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In this work we present a workflow for designing two linear controltechniques applied to the dynamic system quadruple inverted pendulum mounted ona cart (QIP) where the steady state error on cart position is eliminatedthrough a precompensation gain. The first control law designed was based onLQR, technique that stabilizes the system states based on a minimization of thetotal energy of the system states and the second control technique was poleplacement by 2nd order system approximation, this method allowed to define asettling time and overshoot of the desired response of the plant, for thiscontrol the system was considered SISO, being the only output of the plant thehorizontal position of the cart. To eliminate the steady-state error generatedby both linear controllers, an analysis of the stationary response of thesystem under control in the Laplace Domain was performed. The simulationenvironment used to validate the results presented in this paper was Simscapeof Matlab, it is a simulation environment that allowed to simulate the dynamicof nonlinear mechanical systems. The results obtained indicate that bothcontrollers are able to stabilize the plant and move the cart position to thedesired setpoint. Finally, we discuss about the performances of both linearcontrol techniques.

Design and comparison of two linear controllers with precompensation gain for the Quadruple inverted pendulum