Adaptive Backstepping Control for Fractional-Order Nonlinear Systems with External Disturbance and Uncertain Parameters Using Smooth Control

In this paper, we consider controlling a class of single-input-single-output (SISO) commensurate fractional-order nonlinear systems with parametric uncertainty and external disturbance. Based on backstepping approach, an adaptive controller is proposed with adaptive laws that are used to estimate the unknown system parameters and the bound of unknown disturbance. Instead of using discontinuous functions such as the $\mathrm{sign}$ function, an auxiliary function is employed to obtain a smooth control input that is still able to achieve perfect tracking in the presence of bounded disturbances. Indeed, global boundedness of all closed-loop signals and asymptotic perfect tracking of fractional-order system output to a given reference trajectory are proved by using fractional directed Lyapunov method. To verify the effectiveness of the proposed control method, simulation examples are presented.Comment: Accepted by the IEEE Transactions on Systems, Man and Cybernetics: Systems with Minor Revision

Single phase second order sliding mode controller for complex interconnected systems with extended disturbances and unknown time-varying delays

Novel results on complex interconnected time-delay systems with single phase second order sliding mode control is investigated. First, a reaching phase in traditional sliding mode control (TSMC) is removed by using a novel single phase switching manifold function. Next, a novel reduced order sliding mode observer (ROSMO) with lower dimension is suggested to estimate the unmeasurable variables of the plant. Then, a new single phase second order sliding mode controller (SPSOSMC) is established based on ROSMO tool to drive the state variables into the specified switching manifold from beginning of the motion and reduce the chattering in control input. Then, a stability condition is suggested based on the well-known linear matrix inequality (LMI) method to ensure the asymptotical stability of the whole plant. Finally, an illustrated example is simulated to validate the feasible application of the suggested technique

Stabilisation of Time Delay Systems with Nonlinear Disturbances Using Sliding Mode Control

This paper focuses on a class of control systems with delayed states and nonlinear disturbances using sliding mode techniques. Both matched and mismatched uncertainties are considered which are assumed to be bounded by known nonlinear functions. The bounds are used in the control design and analysis to reduce conservatism. A sliding function is designed and a set of sufficient conditions is derived to guarantee the asymptotic stability of the corresponding sliding motion by using the Lyapunov-Razumikhin approach which allows large time varying delay with fast changing rate. A delay dependent sliding mode control is synthesised to drive the system to the sliding surface in finite time and maintain a sliding motion thereafter. Effectiveness of the proposed method is demonstrated via a case study on a continuous stirred tank reactor system

An Adaptive Controller Design for Flexible-joint Electrically-driven Robots With Consideration of Time-Varying Uncertainties

Almost all present control strategies for electrically-driven robots are under the rigid robot assumption. Few results can be found for the control of electrically driven robots with joint flexibility. This is because the presence of the joint flexibility greatly increases the complexity of the system dynamics. What is worse is when some system dynamics are not available and a good performance controller is required. In this paper, an adaptive design is proposed to this challenging problem. A backstepping-like procedure incorporating the model reference adaptive control is employed to circumvent the difficulty introduced by its cascade structure and various uncertainties. A Lyapunov-like analysis is used to justify the closed-loop stability and boundedness of internal signals. Moreover, the upper bounds of tracking errors in the transient state are also derived. Computer simulation results are presented to demonstrate the usefulness of the proposed scheme. Keywords: Adaptive control; Flexible-joint electrically-driven robot; FAT 2. Introduction Control of rigid robots has been well understood in recent years, but most of the schemes ignore the dynamics coming from electric motors and harmonic drivers that are widely implemented in the industrial robots. However, actuator dynamics constitute an important part of the complete robot dynamics, especially in the cases of high-velocity movement and highly varying loads[1],[2]. The main reason for using a reduced model is to simplify complexity of controller design. For each joint, consideration of the flexibility from the M. C. Chien was with the Department of Mechanical Engineering, National Taiwan University of Science and Technology. He is now with the Mechanical and Systems Research Laboratories, Industrial Technology Research Institute, No. 195, Sec. 4, Chung-Hsing Rd., Chutung, Hsinchu, 310, Taiwan, R.O.C. (e-mail: [email protected]). 2 A. C. Huang is with the Department of Mechanical Engineering, National Taiwan University of Science and Technology. No. 43, Keelung Rd., Sec. 4, Taipei, Taiwan, ROC. (Tel:+886-2-27376490, Fax: +886-2-37376460, E-mail: [email protected]). (A. C. Huang provides phone number because he is the corresponding author.

STABILITY AND PERFORMANCE OF NETWORKED CONTROL SYSTEMS

Network control systems (NCSs), as one of the most active research areas, are arousing comprehensive concerns along with the rapid development of network. This dissertation mainly discusses the stability and performance of NCSs into the following two parts. In the first part, a new approach is proposed to reduce the data transmitted in networked control systems (NCSs) via model reduction method. Up to our best knowledge, we are the first to propose this new approach in the scientific and engineering society. The "unimportant" information of system states vector is truncated by balanced truncation method (BTM) before sending to the networked controller via network based on the balance property of the remote controlled plant controllability and observability. Then, the exponential stability condition of the truncated NCSs is derived via linear matrix inequality (LMI) forms. This method of data truncation can usually reduce the time delay and further improve the performance of the NCSs. In addition, all the above results are extended to the switched NCSs. The second part presents a new robust sliding mode control (SMC) method for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise (Wiener process). The key features of the proposed method are to apply singular value decomposition (SVD) to all structural uncertainties, to introduce adjustable parameters for control design along with the SMC method, and new Lyapunov-type functional. Then, a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems are derived via linear matrix inequality (LMI) forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1 by the proposed control rule. Furthermore, the novel Lyapunov-type functional for the uncertain stochastic systems is used to design a new robust control for the general case where the derivative of time-varying delay can be any bounded value (e.g., greater than one). It is theoretically proved that the conservatism of the proposed method is less than the previous methods. All theoretical proofs are presented in the dissertation. The simulations validate the correctness of the theoretical results and have better performance than the existing results