2020 Vol. 41, No. 11

Display Method:
Modeling and Control of Planar Redundant Parallel Robots Based on the Udwadia-Kalaba Method
HAN Jiang, WANG Peng, DONG Fangfang, XIA Lian, CHEN Shan, LU Lei
2020, 41(11): 1183-1196. doi: 10.21656/1000-0887.400363
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The redundantly driven parallel robots were considered. The Udwadia-Kalaba (U-K) method was used to formulate the physical connections of the parallel mechanism as system constraints, and the closed-chain motion equations for the planar 2-DOF redundantly driven parallel robot were established. Firstly, the 2-DOF robot was divided into 3 unconstrained open-chain subsystems. The dynamic equations for the subsystems were obtained with the Lagrangian method. Then, the kinematic constraints were used to describe the physical connections between each subsystem and the end effector, and between each subsystem and the base. The constraint was differentiated and transformed into a 2nd-order Pfaffian standard differential form. With the U-K equations, the analytical solution satisfying the physical constraints was given. According to the U-K theory, the constraints can be added to the unconstrained open-chain system equations to establish the dynamics model for the planar redundantly driven parallel robot. In the trajectory tracking controller design, the desired position or velocity trajectory was formulated as a virtual constraint, and the constraint condition was transformed into a standard Pfaffian differential form. Then the U-K equations were used to solve the output torque required for each driving joint to satisfy a given trajectory constraint. This method does not require auxiliary variables such as Lagrangian multipliers or pseudo-generalized speeds, and can handle both holonomic and non-holonomic constraints. The numerical simulation and analysis results show that, the modeling and controlling method can effectively, systematically and quickly establish the dynamic analytical decoupling model for the planar 2-DOF redundantly driven parallel robot, and realize the high-precision tracking control along a given trajectory.
CADRC for a Class of Underactuated MIMO Systems
XIAO Yougang, ZHU Chengzhen, LU Hao, HAN Kun
2020, 41(11): 1197-1209. doi: 10.21656/1000-0887.390356
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The control of widely used underactuated multi-input multi-output (UMIMO) systems is still an open challenge. The underactuated system was composed of direct drive parts and indirect drive parts. For the direct drive parts, the virtual feedback control laws were designed according to their current states and target states; for the indirect drive parts, the inner uncertainties and external disturbances were estimated through the designed linear extended state observer (ESO), and the virtual feedback control laws were designed to compensate the lumped disturbances in real time. All the virtual control laws were integrated into the comprehensive control law to realize the centralized active disturbance rejection control (CADRC) of the underactuated system, and the stability of the algorithm was strictly proved with the Lyapunov method. Test results indicated that, the whole control system is compact, robust and actively disturbance-rejected, and the control gains are easy to be tuned.
Type-2 Direct T-S Fuzzy Control of Niche Equality Indexes
HAO Yunli, CHENG Xiangyang, WANG Maohua
2020, 41(11): 1210-1223. doi: 10.21656/1000-0887.400376
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Given the important role of niches in the ecosystem and the operability of type-2 direct T-S fuzzy control of the stability of a class of nonlinear systems with parameter uncertainties, the biological individuals’ evolutionary characteristics and adaptive behaviors were integrated with the direct T-S fuzzy type-2 control method, and the niche closeness function was used as a follow-up to type-2 T-S fuzzy control parts. Besides, a type-2 direct T-S fuzzy control method with biological characteristics was proposed to find the niche ecology. The self-adaptation rate of the factor reflects the degree of the adaptive use of the environment by biological individuals. Through comparison of simulation examples, this study reveals that type-2 is superior to type-1 in terms of stability and convergence. The study shows that the type-2 method is conducive to environmental harmony, ecological stability and sustainable development of ecological environment; in the meantime, this method gives fuzzy control a practical physical background.
Vibration Analysis of Rotating Functionally Gradient Nano Annular Plates in Thermal Environment
LIU Xu, YAO Linquan
2020, 41(11): 1224-1236. doi: 10.21656/1000-0887.410090
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Based on the nonlocal elasticity theory and the Kirchhoff thin plate theory, the vibration frequencies of rotating FGM nano annular plates in thermal environment were studied. Firstly, the differential equations for coupled radial and transverse motions of the rotating FGM nano annular plate under temperature changes and surface forces caused by rotating motions were obtained with the Hamiltonian principle, in turn, the transverse vibration of the plate was solved. Then, with the plane stress method, the axially symmetrical midplane internal forces of the annular plate under the action of centrifugal inertia force and the temperature stress distributed along the radial direction were obtained. After this, the differential equation with variable coefficients was solved with the differential quadrature method. Finally, through numerical simulations, the effects of the innerouter diameter ratio, the functionally gradient parameters, the rotation speed, the nonlocal parameters and the temperature on the dimensionless natural frequencies of the annular plate were analyzed.
Analysis on Persistent Homology Characteristics of Failure Processes of Shallow Buried Tunnels Under Multi-Time Explosions
LIU Xiaofei, YOU Shihui
2020, 41(11): 1237-1249. doi: 10.21656/1000-0887.400222
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The failure characteristics of shallow buried tunnels under multi-time explosions make an important research issue in the design and evaluation of protection engineering. It is of great significance to develop a method for early warning of the safety for shallow buried features. The discrete element method was used to establish the mechanical model for the shallow buried tunnel. With the Saint-Venant principle the blast loads were treated as a series of dynamic forces acting uniformly on the surface. Based on the discrete element method, the dynamic response under each blast load and the damage evolution process of the tunnel surrounding rock were obtained. The strength reduction method was used to calculate the safety factor of the surrounding rock. The persistent homology theory was introduced to quantitatively and qualitatively analyze the failure characteristics of the discrete element model under multi-time explosive loads. The results show that, the method of persistent homology can accurately reflect the topological characteristics of the surrounding rock. The maximum 1D barcode connection radius can effectively predict tunnel instability. The work provides a new mathematical method for tunnel safety design and disaster prediction research.
Joint Distribution and Profit Allocation in Urban Transportation Energy Systems
XU Guangcan, SONG Qiankun
2020, 41(11): 1250-1258. doi: 10.21656/1000-0887.410060
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The joint distribution (JD) can greatly reduce the logistics cost and is of obvious significance for the refined oil enterprises in the urban transportation energy system. However, the existing research literatures paid more attention to the problems of cost reduction and efficiency enhancement of distribution, while thought little of the problem of benefit sharing, which is also the key to the joint distribution. According to the characteristics of refined oil distribution, the effects of business, investment and risk factors on the benefit distribution among refined oil enterprises were considered comprehensively, and the comprehensivecorrection Shapley value (CCSV) model was built to study the benefit distribution related to the joint distribution mode for refined oil enterprises. Numerical analysis shows that, the benefit distribution results of refined oil enterprises based on the CCSV model are more objective and reasonable, which can effectively enhance the stability of the joint distribution alliance of refined oil enterprises.
Adaptive Synchronization of Neutral Neural Networks With Mixed Delays and Lévy Noises
GU Fengjiao, GAO Yan, REN Lijia, MA Jianwu, CHEN Lingqi
2020, 41(11): 1259-1274. doi: 10.21656/1000-0887.400350
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The problem of feedback controllers designed to achieve adaptive synchronization was investigated for neutral neural networks with mixed delays and Lévy noises. The noise disturbance in the neural network model was driven by the Lévy stochastic process consisting of the Gaussian process and the Poisson point process, and involving continuous disturbances as well as discontinuous synaptic noises. Based on the Lyapunov functional, the It?s formula and the inequality analysis technique, the criteria to ensure adaptive stabilization for the error system were built. Moreover, the update rate of the feedback controller was given to enhance the adaptive synchronization of the response system and the drive system. Results of a simulation example show the effectiveness of the theoretical analysis.
Codimension-2 Bifurcation Dynamics and Infinity Analysis of a Class of Lorenz Chaos Systems With Memristors
HUANG Jun, CHEN Yuming
2020, 41(11): 1275-1283. doi: 10.21656/1000-0887.410023
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Based on the classical Lorenz system, a class of 3D memristive chaotic systems were obtained through feedback control, and the local high codimensional bifurcation and the infinite global dynamic behavior of the system were studied. Firstly, according to the average theory, the zeroHopf bifurcation behavior at the origin equilibrium point was analyzed. Secondly, with the center manifold theory, the doublezero bifurcation at the origin of the system was investigated. Finally, according to the Poincaré compactification method, the dynamics at infinity of the system was discussed.
On a Class of High-Order Nonlinear Singular Perturbed Nonlocal Systems’ Steady State Robin Problem
XU Jianzhong, WANG Weigang, MO Jiaqi
2020, 41(11): 1284-1291. doi: 10.21656/1000-0887.410049
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A class of high-order nonlinear integral-differential singular perturbation systems’ steady state Robin problem was discussed. Firstly, the theory of differential inequality for the high-order nonlinear nonlocal differential system was built. Then, the outer solution to the problem was structured and the boundary layer corrective term was obtained by means of the local coordinate system. Thus the formal asymptotic expansion of the solution was got. Finally, the uniform validity of the asymptotic expansion of the solution was proved with the theory of differential inequality.
A Class of 2nd-Order Singularly Perturbed Time Delay Nonlinear Problems With 2 Parameters
ZHU Hongbao, CHEN Songlin
2020, 41(11): 1292-1296. doi: 10.21656/1000-0887.410082
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A class of 2nd-order singularly perturbed time delay nonlinear problems were considered. The asymptotic solution to the problem was obtained with the singular perturbation method. Firstly, The outer solution was constructed by means of the singular perturbation method. Then, a stretched variable was introduced, the boundary layer correction of the solution was obtained, and the asymptotic analytic expansion solution to the problem was also given. Finally, under suitable conditions, the theory of differential inequalities was applied to prove the uniformly valid asymptotic expansion of the solution to the original problem.