This case study presents the design and experimental evaluation of two controllers for vertical stabilization of two-wheeled robot. The first one is a conventional linear quadratic Gaussian (LQG) controller with 17th-order Kalman filter used for state estimation. This controller ensures robust stability of the closed-loop system and good nominal performance. The second one is a μ controller ensuring both robust stability and robust performance. Due to the lack of accurate analytical robot model, the controllers design is based on models derived by closed-loop identification from experimental data. The robot uncertainty is approximated by an input multiplicative uncertainty which leads to a μ controller of order 44, subsequently reduced to 30. The yaw motion is controlled by using a proportional-integral (PI) controller on the basis of yaw angle estimate obtained by a separate second order Kalman filter. A software in MATLAB®/Simulink® environment is developed for generation of control code which is embedded in the Texas Instruments Digital Signal Controller TMS320F28335. Results from the simulation of the closed-loop system as well as experimental results obtained during the real-time implementation of the designed controllers are given. The theoretical investigation and experimental results confirm that the closed-loop system achieves robustness in respect to the uncertainties related to the identified robot model.

Chapter Contents:

• 7.1 Robot description
• 7.2 Closed-loop identification of robot model
• 7.2.1 Dynamic models from u to φ̇
• 7.2.2 Dynamic models from φ̇ to θ̇
• 7.2.3 Dynamic model of the yaw motion
• 7.3 Derivation of uncertain models
• 7.3.1 Signal-based uncertainty representation
• 7.3.2 Input multiplicative uncertainty representation
• 7.4 LQG controller design
• 7.5 Controller design
• 7.6 Comparison of designed controllers
• 7.7 Experimental evaluation
• 7.8 Notes and references

Inspec keywords: linear quadratic Gaussian control; Kalman filters; robots; uncertain systems; three-term control; control system synthesis; closed loop systems; wheels; state estimation; robust control

Other keywords: yaw motion; μ controller; Matlab-Simulink environment; PI controller; controller design; input multiplicative uncertainty; 17th-order Kalman filter; yaw angle estimate; control code generation; proportional-integral controller; LQG controller; two-wheeled robot; robust control; closed-loop identification; robust performance; robot uncertainty; vertical stabilization; closed-loop system; second order Kalman filter; linear quadratic Gaussian controller; robust stability; Texas Instruments Digital Signal Controller TMS320F28335; state estimation; analytical robot model

Subjects: Signal processing theory; Simulation, modelling and identification; Control system analysis and synthesis methods; Optimal control; Robotics; Stability in control theory