SDRE Control Applied to the Wheel Speed of a Compressed

Copyright © 2017 Alexandre de Castro Alves et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Renewable energy sources for vehicles have been the motivation of many researches around the world.The reduction of fossil fuels deposits and increase of the pollution in cities bring the need of more efficient and cleaner energy sources. In this way, this work will present the application of a compressed air engine applied to a bicycle. The engine is composed of two pneumatic cylinders connected to the bicycle wheel through a crank-connecting-rod mechanism. In order to control the velocity of the bicycle, a strategy of control composed of two controls was implemented: a feedback and a feed forward control. For feedback control, the State-Dependent Riccati Equation (SDRE) control and also a proportional-derivative (PD) control are considered, considering three cases for velocity bicycle variation: 10 km/h, 20 km/h, and 30 km/h.The equations of motion of the system were obtained through the Lagrangian energy method. Numerical simulations were performed in order to analyze the dynamics of the system and the efficiency of the controllers.

1. Introduction

Connecting rod

In a reciprocating piston engine, the connecting rod or conrod connects the piston to the crank or crankshaft. The connecting rod was invented sometime between 1174 to 1200 when a Muslim inventor, engineer and craftsman named al-Jazari built five machines to pump water for the kings of the Turkish Artuqid dynasty — one of which incorporated the connecting rod. Transferring rotary motion to reciprocating motion was made possible by connecting the crankshaft to the connecting rod, which was described in the "Book of Knowledge of Ingenious Mechanical Devices". The double-acting reciprocating piston pump was the first machine to offer automatic motion, but its mechanisms and others such as the cam, would also help initiate the Industrial Revolution.

Compound connecting rod

Many-cylinder multi-bank engines such as a V-12 layout have little space available for that many connecting rod journals on a limited length of crankshaft. This is a difficult compromise to solve and its consequence has often led to engines being regarded as failures.

The simplest solution, almost universal in road car engines, is to use simple rods.This requires the rod bearings to be narrower, increasing bearing load and the risk of failure in a high-performance engine. This also means the opposing cylinders are not exactly in line with each other.

In certain types of engine, the master rod carries one or more ring pins to which are bolted the much smaller big ends of slave rods on other cylinders. Radial engines typically have a master rod for one cylinder and slave rods for all the other cylinders in the same bank. Certain designs of V engines use a master/slave rod for each pair of opposite cylinders. A drawback of this is that the stroke of  the subsidiary rod is slightly shorter than the master, which increases vibration in a V engine. The usual solution for high-performance aero-engines isa "forked" connecting rod. One rod is split in two at the big end and the other is thinned to fit into this fork. The journal is still shared between cylinders. The Rolls-Royce Merlin used this style.

Crank linkage of the type and characteristics

The use of the internal combustion engine crank linkage of many types, according to kinematics perspective can be pided into three categories,namely: Heart crank linkage, the eccentric crank linkage and the main vice-link crank linkage. Centre crank linkage is characterized by the cylinder through the center line of the crankshaft rotation centre and perpendicular to the axis of rotation of the crank. This type of linkage in the internal combustion engine crank in the most widely used. The single-engine general, tied for linkage with the use of the V-shaped chaxing link the internal combustion engine, and the home of the piston internal combustion engine crank linkage fall into this category. Eccentric crank linkage is characterized by vertical cylinder centerline of the crankshaft rotating in the center, but not by crankshaft rotary centre, the cylinder centerline distance between the crankshaft with a rotary axis offset e. This crank linkage institutions can reduce the swelling in the itinerary of the piston and cylinder intramural largest lateral pressure so that the pistons in the expansion programme and pressure reduction programme in the cylinder wall at the role of lateral pressure on both sides of the relatively uniform size. Vice-link the main crank linkage is characterized by: the internal combustion engine cylinder with a main link, the other out vice-link cylinder used, these are not direct link to the bottom of the crank pins, but on sale through the deputy link with in the main link of the big heads, formed a "joint" movement, such institutions also sometimes referred to as "joint song stalk linkage ".Crank linkage in the joint, a crank can put a few of connecting rod and piston, This structure will shorten the length of the internal combustion engine, compact and widely used in high-power locomotives used tanks and V-shaped internal combustion engine.