Dynamics and optimal control of multibody systems using fractional generalized divide-and-conquer algorithm
In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control...
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| Published in: | Nonlinear dynamics Vol. 102; no. 3; pp. 1611 - 1626 |
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| Language: | English |
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| Abstract | In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control method and embedded fractional algorithms to control the nonlinear behavior of a multibody system. The fractional Brunovsky canonical form of the tracking error is proposed for a generalized divide-and-conquer algorithm (GDCA) customized for having a shortened memory buffer and faster computational time. The suite of a GDCA is highly efficient. It lends itself easily to the parallel computing framework, that is used for the inverse and forward dynamic formulations. This technique can effectively address the issues corresponding to the inverse dynamics of fully actuated closed-chain systems. Eventually, a new stability criterion is proposed to obtain the optimal torque control using the new fractional Brunovsky canonical form. It is shown that fractional controllers can robustly stabilize the system dynamics with a smaller control effort and a better control performance compared to the traditional integer-order control laws. |
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| AbstractList | In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control method and embedded fractional algorithms to control the nonlinear behavior of a multibody system. The fractional Brunovsky canonical form of the tracking error is proposed for a generalized divide-and-conquer algorithm (GDCA) customized for having a shortened memory buffer and faster computational time. The suite of a GDCA is highly efficient. It lends itself easily to the parallel computing framework, that is used for the inverse and forward dynamic formulations. This technique can effectively address the issues corresponding to the inverse dynamics of fully actuated closed-chain systems. Eventually, a new stability criterion is proposed to obtain the optimal torque control using the new fractional Brunovsky canonical form. It is shown that fractional controllers can robustly stabilize the system dynamics with a smaller control effort and a better control performance compared to the traditional integer-order control laws. |
| Author | Poursina, Mohammad Dabiri, Arman Machado, J. A. Tenreiro |
| Author_xml | – sequence: 1 givenname: Arman orcidid: 0000-0002-4407-4314 surname: Dabiri fullname: Dabiri, Arman email: adabiri@siue.edu organization: Department of Mechanical and Mechatronics Engineering, Southern Illinois University Edwardsville – sequence: 2 givenname: Mohammad surname: Poursina fullname: Poursina, Mohammad organization: Department of Engineering and Science, University of Agder – sequence: 3 givenname: J. A. Tenreiro surname: Machado fullname: Machado, J. A. Tenreiro organization: Department of Electrical Engineering, Institute of Engineering, Polytechnic Institute of Porto |
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| Keywords | Parallel computing Optimal control Multibody dynamics Open-chain system Fractional control PID LQR Closed-chain system Computed-torque control Divide and conquer algorithm |
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| References_xml | – reference: DasSFunctional Fractional Calculus2011BerlinSpringer1225.26007 – reference: PoursinaMAndersonKSCanonical ensemble simulation of biopolymers using a coarse-grained articulated generalized divide-and-conquer schemeComput. Phys. Commun.2013184365266030070511302.82137 – reference: KhanIAndersonKPerformance investigation and constraint stabilization approach for the orthogonal complement-based divide-and-conquer algorithmMech. Mach. Theory201367111121 – reference: OustaloupALevronFMathieuBNanotFMFrequency-band complex noninteger differentiator: characterization and synthesisIEEE Trans. Circuits Syst. I Fund. Theory Appl.20004712539 – reference: DabiriAMoghaddamBMachadoJTOptimal variable-order fractional pid controllers for dynamical systemsJ. Comput. Appl. Math.2018339404837876761392.49033 – reference: PetrasIFractional-Order Nonlinear Systems: Modeling, Analysis and Simulation2011BerlinSpringer1228.34002 – reference: Dabiri, A., Nazari, M., Butcher, E.A.: Minimal phase-variable canonical state-space realizations and initializations for linear time-invariant multi-term fractional differential equations. In: American Control Conference (ACC), Milwaukee, WI, May 24–26 (2018) – reference: MalczykPFraczekJA divide and conquer algorithm for constrained multibody system dynamics based on augmented lagrangian method with projections-based error correctionNonlinear Dyn.20127018718892991319 – reference: PodlubnyIFractional-order systems and pi/sup/spl lambda//d/sup/spl Mu//-controllersIEEE Trans. Autom. Control199944120821416669371056.93542 – reference: BhaleraoKDPoursinaMAndersonKSAn efficient direct differentiation approach for sensitivity analysis of flexible multibody systemsMultibody Syst. 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| SubjectTerms | Acceleration Algorithms Automotive Engineering Canonical forms Chains Classical Mechanics Computing time Control Control methods Control stability Control systems Control theory Dynamic models Dynamic stability Dynamical Systems Engineering Inverse dynamics Mechanical Engineering Multibody systems Nonlinear control Optimal control Original Paper Stability criteria System dynamics Torque Tracking errors Vibration |
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