Modeling And Control Of Self-Balanced Bicycle

Gyroscopes have been widely used in stabilizing both the rolling motion of large ships and trajectories of spacecrafts and satellites.It goes back to 1905,when Irish-Australian mechanical engineer Louis Brennan studied and implemented the idea of stabilizing a monorail using the precession effect of the gyroscope for the first time.Though gyroscopes have been used for stability and navigation control of large-scale vehicles,however,it has rarely been applied in small ground based vehicles.In this study,a bicycle is modeled and statically stabilized using Control Moment Gyroscope(CMG)as an actuator.A CMG consists of a spinning flywheel mounted in a gimbal that tilts the flywheel.When a torque is applied to an axis normal to the spinning axis of flywheel,it causes the change in spin angular momentum of flywheel,which finally results in the precession of gyroscope along the third axis orthogonal to both the torque and spin axes.The main idea is to control the precession speed of gyroscope relative to the body(i.e.bicycle)in order to generate a stabilizing moment.We start with derivation of equations of motion for an unmanned bicycle with a gyroscope mounted on its top using Langrangian mechanics.The upright position of the bicycle is defined as equilibrium position and model is linearized about this point.A CMG is designed to create the required precession torque in order to keep the bicycle in upright position.Balancing of a bicycle and an inverted pendulum can be considered as a same problem for the reason that they have similar system dynamics.Hence,a PD controller is designed using a so called Polynomial method for the control of gyroscope's precession speed.The clear physical meaning of polynomial method's design parameters helps to reach a good compromise among different trade-offs during controller design.To validate our system,MATLAB/SIMULINK model is used for simulations.After finishing several simulations of the model,an inverted pendulum system is designed and fabricated to emulate the bicycle dynamics.The simulation and experimental results demonstrate the effectiveness of the polynomial method in designing low-order controllers for highly nonlinear systems.To Sum up,a self-balancing bicycle could form the basis for environment friendly and space efficient vehicles.Modeling,Analysis,and Control of a bicycle remain a challenge for researchers due to its non-intuitive nature.In this work,a CMG and a PD controller is designed and implemented to balance an unmanned bicycle.Furthermore,at the end of this thesis,a separate study on parameter estimation of a two-mass system is also presented.