 ties saller on average [],[]. Their ajor defect is eission of toic copounds such as CO, CO, NO, HC contained in ehaust gases. This factor, together with the increase in environental requireents, akes producers and constructors introduce a nuber of changes and iproveents so that their products eet progressively ore restrictive eission standards. As a consequence, the produced vehicles are equipped with precise, coplicated systes which are epensive to repair. Despite all their defects, cobustion vehicles are still very coon firstly, because of the relatively long distances they cover on one tank of petrol it results fro the ratio of power to energy obtained fro kg of 4J fuel, and to energy obtained fro kg of J battery[]. n recent years electric vehicles are getting ore and ore popular. They offer a nuber of advantages, such as high efficiency, siple construction and steering, however, not enough charging stations, sall distances they cover and a long tie of charging in coparison to refuelling of a traditional vehicle put the at a distinct disadvantage. Nevertheless, those probles, thanks to rapid technology developent, will be probably easy to tackle with in the near future. Their ain advantage is the fact that the vehicles with electric engines do not produce ehaust fues and electricity ay be obtained fro renewable energy sources, e.g. solar energy obtained fro photovoltaic cells. Prooting electric vehicles through granting financial incentives, free parking and free charging, etc. [3], [4], are additional benefits. Despite the nuber of advantages, electric vehicles Content fro this work ay be used under the ters of the Creative Coons Attribution 3. licence. Any further distribution of this work ust aintain attribution to the authors and the title of the work, journal citation and DO. Published under licence by OP Publishing Ltd
Scientific Conference on Autootive Vehicles and Cobustion Engines KONOT 6 OP Publishing OP Conf. Series: aterials Science and Engineering 48 6 3 doi:.88/757-899x/48//3 do not present a large share of the global autootive arket. n order to eet present epectations and requireents connected to environental protection, the idea of an urban, two-wheeled, electric and self-balancing vehicle which is environentally friendly and has wide options for use, was drawn.. Principle of operation The first self-balancing vehicles were constructed in the first half of the th century, but they were not very popular, ainly because they did not have autoated systes enabling control over the vehicle's pitch angle. With tie, new self-balancing vehicles were constructed, and the ost known are Segway vehicles. The Segway's idea is based on the concept of inverted pendulu figure. Figure. nverted pendulu odel. where: ass of vehicle platfor, point ass attached to the end of a rod, L length of the rod, α daping ratio, φ pivot angle, coordinate describing oveent of the centre of the ass of the platfor, g weight force applied to the point ass. The syste has a siple structure and principle of operation. By oving the vehicle platfor horizontally, the rod with the point ass concentrated in its end should be balanced vertically φ. The proble that needs to be solved is the control of the vehicle, which is instable. Dean Kaen Segway's inventor, created a very siple solution based on a huan brain behaviour [5]. A an, when leaning forward, for eaple, saves hiself fro falling by putting his leg in the direction he is leaning to. Segway works in the sae way. The horizontal position with the pitch angle equalling zero φ is 'noral' for the vehicle. The oent we tilt the vehicle, it reads fro the gyroscopic sensors the value of the pitch angle and then reacts correspondingly by transferring the corrected strength value to the wheels in order to prevent the construction fro falling, which akes it ove until the pitch is eliinated. This ethod is called dynaic stabilization. A atheatical odel of a selfbalancing vehicle ay be written down in the for of differential equations of the inverted pendulu oveent of the figure. Deriving the forulae was skipped.
Scientific Conference on Autootive Vehicles and Cobustion Engines KONOT 6 OP Publishing OP Conf. Series: aterials Science and Engineering 48 6 3 doi:.88/757-899x/48//3 l cos sin l l cos gl sin α Bringing the above syste to the for of linear function, assuing sall tilts, we get the following for of equations: sin cos The above forula ay be presented in the following way: l l l gl l l g t is noticeable, that the forula in brackets coprises of constants and adopts a constant value and that is why it ay be replaced with a deterined constant. l c l l c g The equation 4 has to be tested by the Routh Hurwitz stability criterion, having developed it earlier into the for of characteristic equation. Theore. Stability precondition f a given polynoial is a Hurwitz polynoial, then all its coefficients are positive. Theore. Hurwitz stability sufficient condition A given polynoial is a stable polynoial only if all its principal inors are positive. Assuing the solution in the for of φte rt, calculating subsequent derivatives and putting the into the equation 4 we get the characteristic equation 5: 3 4 g r 5 c According to the Routh Hurwitz stability criterion, precondition of single-root polynoial coefficients was not satisfied, because the constant c assues negative value, it results fro the equations 4 and 5. The syste has instable balance location with the angle φ, that is with initial position for regulation by steering algorith. 3. Concept of the vehicle n the world, there are various solutions used in self-balancing vehicles, such as Segway or E.D.W.A.R.D, constructed by students in Adelaide, the vehicle which is an interesting object with three operating odes. A concept of a two-wheeled, self-balancing, electric vehicle with seats presented in figure was based on the odel in Figure. The basic assuption was to design a light, electric vehicle whilst, first of all, putting safety in the first place. The vehicle has unusual appearance 3
Scientific Conference on Autootive Vehicles and Cobustion Engines KONOT 6 OP Publishing OP Conf. Series: aterials Science and Engineering 48 6 3 doi:.88/757-899x/48//3 with regular shapes and copact structure that allows two people with soe sall baggage to travel cofortably. Figure. Concept of the self-balancing vehicle. The frae is the basic eleent which, according to assuptions, is supposed to be ade of light alloy aterial. Hub-less wheels that increase side visibility, are also worth noticing. Two electric engines that allow to steer each wheel separately, for eaple during rotating in place, are supposed to be driving eleents. The steering syste contained in a icroprocessor controller and a syste of sensors easuring pitch angle of the vehicle, aong others, are the heart of the construction. A sliding windscreen akes it possible to travel with open passenger space on sunny, and closed on rainy days. Drive and steering eleents are located between lower cover and the floor board, which allows to ake better use of space. The vehicle is supposed to be easy to disantle in order to have easy access to individual devices. At the oent the assuption is to steer the vehicle with one lib only. Another assuption is to work in a few stabilization odes and using state-of-the-art technologies to counicate with the vehicle through obile devices, for eaple. 4. Control syste An outline of the control syste for the siplified odel of the inverted pendulu shall be described. Operation of PD and LQR regulators shall be presented. n order to analyze a siple syste the ATLAB progra with ipleented PD and LQR regulator was used [6], [7]. A sall pendulu odel with the oent of inertia and the rod ass instead of the point ass attached to its end as well as friction were taken into account. b- coefficient of linear duping - oent of inertia of the rod - ass of the rod u- forcing l gl l b l u 6 4
The above presentation will be transfored into state-space representations. Thanks to state-space representations the relations between forcing and response are derived and they can be connected by state variables 7. n order to derive the state forula, the following state variables should be assued: 4 3 7 After transforations we get state equations written in the atri for u l l l l l gl l lb l gl l b l u y 8 Output atri has two lines, as the response of y syste consists of two eleents, that is the location of the cart and pivot point of the pendulu φ. The siulation was perfored of the following data:.6[kg] ass of the cart.[kg] ass of the pendulu b.[n//s] coefficient of linear duping l.3 [] distance between the centre of the ass of the pendulu and pivot ais.3 [kg* ] oent of inertia of the pendulu The requireents for the syste: achieving the wanted position in the tie of up to 5 seconds, rise tie for less than.5s, pitch angle of the pendulu always saller than fro vertical location, steady-state error saller than % for and φ. Then the siulation was perfored. Below there are the results for various options of operation of the regulators. The PD regulator was analyzed as first. The value of all forcing coefficients equalling was the starting point. The syste did not eet the requireents, so the control paraeters had to be changed appropriately. By trial and error, the control paraeters that allowed to eet the requireents were selected. The course of the response presented in figure 3 is satisfying because the basic requireents for the syste were et: the pitch angle is not higher than.5 and, at the sae tie, the pendulu is stabilized after seconds. ts course is sudden, but it ay be optiised by selecting the right forcing coefficients. Scientific Conference on Autootive Vehicles and Cobustion Engines KONOT 6 OP Publishing OP Conf. Series: aterials Science and Engineering 48 6 3 doi:.88/757-899x/48//3 5
Scientific Conference on Autootive Vehicles and Cobustion Engines KONOT 6 OP Publishing OP Conf. Series: aterials Science and Engineering 48 6 3 doi:.88/757-899x/48//3 Figure 3. Response of the inverted pendulu controlled by PD. Figure 4. Response of the inverted pendulu controlled by LQR. 6
Scientific Conference on Autootive Vehicles and Cobustion Engines KONOT 6 OP Publishing OP Conf. Series: aterials Science and Engineering 48 6 3 doi:.88/757-899x/48//3 The LQR regulator was analysed as second. The work with LQR regulator consists in selecting proper weights and iniising costs between syste errors and the effort put into controlling. First, the sae weights were selected but the syste did not eet the requireents. Net, the weights that reduce control follow errors were odified, but they increase the force put into controlling and so increase the need for energy. The pitch angle of the pendulu and the rise tie presented in figure 4 are satisfying, the pendulu is stable after.5 seconds. Precopensation was also added. t is done to iniise steady-state error. Both PD and LQR regulators are suitable to be used in the control syste of the self-balancing vehicle. n practical control systes cobinations of both regulators are soeties applied in order to iprove the quality of control. 5. Conclusion This article presents the concept of a two-wheeled, self-balancing electric vehicle as an individual eans of transport. Such a vehicle could be used in the city centres, as it is environentally friendly and easy to control. The use of electric engines helps eliinate such subasseblies as a gear bo used in traditional vehicles thus decreasing the ass and increasing the accessible space. t could successfully function in the network of rental copanies - one could rent the vehicle in one place and leave it in another without the need to return to the initial spot. n recent years nuerous concept odels of self-balancing vehicles for urban traffic have been developed. Developent of the technology based on dynaic stabilization lets the driver control the vehicle of this type ore effectively with iniizing the losses during controlling the vehicle. The presented concept proves that it is a construction that can be based on the inverted pendulu odel and control balance with the use of siple regulators, such as PD or LQR. Despite its unusual design, the vehicle can be viewed as fully functional in everyday life. 7
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