Continuous non‐singular terminal sliding‐mode control of permanent magnet spherical actuator for trajectory tracking based on a modified nonlinear disturbance observer

Wen, Yan; Liu, Zhongyang; Wang, Qunjing; Li, Guoli

doi:10.1049/elp2.12196

Cited by 2 publications

(2 citation statements)

References 33 publications

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“…It has the characteristics of a simple design structure, strong practicability, accurate observation results, and so on. It is widely used in the control system [20,21,22,23] The literature in Ref. [24] applies the disturbance observer to industrial robots and proposes a sliding mode controller based on the disturbance observer to perform robust control on the robot and improve the trajectory tracking accuracy of the robot.…”

Section: Introductionmentioning

confidence: 99%

Backstepping control of three‐degree‐of‐freedom hybrid magnetic bearing based on non‐linear disturbance observer

Chengzi,

Yucheng,

Yan

et al. 2023

IET Electric Power Appl

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A backstepping controller based on a non‐linear disturbance observer (NDOB) was created to enhance the dynamic performance and reliability of three‐degree‐of‐freedom hybrid magnetic bearings. After the structure of three‐degree‐of‐freedom hybrid magnetic bearings is introduced, the mathematical model is established, and the equation of the state is derived by the equivalent magnetic circuit technique. Based on the mathematical model, non‐linear disturbance observer (NDOB) is designed and is used to predict the system disturbance, and the backstepping control algorithm is compensated. To verify the effectiveness of the proposed controller, the backstepping controller, proportion integration differentiation controller, and backstepping controller based on a NDOB were compared by simulation and experiment. Results show that the backstepping controller based on a NDOB has better dynamic performance and robustness.

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Section: Introductionmentioning

confidence: 99%

Backstepping control of three‐degree‐of‐freedom hybrid magnetic bearing based on non‐linear disturbance observer

Chengzi,

Yucheng,

Yan

et al. 2023

IET Electric Power Appl

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“…Current circulates in the stator’s electromagnetic coils, and the interaction of the electromagnetic field of the stator’s EMs with the magnetic field of the rotor’s PMs generates the three-DOF turn motion of the rotor (Sun and Lee, 2014; Liu et al , 2017b; Chen et al , 2020). The dynamics of the rotor’s turn motion are determined by Euler–Lagrange equations (Wen et al , 2022; Rigatos, 2015a; Rigatos and Karapanou, 2020). This dynamic model receives as control inputs three torque variables which determine rotation by a certain angle around the axes of a cartesian coordinate frame (Xia et al , 2010; Li et al , 2018; Li et al , 2019).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear optimal control for permanent magnet synchronous spherical motors

Rigatos,

Abbaszadeh,

Siano

et al. 2023

RIA

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Purpose Permanent magnet synchronous spherical motors can have wide use in robotics and industrial automation. They enable three-DOF omnidirectional motion of their rotor. They are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. Unlike conventional synchronous motors, permanent magnet synchronous spherical motors consist of a fixed inner shell, which is the stator, and a rotating outer shell, which is the rotor. Their dynamic model is multivariable and strongly nonlinear. The treatment of the associated control problem is important. Design/methodology/approach In this paper, the multivariable dynamic model of permanent magnet synchronous spherical motors is analysed, and a nonlinear optimal (H-infinity) control method is developed for it. Differential flatness properties are proven for the spherical motors’ state-space model. Next, the motors’ state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point, which is defined by the present value of the motors’ state vector and by the last sampled value of the control input vector. For the approximately linearized model of the permanent magnet synchronous spherical motors, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains, an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops. Findings Due to the nonlinear and multivariable structure of the state-space model of spherical motors, the solution of the associated nonlinear control problem is a nontrivial task. In this paper, a novel nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of permanent magnet synchronous spherical motors. The method is based on approximate linearization of the motor’s state-space model with the use of first-order Taylor series expansion and the computation of the associated Jacobian matrices. Furthermore, the paper has introduced a different solution to the nonlinear control problem of the permanent magnet synchronous spherical motor, which is based on flatness-based control implemented in successive loops. Research limitations/implications The presented control approaches do not exhibit any limitations, but on the contrary, they have specific advantages. In comparison to global linearization-based control schemes (such as Lie-algebra-based control), they do not make use of complicated changes of state variables (diffeomorphisms) and transformations of the system's state-space description. The computed control inputs are applied directly to the initial nonlinear state-space model of the permanent magnet spherical motor without the intervention of inverse transformations and thus without coming against the risk of singularities. Practical implications The motion control problem of spherical motors is nontrivial because of the complicated nonlinear and multivariable dynamics of these electric machines. So far, there have been several attempts to apply nonlinear feedback control to permanent magnet-synchronous spherical motors. However, due to the model’s complexity, few results exist about the associated nonlinear optimal control problem. The proposed nonlinear control methods for permanent magnet synchronous spherical motors make more efficient, precise and reliable the use of such motors in robotics, electric traction and several automation systems. Social implications The treated research topic is central for robotic and industrial automation. Permanent magnet synchronous spherical motors are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. The solution of the control problem for the nonlinear dynamic model of permanent magnet synchronous spherical motors has many industrial applications and therefore contributes to economic growth and development. Originality/value The proposed nonlinear optimal control method is novel compared to past attempts to solve the optimal control problem for nonlinear dynamical systems. Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation which is used for computing the feedback gains of the controller is new, and so is the global stability proof for this control method. Compared to nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed into the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes, which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. Furthermore, the second control method proposed in this paper, which is flatness-based control in successive loops, is also novel and demonstrates substantial contribution to nonlinear control for robotics and industrial automation.

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Continuous non‐singular terminal sliding‐mode control of permanent magnet spherical actuator for trajectory tracking based on a modified nonlinear disturbance observer

Cited by 2 publications

References 33 publications

Backstepping control of three‐degree‐of‐freedom hybrid magnetic bearing based on non‐linear disturbance observer

Backstepping control of three‐degree‐of‐freedom hybrid magnetic bearing based on non‐linear disturbance observer

Nonlinear optimal control for permanent magnet synchronous spherical motors

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