Mathematical Modelling , Simulation and Validation of Two wheeled self balancing robot

An Analytical and Experimental Approaches

Robot

Project Information

Project Overview

The main Idea of this project revolves around the classical problem of Balancing inverted pendulum with active controller design. This project focuses on Mathematical Modelling of the components used , Design of PID Controller with identified system in Matlab and Implementing the designed controller in modelled robot to give comparative analogy and proof of system identification as well as stable control design.

Methodology

Mathematical modelling of the major components of the system had been done both via classical techniques of as well as modern Data driven approaches.

  • PMDC Modelling
    • The Data driven approaches had been deployed for modelling the PMDC where the output of PMDC Motor speed was logged with the tacheometer. Thus these datas are then used for modelling the second order Transfer function with SGD followed by Control system toolbox. The model was cross validated for accuracy.
  • Driver & Sensor modelling
    • The driver & sensor both are modelled in realm of first order accounting their delays and gains to get relavent transfer functions.
  • Chassis modelling
    • The chassis had been modelled classically with the Vector components and Resolution to account dynamics of systems.
    Features
    Optical tacheometer
    Localization Results
    Experimental set of motor-generator Set
    The system design plays crutual role as identifying the components as well as tuning controller plays crutial role. The controller design was done as a closed loop of controller followed by Zero order Hold symbolizing the sample time of controller whereas the o/p of controller fed to driver transfer function , Moder TF , Chassis Tf where o/p is observed whereas the closed loop is deployed with sensor in feedback symbolizing the delay in the state of given and observed state. The simulation environment should be done with inclusion of the noises symbolizing distrubances. The Tuning of PID had been done with the system being stable after controller's satisfying performance
    Localization Results
    Simulated responses
    After modelling & validation for TF of Components , Robot fabrication is done with Arduino as controller , DC motor as actuator, Wooden 2 storyed frame , L298N Driver and MPU6050 as IMU which was powered by 12 V LiPo battery. The PID controller is implemented within arduino as software implementation. The PID controller had been used to continuously generate adaquate amount of the motor torque in correct direction thus avoiding the falling of robot.

    Results

    Features
    Real Robot angle of tilt
    Localization Results
    Comparision between real and simulated angle of tilt

    The robot was Balanced and from the result it is clear that the modelling had been quite successful as both ar in close cohision. The tunung as well as randomness in the environmental conditions make the controller design challanging , however irrespective of the forces, robot stand still signifying the system design successful.

    Conclusion

    The analytical and experimental approaches gives both quality of the real world system limitations as well as ability for control and make inheriently unstable system stable. The significance of system identification as well as mathematical design is demonstrated as the effective inclision of simulations could have been done. however there are certain limitations such as:

  • System had been liniarized indicating controller is ineffective if the angle of tilt is greater than 10 degree
  • Sensor carrys lots of noise which trigger false input.
    • optimal controller shall make it more robost and realizable.