Lyapunov-Based PD Linear Control of the Oscillatory Behavior of a Nonlinear Mechanical System: The Inverted Physical Pendulum with Moving Mass Case

<table>Simulation of the closed-loop system starting from <math id="M194" xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>0.6,0.8</mn><mo stretchy="false">)</mo></math> and <math id="M195" xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mrow><mi>q</mi></mrow><mo>̇</mo></mover><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo>.</mo></math></table>

Mathematical Problems in Engineering

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Figure 2

Figure 2: Lyapunov-Based PD Linear Control of the Oscillatory Behavior of a Nonlinear Mechanical System: The Inverted Physical Pendulum with Moving Mass Case 

Figure 2 | Lyapunov-Based PD Linear Control of the Oscillatory Behavior of a Nonlinear Mechanical System: The Inverted Physical Pendulum with Moving Mass Case 