Vibration Control of Flexible Link Manipulator Using SDRE Controller and Kalman Filtering

Abstract

Abstract:The problem of estimating the flexural states while applying State-Dependent Riccati Equation (SDRE) technique to flexible link manipulator (FLM) is the focus of this paper. The proposed method investigates the effect of employing Kalman Filter as state estimator in the case of the deterministically modelled FLM. The dynamic model of the FLM is derived through combined Euler Lagrangian-Assumed modes approach based on two significant modes, resulting in a nonlinear model with six states. The information of states being crucial to the imple mentation of SDRE controller, the state estimator based on Kalman filter designed in this paper, minimizes the effect of noises that may corrupt the state measurements. Simulation results reveal the effectiveness of Kalman filter based SDRE controller for accurate positioning and vibration suppression of the FLM.

Dynamic Modeling of Planar Multi-Link Flexible Manipulators

“…Assuming that the tip of each link is free of the dynamic constraints, the mass boundary conditions presented in [6,28] are used in this paper which are given by Equations ( 23) and (24), where J Di is the moment of inertia at the end of the link i, m Di is the actual mass at the end of the link i, and M Di accounts for the contributions of the masses of the distal links, hubs, and payloads non-collocated at the end of the link i, weighted by the relative distance from the axis Y i (shearing axis at the end of link i) [6]. The contribution of M Di is not included in the mode shape analysis in [6,28].…”

“…In [18], AMM is used in conjunction with recursive Gibbs-Appell formulation to obtain the dynamic model of flexible cooperative mobile manipulators that are kinematically and dynamically constrained. Explicit dynamic models of the one-link flexible arm [19][20][21][22][23][24][25][26][27] and the two-link flexible arm [6,[28][29][30][31][32][33] have been derived and methods to obtain the mathematical model of a general n-link flexible arm [6] have been formulated based on AMM.…”

Review on Modeling and Control of Flexible Link Manipulators

“…Saeed et al (2019) and Badfar and Abdollahi (2019) modeled the dynamics of rigid-flexible manipulators using the AMM technique. Other recent works on single-link FLMs using AMM include, but are not limited to, the studies done by Ouyang et al (2017), Reddy and Jacob (2017), Meng et al (2018), and Zhang et al (2019a). Furthermore, the AMM was used to model two-link FLMs by Lochan and Roy (2018), , and Lochan et al (2020).…”

“…To overcome this problem, Mosayebi et al (2012) proposed input-output control of FLM based on a nonlinear high gain observer to estimate the elastic degrees of freedom and their time derivatives. Reddy and Jacob (2017) proposed the Kalman filter based statedependent Riccati equation controller for accurate positioning and vibration suppression of the FLM. Ripamonti et al (2017) presented model-based sliding mode control for vibration suppression of a three-link flexible manipulator using the linear and nonlinear sliding surface.…”

“…trajectory tracking control(Si et al, 2017;Huan and Xian, 2017; Lochan et al, 2020) (e) Vibration control(Reddy and Jacob, 2017) (f) Motion control(Wang et al, 2017;Zhang and Yu, 2001;Tian et al, 2002) (g) Force control(Rigatos and Busawon, 2018;Bazaei and Moallem, 2010) (h) Hybrid control (position and force(Matsuno and Yamamoto, 1993;Wang et al, 2020), position and vibration(Singh and Ohri, 2018), trajectory tracking and vibration (Garcia-Perez et al, 2019), and other combinations)There are various control schemes reported in the literature, depending on the control problems. Jing et al (2019) presented a state-of-the-art review on kinematic analysis and dynamic stable control of space flexible manipulators and pointed out existing problems and suggestions on dynamic stable control.…”