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LQG Control Design for Balancing an Inverted Pendulum Mobile Robot

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Figure

Figure 1), and Lgoverned by a equation of motion relating the forces
Figure 2solution. The principles of a LQR controller is given in its matrices . Here is the state space system represented with A , B , and C  with the LQR controller
Figure 3L  However, we also assume disturbances in form of noise,
Figure 6 gives the time response of the system with a step input simulated by use of lsim function in MATLAB

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