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PLL Equivalent Augmented System Incorporated with State Feedback Designed by LQR

Somsak Wanchana, Taworn Benjanarasuth, Noriyuki Komine, and Jongkol Ngamwiwit
International Journal of Control, Automation, and Systems, vol. 5, no. 2, pp.161-169, 2007

Abstract : The PLL equivalent augmented system incorporated with state feedback is proposed in this paper. The optimal value of filter time constant of loop filter in the phase-locked loop control system and the optimal state feedback gain designed by using linear quadratic regulator approach are derived. This approach allows the PLL control system to employ the large value of the phase-frequency gain K_d and voltage control oscillator gain K_0. In designing, the structure of phase-locked loop control system will be rearranged to be a phase-locked loop equivalent augmented system by including the structure of loop filter into the process and by considering the voltage control oscillator as an additional integrator. The designed controller consisting of state feedback gain matrix K and integral gain k_I is an optimal controller. The integral gain k_I related to weighting matrices q and R will be an optimal value for assigning the filter time constant of loop filter. The experimental results in controlling the second-order lag pressure process using two types of loop filters show that the system response is fast without steady-state error, the output disturbance effect rejection is fast and the tracking to step changes is good.

Keyword : Linear quadratic regulator, phase-locked loop, PLL equivalent augmented system, process control system.

 
 
 
 
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