A Robust Fuzzy PD Inverse Dynamics Decoupling Control of Spherical Motion Mechanism With Fuzzy Linear Extended State Observer

Abstract

In this paper, a robust adaptive fuzzy proportional-derivative inverse dynamics decoupling control scheme with fuzzy-based linear extended state observer (FLESO) is presented and applied to the trajectory tracking control of a two degree-of-freedom (2-DOF) spherical motion mechanism (SMM). The dynamics of the SMM has the characteristics of multivariable nonlinearity, uncertainties and strong coupling. Uncertainties like the modeling errors and external disturbances affect the tracking performance, and coupling increases the difficulty of controller design and reduces the tracking precision. Therefore, a novel hybrid control scheme that is composed of a fuzzy proportional-derivative (FPD) feedback control with varying gains, inverse dynamic model-based feed-forward decoupling term, FLESO with varying bandwidth, and robust term is developed. The novel control strategy combines the advantages of simplicity and easy design of the FPD control, the effectiveness of the FLESO to handle the modeling errors and external disturbances, and the robustness of the robust term to estimation errors of the FLESO. First, introduce the structure of the SMM and establish the dynamic model. Second, the feed-forward decoupling principle is derived based on the inverse dynamic model. Then the FPD control with two-inputs and two-outputs is designed, whose rule base is derived by the phase plane method. The linear extended state observer is designed, whose bandwidth is tuned via the fuzzy logic system. Furthermore, the asymptotic stability of the proposed controller is proved by the Lyapunov theorem. Finally, the high tracking performance of the proposed controller is validated via both simulation and experiment results. INDEX TERMS Robust and adaptive control, fuzzy proportional-derivative control, fuzzy-based linear extended state observer, inverse dynamics decoupling control, spherical motion mechanism

Output Recurrent Fuzzy Broad Learning Systems for Adaptive MIMO PID Control: Theory, Simulations, and Application

“…of the ORFBLS identifier. By following [28], [32]- [34], it is necessary to find the error objective function 𝐸(𝑘) which is established from the difference among the actual system response 𝒚 and the estimated system response 𝒚 ̂ obtained from (14) in the form:…”

Modeling and Robust Tracking Decoupling Control of a Coaxial Unmanned Helicopter Based on the Improved Alternating Direction Method of Multipliers

“…Of course, it can also be concluded that λ * is the optimal solution, and we do not make additional assumptions about matrices A, B and vector B in constraints nor do we require matrices A and B to have perfect permutation. e following will give the convergence result of solving formula (13) with the classical ADMM algorithm:…”

“…e above formula (21) is called the optimal condition of the classical ADMM algorithm. If x * , y * , λ * is the optimum of formula (13), then formula (21) is satisfied; on the contrary, if there is x * , y * , λ * satisfying (21), it is the best point of (13). In equation ( 21), the first line is called the initial problem feasibility condition; that is, the best point must satisfy the equality constraint of equation (12); the second and third lines are called dual-use conditions, where Operator z represents the subdifferential or subgradient operators that is described in detail in the previous section.…”

“…We consider the following forms of problem optimization: min x,y f(x) + g(y), s.t.Ax + By � b, (13) where x ∈ X, y ∈ Y is the optimization variable and f: R ⟶ R ∪ +∞ { }, g: R m ⟶ R ∪ +∞ { } is a convex function, and these initial problems can be transformed into the form of formula (13) after redefining the variables. For example, given y � Ax, the original problem minf(x) + g(Ax) can be transformed into (13), where B � − 1, b � 0. In some problems, object functions have good properties such as strictly convex or squared convex functions or having a continuous Lipchitz gradient and so on.…”

“…A robust adaptive fuzzy relative-derived inverse dynamic disengagement control based on the fuzzy linear extended state is proposed and applied to trajectory tracking of the two-degree-of-freedom spherical motion mechanism. The simulation and experimental results ensure the high performance of the controller [ 13 ]. Based on the high-dimensional nonlinear system model of the gyro-stabilized platform, a robust control design method for multiple input-output objects is proposed based on eigen structure assignment and quantitative feedback theory.…”