Vertical Subsystem Research Articles

Robust Pointing Control of Marching Tank Gun With Matched and Mismatched Uncertainty

This article focuses on a robust control scheme for pointing control of the marching tank gun. Both matched and mismatched uncertainties, which may be nonlinear (possibly fast) time varying but bounded, are considered. First, the pointing control system is constructed as a coupled, nonlinear, and uncertain dynamical system with two interconnected (horizontal and vertical) subsystems. Second, for the horizontal pointing control, robust control is proposed to render the horizontal subsystem to be practically stable. Third, for the vertical pointing control, an uncertainty bound-based state transformation is constructed in a similar way of backstepping to convert the original mismatched system (i.e., the vertical subsystem) to be locally matched and then robust control is proposed to render the transformed system to be practically stable. Finally, it is proved that when the transformed system is rendered to be practically stable, the original system renders the same performance; therefore, vertical pointing control is achieved. This work should be among the first ever endeavor to cast all the coupling, nonlinearity, and (both matched and mismatched) uncertainty into the pointing control framework of the marching tank gun.

Coadjoint Orbits and Time-Optimal Problems for Step-$$2$$ Free Nilpotent Lie Groups

The coadjoint orbits and the Casimir functions are described for free nilpotent Lie groups of step $$2$$ . The symplectic foliation consists of affine subspaces in the Lie coalgebra. Left-invariant time-optimal problems are considered on Carnot groups of step $$2$$ for which the set of admissible velocities is a strictly convex compact set in the first layer of the Lie algebra that contains the origin in its interior. The first integrals of the vertical subsystem of the Hamiltonian system of the Pontryagin maximum principle are described. For two-dimensional coadjoint orbits, the constancy and periodicity properties of the solutions of this subsystem, as well as the phase flow, are described.

Periodic Time-Optimal Controls on Two-Step Free-Nilpotent Lie Groups

For two-step free nilpotent Lie algebras, we describe symplectic foliations and Casimir functions. A left-invariant time-optimal problem is considered in which the set of admissible controls is given by a strictly convex compact set in the first layer of the Lie algebra that contains the origin in its interior. We describe integrals for the vertical subsystem of the Hamiltonian system of the Pontryagin maximum principle. The properties of solutions to this system for low ranks of the Poisson bivector are described.

Improved integral backstepping control of variable speed motion systems with application to a laboratory helicopter

This paper proposes an improved method of integral backstepping for real time control of a laboratory helicopter with variable speed rotors known as the Two-Rotor Aero-dynamic System (TRAS). The coupled system is decomposed into the horizontal subsystem (HS) and the vertical subsystem (VS) and traditional backstepping, augmented with direct integral action is designed for each subsystem. The transient response to both constant and time varying references is then simultaneously improved by modifying an already proposed method called dual boundary conditional integration. A switching technique is also employed to enhance the tracking response of the undamped HS for its bi-directional motor which exhibits jerking effects. Experimental results show that the proposed approach yields improved transient and tracking performance when compared to previously proposed methods exploiting conditional integration earlier proposed for improving the transient response of controlled nonlinear systems with integral action. The results also show the robustness of the proposed method in the presence of the coupling effects and additional external disturbance applied to the system in the form of a wind gust.

Dual boundary conditional integral backstepping control of a twin rotor MIMO system

Conditional integration is a technique used to improve the transient performance of controllers with integral action. This paper proposes a novel modification of this technique and integral backstepping for the control of a Twin Rotor MIMO System (TRMS) to ensure efficient asymptotic output regulation of the system without degrading the transient response. The control objectives are to stabilize the helicopter-like system, reach a desired position and precisely track a given trajectory in the presence of significant cross couplings. The TRMS is decoupled into the vertical subsystem (VS) and the horizontal subsystem (HS) and an integral backstepping controller (IBC) is designed for each subsystem with the cross couplings considered as uncertainties. An adaptable integral gain law, which can be applied to any continuous control law, is then formulated to provide integral action conditionally within two (outer and inner) boundary layers, based on the output tracking error and reference signals. Simulation results show that the obtained dual boundary conditional integral backstepping control (DBCIBC) approach achieves robust output regulation in the presence of the system's uncertainties and external disturbances whilst maintaining a good transient response. Furthermore, comparisons with three available methods in the literature also indicate that the DBCIBC significantly improves performance in terms of error and control signal indices especially for the case of tracking a time varying reference input where the error index in the VS is reduced by over 50% on an average.

Maxwell Strata and Conjugate Points in the Sub-Riemannian Problem on the Lie Group SH(2)

We study local and global optimality of geodesics in the left invariant sub-Riemannian problem on the Lie group SH(2). We obtain the complete description of the Maxwell points corresponding to the discrete symmetries of the vertical subsystem of the Hamiltonian system. An effective upper bound on the cut time is obtained in terms of the first Maxwell times. We study the local optimality of extremal trajectories and prove the lower and upper bounds on the first conjugate times. We also obtain the generic time interval for the n-th conjugate time which is important in the study of sub-Riemannian wavefront. Based on our results of n-th conjugate time and n-th Maxwell time, we prove a generalization of Rolle's theorem that between any two consecutive Maxwell points, there is exactly one conjugate point along any geodesic.

Extremal Trajectories and Maxwell Strata in Sub-Riemannian Problem on Group of Motions of Pseudo-Euclidean Plane

We consider the sub-Riemannian length minimization problem on the group of motions of pseudo-Euclidean plane that form the special hyperbolic group SH(2). The system comprises of left invariant vector fields with 2-dimensional linear control input and energy cost functional. We apply the Pontryagin maximum principle to obtain the extremal control input and the sub-Riemannian geodesics. A change of coordinates transforms the vertical subsystem of the normal Hamiltonian system into the mathematical pendulum. In suitable elliptic coordinates, the vertical and the horizontal subsystems are integrated such that the resulting extremal trajectories are parametrized by the Jacobi elliptic functions. Qualitative analysis reveals that the projections of normal extremal trajectories on the xy-plane have cusps and inflection points. The vertical subsystem being a generalized pendulum admits reflection symmetries that are used to obtain a characterization of the Maxwell strata.

Adaptive second-order sliding mode controller for a twin rotor multi-input–multi-output system

In this study, an adaptive second-order sliding mode (SOSM) controller is proposed to control a laboratory helicopter called the twin-rotor multi-input–multi-output system (TRMS). The design objectives of the controller are to stabilise the TRMS in significant cross couplings, reach a desired position and accurately track a specified trajectory. The TRMS model is divided into a horizontal and a vertical subsystem (VS). The cross coupling existing between the two subsystems is considered as the system uncertainty. A simple adaptive tuning law is developed for the SOSM controller to deal with the bounded system uncertainty. The major advantage offered by this adaptive SOSM controller is that advance knowledge about the upper bound of system uncertainty is not a necessary requirement. The adaptive SOSM controller for the VS uses a proportional plus integral sliding surface to counter the offset present in the pitch angle. System robustness and the stability of the controller are proved by using the Lyapunov criterion. Apart from imparting robustness, the proposed adaptive SOSM controller reduces undesired chattering in the control input and thus is suitable for application in practical motion control applications. The proposed control scheme is validated by simulation results and is compared against the existing proportional-integral-derivative controllers to show that the overall performance of the proposed adaptive SOSM controller is better in the aspects of error and control indices.

Controller Design of Quadrotor Aerial Robot

This paper deduced the nonlinear dynamic model of a quadrotor aerial robot, which was a VTOL (vertical tale-off and landing) unmanned air vehicle. Since that is a complex model with the highly nonlinear multivariable strongly coupled and under-actuated property, the controller design of it was very difficult. Aimed at attaining the excellent controller, the whole system can be divided into three interconnected parts: attitude subsystem, vertical subsystem, position subsystem. Then nonlinear control strategy of them has been described, such as SDRE and Backstepping. The controller design was presented to stabilize the whole system. Through simulation result indicates, the various models have shown that the control law stabilize a quadrotor aerial robot with good tracking performance and robotness of the system.

Systematic Analysis and Research on Logistics Network

Logistics network is the most meaningful macro-form of logistics system in nowadays. But the existing research and application of logistics network lacked of systematic theory guidance, and it leading to the logistics resources scattered and industrial development unbalanced, which greatly hindered the efficiency improvement of logistics network. From a perspective of whole system and based on system theories, this paper presents a novel stereoscopic structure for logistic networks capable of describing the essence by dividing the system into horizontal sub-system that include infrastructure network, logistics organization network, logistics information network and vertical subsystem that include demand networks, logistics function network, target customer network. In addition, a summary is proposed to specifically the difference and relationship between logistics network and supply chain. The holistic standpoint provides an inspiration for the logistics network development, and laid an important theoretical basis for the efficient use of logistics resources and logistics network optimization.

A Novel Fuzzy-Sliding and Fuzzy-Integral-Sliding Controller for the Twin-Rotor Multi-Input–Multi-Output System

In this paper, a novel fuzzy-sliding and fuzzy-integral-sliding controller (FSFISC) is designed to position the yaw and pitch angles of a twin-rotor multi-input-multi-output system (TRMS). With the coupling effects, which are considered as the uncertainties, the highly coupled nonlinear TRMS is pseudodecomposed into a horizontal subsystem and a vertical subsystem (VS). The proposed FSFISC consists of a fuzzy-sliding controller and an FISC for the horizontal and the VSs, respectively. The reaching conditions and the stability of the TRMS with the proposed controller are guaranteed. Simulation results are included to indicate that TRMS with the presented FSFISC can greatly alleviate the chattering effect and remain robust to the external disturbances. In addition, the performance comparisons with the proportional-integral-differential (PID) approach using a modified real-value-type genetic algorithm are provided to show that the FSFISC has better performance in the aspects of error and control indexes.