Robust output feedback control of time-delay nonlinear systems with dead-zone input and application to chemical reactor system

Nonlinear Dynamics - This paper investigates the problem of robust output feedback control for a class of time-delay nonlinear systems with unknown continuous time varying output function. Unlike...     

Exploring the analogy for adaptive attitude control of a ground-based satellite system

Equations of motion for a special system pertaining to the class of mixed nonholonomic mechanical systems are studied in the modern setting of geometric mechanics. The presented attitude control test bed is intended to provide an experimental facility that, in certain senses, emulates the dynamics of on-orbit conditions in the laboratory site, allowing the evaluation of path planning and feedback control algorithms. This paper demonstrates the feasibility of the approach and proposes a concurrent solution to the attitude tracking control problem that, due to uncertainties of the parameters, is likely to require effective adaptive aptitudes. Moreover, the invariance with respect to Lie group actions of governing dynamics and measurable output readings has allowed the investigation of controllability and observability in an intrinsic manner.     

Magnetic torque attitude control of a satellite using the state-dependent Riccati equation technique

A non-linear attitude control method for a satellite with magnetic torque rods using the state-dependent Riccati equation (SDRE) technique has been developed. The magnetic torque caused by the interaction with the Earth's magnetic field and the magnetic moment of torque rods plays a role of the control torque. The detailed equations of motion for this system are presented using angular velocity and quaternions. The SDRE controller is developed for the non-linear systems which can be formed in pseudo-linear representations using the state-dependent coefficient (SDC) method without linearization procedure. The aim of this control system is to achieve a stable attitude within 5°, and minimize the control effort. The stability regions for the SDRE controlled satellite system are estimated through the investigation of the stability conditions developed for pseudo-linear systems and the application of Lyapunov's theorem. For comparisons, the Linear Quadratic Regulator (LQR) method using the solution of the algebraic Riccati equation (ARE) is also applied to this non-linear system. The performance of the SDRE non-linear control system demonstrates more robustness and stability than the LQR control system when subjected to a wide range of initial conditions.     

Estimate of the control threshold value in the problem on a time-optimal satellite attitude transition maneuver

The time-optimal problem is considered for a nonlinear Lagrangian system with one degree of freedom. The system is controlled by a force bounded in absolute value, and all noncontrol forces are potential.We study the properties of optimal synthesis on the phase cylinder and indicate the conditions under which it has the simplest structure, namely, involves at most one switching for any initial conditions. The approach is used to specify the structure of the well-known solution in the classical problem on the time-optimal satellite attitude transition maneuver in the orbit plane.     

Advances in dynamics and control of tethered satellite systems

The concept of tethered satellite system （TSS） promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and interesting problems related to their dynamics, control, and physical implementation. Over the past decades, this exciting topic has attracted significant attention from many researchers and gained a vast number of analytical, numerical and experimental achievements with a focus on the two essential aspects of both dynamics and control. This review article presents the historic background and recent hot topics for the space tethers, and introduces the dynamics and control of TSSs in a progressive manner, from basic operating principles to the state-of-the-art achievements.     

硅微隧道式加速度计的输出反馈控制电路设计

为提高硅微隧道式加速度计的灵敏度,必须设计出高灵敏度的输出和反馈控制电路。在电路设计中,通过采用行之有效的措施来降低噪声和干扰可达到提高灵敏度的目的,如：将隧道式加速度计敏感单元的参考地设置为同一的大地;采用能抑制隧道式加速度计敏感单元和半导体器件所产生的1/f噪声的低噪声运算放大器;在电压信号放大过程中,尽量抑制干扰和噪声;且在电压反馈电路设计中,保护敏感单元不受损坏等措施。测试结果为标定因数1.2659V/g,其非线性度小于1%,可见在提高线性度的基础上也提高了灵敏度。     

Adaptive output feedback control of uncertain nonlinear chaotic systems based on dynamic surface control technique

In this paper, an adaptive output feedback control algorithm based on the dynamic surface control (DSC) is proposed for a class of uncertain chaotic systems. Because the system states are assumed to be unavailable, an observer is designed to estimate those unavailable states. The main advantage of this algorithm can overcome the problem of “explosion of complexity” inherent in the backstepping design. Thus, the proposed control approach is simpler than the traditional backstepping control for the uncertain chaotic systems. The stability analysis shows that the system is stable in the sense that all signals in the closed-loop system are uniformly ultimately bounded (UUB) and the system output can track the reference signal to a bounded compact set. Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

Bifurcation analysis for T system with delayed feedback and its application to control of chaos

In this paper, a three-dimensional autonomous nonlinear system called the T system which has potential application in secure communications is considered. Regarding the delay as parameter, we investigate the effect of delay on the dynamics of T system with delayed feedback. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associated characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, by using the normal form theory and center manifold argument, we derive the explicit formulas determining the stability, direction and other properties of bifurcating periodic solutions. Finally, we give several numerical simulations, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable steady state or a periodic orbit.     

Averaging method for discrete systems and its application to control problems

We propose and justify algorithms for partial and complete averaging of systems of discrete equations and inclusions. On the basis of the averaging schemes obtained, we construct algorithms for the numerical asymptotic solution of problems of optimal control for discrete systems.Translated from Neliniini Kolyvannya, Vol. 7, No. 2, pp. 241–254, April–June, 2004.     

Study on synchronization and parameters insensitivity of a class of hyperchaotic systems using nonlinear feedback control

A class of hyperchaotic systems has strong noise robustness. When conventional synchronization algorithms are used in this system, however, the convergence rate of synchronization is slow, and the synchronization performances are very sensitive to the parameters of response system. To resolve the problems, synchronization using nonlinear feedback control is proposed. According to Hurwitz stability theory, designing a nonlinear controller can make the real parts of the eigenvalues of the error equation’s Jacobian matrix negative. And the absolute values of the eigenvalues are larger, the convergence rate of synchronization is faster. Besides, the theoretical results of parameters insensitivity are given. Finally, numerical simulations are given to verify and test the correctness and effectiveness of the methods we proposed.     

Using the delayed feedback control and saturation control to suppress the vibration of the dynamical system

In the present paper, the delayed feedback control is applied to suppress or stabilize the vibration of the primary system in a two degree-of-freedom dynamical system with parametrically excited pendulum. The case of a 1:2 internal resonance between pendulum and primary system is studied. The method of multiple scales is applied to obtain second-order approximations of the response of the system. The system stability and bifurcations of equilibrium point of the averaged equations are computed. It is shown that the delayed feedback control can be used to suppress the vibration or stabilize the system when the saturation control is invalid. The vibration of the primary system can be suppressed by the delayed feedback control when the original system is in the single-mode motion. The effect of gain and delay on the vibration suppression is discussed. As the delay varies at a fixed value of the gain, the vibration of the primary system can be suppressed at some values of the delay. The vibration suppression performance of the system is improved at a large value of the gain. The vibration of the primary system could be suppressed about 56% compared with the original system by choosing the appropriate values of gain and delay. The delayed feedback control also can be used to stabilize the system when the original system is unstable. The gain and delay could be chosen as the controlling parameters. Numerical simulation is agreement with the analytical solutions well.     

Adaptive synchronization of the energy resource systems with mismatched parameters via linear feedback control

Synchronization of energy resource systems with mismatched parameters is investigated. An adaptive linear feedback control scheme for the synchronization of energy resource systems is proposed when the parameters of the master system are unknown and different from those of the slave system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two slightly mismatched chaotic systems asymptotically synchronized. Finally, numerical simulations are performed to verify the proposed results.     

Time-delayed feedback control of improved friction-induced model: application to moving belt of particle supply device

Nonlinear Dynamics - In this paper, based on the original friction-induced oscillation, we propose a new friction-induced mathematical model associated with moving belt of particle supply device....     

Adaptive fuzzy backstepping output feedback control of nonlinear uncertain time-delay systems based on high-gain filters

In this paper, an adaptive fuzzy output feedback control approach is developed for a class of SISO uncertain nonlinear strict-feedback systems. The considered nonlinear systems contain unknown nonlinear functions, unknown time-varying delays and unmeasured states. The fuzzy logic systems are first used to approximate the unknown nonlinear functions, and then a high-gain filter is designed to estimate the unmeasured states. Combining the backstepping recursive design technique and adaptive fuzzy control design, an adaptive fuzzy output feedback backstepping control method is developed. It is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and both the observer error and tracking error converge to a small neighborhood of the origin. Two key advantages of our scheme are that (i) the high-gain filter is designed to estimate unmeasured states of time-delay nonlinear system, and (ii) the virtual control gains are functions. A simulation is included to illustrate the effectiveness of the proposed approach.     

Output feedback regulation of time-delay nonlinear systems with unknown continuous output function and unknown growth rate

Nonlinear Dynamics - This paper is concerned with the global regulation via output feedback for the time-delay nonlinear systems with unknown continuous output function and unknown growth rate....     

Decentralized adaptive fuzzy control of large-scale nonaffine nonlinear systems by state and output feedback

This paper develops two novel decentralized adaptive fuzzy control methods of large-scale nonaffine uncertain nonlinear systems. By using a fuzzy inference system and implicit function theorem, a decentralized direct adaptive state feedback fuzzy control algorithm is firstly presented for a class of large-scale nonaffine continuous-time systems. By using a high-gain observer to reconstruct the system states, an extension is made to a decentralized output feedback control of unmeasurable interactive nonaffine systems. The decentralized adaptive fuzzy control schemes via state and output feedback guarantee the stability of the closed-loop large-scale systems. The effectiveness of the developed approaches is demonstrated through simulation results of a platoon of vehicles within an automated highway system.