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Dynamic modelling of a projectile launcher with controlled double inverted pendulum
Published in Alka Mahajan, Parul Patel, Priyanka Sharma, Technologies for Sustainable Development, 2020
P.S. Savnani, M.M. Chauhan*, A.I. Mecwan, R.N. Patel
The system is analysed using a mathematical model derived using Lagrangian mechanics approach to the double inverted pendulum incorporating the dynamics of the system. Furthermore, the simulation results match with the experimental results thus, proving the applicability of this model. The equation obtained from the curve fitting data for the input parameters used in the simulation will vary with another set of data. As, this model predicts the trajectory and the launch parameters accurately, it has widespread applications in industrial launchers, weapons technology, sports training machines etc. The present model can be further extended by considering the frictional forces and air resistance to predict more realistic behaviour of the launching mechanism.
Sliding Mode Control of Pendulum Systems
Published in Vadim Utkin, Jürgen Guldner, Jingxin Shi, Sliding Mode Control in Electro-Mechanical Systems, 2017
Vadim Utkin, Jürgen Guldner, Jingxin Shi
An example of a two-step design will be described in Section 5.6 for linear time-varying systems. Three nonlinear pendulum systems based on the above design procedures will be studied in the following section. The specific design procedures for selecting a sliding manifold and discontinuous control for a cart pendulum, a double-inverted pendulum, and a rotational inverted pendulum will be demonstrated. The theoretical studies will be complemented by simulation and experimental results.
Linear Time-Invariant SISO Systems
Published in Hebertt Sira-Ramírez, Sunil K. Agrawal, Differentially Flat Systems, 2018
Hebertt Sira-Ramírez, Sunil K. Agrawal
leads to the following nonlinear model for the double inverted pendulum on a cart () (M+2m)x¨+2mLθ¨1 cosθ1−2mLθ˙12 sinθ1−mLθ¨2 cosθ2+mLθ˙22 sinθ2=f2mLx¨ cosθ1+2mL2θ¨1−mL2θ¨2 cos(θ1+θ2)+mL2θ˙22 sin(θ1+θ2)−2mgL sinθ1=0mL2θ¨2−mLx¨ cosθ2−mL2θ¨1 cos(θ1+θ2)+mL2θ˙12 sin(θ1+θ2)−mgL sinθ2=0
Control of rotary double inverted pendulum system using LQR sliding surface based sliding mode controller
Published in Journal of Control and Decision, 2022
Sondarangallage D.A. Sanjeewa, Manukid Parnichkun
The rotary double inverted pendulum system in Figure 1 consists of a motor-driven arm and serially connected un-actuated two pendulums which are constrained to rotate freely about their pivot axis in the vertical plane while the motor-driven arm rotates in the horizontal plane. The arm of this system is driven by a DC motor using belt and pulley transmission. Parameters of the system are provided in Table 1.