Furuta Pendulum -- A Tensor Product Model-Based Design Approach Case Study

The main purpose of this paper to demonstrate how to apply basic convex optimization on robot controller design specifically on the example of the inverted Furuta pendulum. The work shows how convex optimization can be implemented and that the Tensor Product-based approach could be easily applied for robot stabilization. The design stages are shown from the quasi Linear Parameter Varying form of the Lagrange-Euler equations through giving a deeper insight into Tensor Product model transformation until the optimal control problem formulation via Linear Matrix Inequalities. The design method is well supported by TPtool and CVX Mat Lab toolboxes that are both convenient to use. Numerical simulations have also been performed to show the power of the computational solution of robot stabilization.