Motion Control and Vibration Suppression of Flexible Lumped Systems via Sensorless LQR Control

Abstract

Original scientific paperThis work attempts to achieve motion control along with vibration suppression of flexible systems by developing a sensorless closed loop LQR controller. Vibration suppression is used as a performance index that has to be minimized so that motion control is achieved with zero residual vibration. An estimation algorithm is combined with the regular LQR to develop sensorless motion and vibration controller that is capable of positioning multi degrees of freedom flexible system point of interest to a pre-specified target position with zero residual vibration. The validity of the proposed controller is verified experimentally by controlling a sensorless dynamical system with finite degrees of freedom through measurements taken from its actuator.Key words: Sensorless control, Vibration suppression, Reaction force observer, Optimal control, Action reaction state observer Fleksibilni slijedni sustav s koncentriranim parametrima sa suzbijanjem vibracija korištenjem LQR-a bez senzora. U ovom radu opisan je fleksibilni slijedni sustav sa suzbijanjem vibracija upravljan LQR regulatorom u zatvorenom upravljačkom krugu bez senzora. Vibracije su korištene u težinskoj funkciji koja se minimizira s ciljem eliminiranja rezidualnih vibracija iz slijednog sustava. Kombinirajući algoritam estimacije s klasičnim LQRom, razvijen je regulator za upravljanje gibanjem i vibracijama bez korištenja senzora, koji je sposoban pozicionirati odreenu točku fleksibilnog sustava s više stupnjeva slobode u predefiniranu željenu točku bez preostalih vibracija. Validacija predloženog regulatora provedena je eksperimentalno upravljajući dinamičkim sustavom s konačnim brojem stupnjeva slobode uz korištenje mjerenja s aktuatora.Ključne riječi: upravljanje bez senzora, suzbijanje vibracija, observer reakcijske sile, optimalno upravljanje, observer stanja akcije i reakcije

Investigation of interactions between mechanical and electrical components of a motion platform

“…These models usually include two [3] or three [4], [11] lumped masses connected with flexible elements. For the control of flexible robot arms even four or more lumped mass models are employed [6].…”

“…4. Closed-loop frequency response function plot of the SISO system models given in equations (11) and (12) obtained with PI control with parameters K P = 1 and K I = 1000. be approximately found by setting R a = 0 in (12) and finding the denominator roots, which in turn yields:…”

“…In this study, a classical PI controller is employed for both cases. In determining the controller parameters one can note that the transfer functions given in (11) and (12) both posses an open-loop zero at s = 0, hence both systems are natural "differentiators" up to a certain frequency. This can also be observed in the FRF given in Fig.…”

“…while trying to obtain a closed loop transfer function from reference command to load speed equal to or at least very close to unity [5]. For this purpose, several techniques including resonance ratio control [1], model-predictive control (MPC) [12], robust control [7], resonant control [10], and techniques employing complicated sensor [8] and observer structures [11], [6], [2] are employed. During modelling and control phases, ,as also indicated by Szabat et.…”