毕业设计&课设-基于MATLAB Simulink和Simscape Multibody的自平衡机器人分析与LQG最优.zip

# Optimal LQG controller design for self-balancing robot  ## LQG controller design process with MATLAB & Simulink® **Control requirements:** follow a sinusoidal position reference with an 0.5m amplitude and 15s period remaining stable. The tolerance allowed is 1s in time and 10cm in position. **[Formulation of plant model:](LinearAnalysis.m)** - Euler-Lagrange equations - Non-linear model state-space representation - Non-linear model linearization around a fixed point - LTI model state-space representation - Sensor modeling: Quadrature encoder and IMU (Ref. MPU6050) with gyroscope and accelerometer **[Full-state feedback design](ControllerDesign.m):** - Controllability analysis - Manual pole placement - Linear Quadratic Regulator (LQR) design - Non-minimal phase system analysis **[Full-state estimator design:](ControllerDesign.m)** - Observability analysis - Manual estimator's pole placement - Linear Quadratic Estimator (Kalman filter) design ## Mechanical model with Simscape Multibody™ In order to have a more reliable simulation, a mechanical model of the robot was implemented with Simscape Multibody™ (formerly SimMechanics™) which provides a multibody simulation environment for 3D mechanical systems. An automatically generated 3D animation provides a visualization of the system's dynamic. | Following reference (LQR) | Disturbance rejection (LQR) | |:-------------------------:|:---------------------------:| ||| An interesting feature of this model is the wheel-floor contact model by using the external *Simscape Multibody Contact Forces Library*. The contact is modeled as a *sphere to plane force* and, as a small disclaimer, it's working but with a different behavior from the previous analysis. It's neccesary to tune the different parameters to make it works as supposed: Contact stiffness, contact damping, static and kinetic friction, etc. (If you find the parameters to make it works please make a pull request!). ## Contributing Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change. ## Author and institution Gonzalo Gabriel Fernández. Rodrigo Gonzalez (advisor). **Facultad de Ingeniería, Universidad Nacional de Cuyo**