Finite-Time Stability of a Time-Delay Fractional-Order Hydraulic Turbine Regulating System

Finite-time terminal sliding mode control of a time-delay fractional-order hydraulic turbine regulating system (HTRS) is studied. First, an improved Adams–Bashforth–Moulton algorithm is introduced to solve the fractional-order nonlinear system with a time delay. Then, given the unique advantage of fractional calculus and the great influence that time delay has on system stability, a time-delay fractional-order HTRS is introduced. Moreover, by means of a frequency distribution model, the transformation of the fractional-order HTRS is realized. To stabilize the system under the influence of a random disturbance, a novel terminal sliding surface and a controller are proposed, and the detailed mathematical deduction for system stability is given. Finally, the simulation results, compared with traditional proportional-integral-derivative control and the conventional sliding mode control in the existing literature, demonstrate the validity and significant advantages of the proposed finite-time control scheme.

[1]  Diyi Chen,et al.  Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system , 2015 .

[2]  H. Momeni,et al.  Linear Matrix Inequality Based Fractional Integral Sliding-Mode Control of Uncertain Fractional-Order Nonlinear Systems , 2017 .

[3]  Jay Singh,et al.  Two degree of freedom internal model control-PID design for LFC of power systems via logarithmic approximations. , 2017, ISA transactions.

[4]  Jiandong Yang,et al.  Surge wave characteristics for hydropower station with upstream series double surge tanks in load rejection transient , 2017 .

[5]  Zhihong Man,et al.  Continuous finite-time control for robotic manipulators with terminal sliding mode , 2003, Autom..

[6]  YangQuan Chen,et al.  A new collection of real world applications of fractional calculus in science and engineering , 2018, Commun. Nonlinear Sci. Numer. Simul..

[7]  Shouming Zhong,et al.  Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems , 2014, Autom..

[8]  Nan Zhang,et al.  An evolving T-S fuzzy model identification approach based on a special membership function and its application on pump-turbine governing system , 2018, Eng. Appl. Artif. Intell..

[9]  Bin Wang,et al.  Robust Takagi-Sugeno fuzzy control for fractional order hydro-turbine governing system. , 2016, ISA transactions.

[10]  Zhihong Man,et al.  Continuous Fast Nonsingular Terminal Sliding Mode Control of Automotive Electronic Throttle Systems Using Finite-Time Exact Observer , 2018, IEEE Transactions on Industrial Electronics.

[11]  Qijuan Chen,et al.  Nonlinear Dynamical Analysis of Hydraulic Turbine Governing Systems with Nonelastic Water Hammer Effect , 2014, J. Appl. Math..

[12]  C. Bao,et al.  Water Resources Flows Related to Urbanization in China: Challenges and Perspectives for Water Management and Urban Development , 2011, Water Resources Management.

[13]  Huanhuan Li,et al.  Nonlinear modeling and dynamic analysis of a hydro-turbine governing system in the process of sudden load increase transient , 2016 .

[14]  Bin Wang,et al.  Finite time takagi-sugeno fuzzy control for hydro-turbine governing system , 2018 .

[15]  Xiaohui Yuan,et al.  Nonlinear dynamic analysis and robust controller design for Francis hydraulic turbine regulating system with a straight-tube surge tank , 2017 .

[16]  Nan Zhang,et al.  Design of a fractional-order PID controller for a pumped storage unit using a gravitational search algorithm based on the Cauchy and Gaussian mutation , 2017, Inf. Sci..

[17]  Saurabh Verma,et al.  A note on Katugampola fractional calculus and fractal dimensions , 2018, Appl. Math. Comput..

[18]  Diyi Chen,et al.  Modeling oscillation modal interaction in a hydroelectric generating system , 2018, Energy Conversion and Management.

[19]  Yuning Zhang,et al.  Experimental Study of Load Variations on Pressure Fluctuations in a Prototype Reversible Pump Turbine in Generating Mode , 2017 .

[20]  Wencheng Guo,et al.  Modeling and dynamic response control for primary frequency regulation of hydro-turbine governing system with surge tank , 2018, Renewable Energy.

[21]  Yuning Zhang,et al.  A review of rotating stall in reversible pump turbine , 2017 .

[22]  Guanghui Sun,et al.  Practical tracking control of linear motor via fractional-order sliding mode , 2018, Autom..

[23]  Shaocheng Tong,et al.  Adaptive fuzzy tracking control design for permanent magnet synchronous motors with output constraint , 2016, Nonlinear Dynamics.

[24]  Sara Dadras,et al.  A Note on the Lyapunov Stability of Fractional-Order Nonlinear Systems , 2017 .

[25]  Chen Sheng,et al.  Stability analysis of governor-turbine-hydraulic system by state space method and graph theory , 2016 .

[26]  Leonid Fridman.  Technical Committee on Variable Structure and Sliding-Mode Control [Technical Activities] , 2016 .

[27]  Y. Chen,et al.  Lyapunov stability of fractional-order nonlinear systems: A distributed-order approach , 2014, ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014.

[28]  I. Podlubny.  Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

[29]  Vasily E. Tarasov,et al.  Macroeconomic models with long dynamic memory: Fractional calculus approach , 2018, Appl. Math. Comput..

[30]  Yuhua Cheng,et al.  Design of optimal lighting control strategy based on multi-variable fractional-order extremum seeking method , 2018, Inf. Sci..

[31]  Wencheng Guo,et al.  Hopf bifurcation control of hydro-turbine governing system with sloping ceiling tailrace tunnel using nonlinear state feedback , 2017 .

[32]  Jing Zhou,et al.  Robust Adaptive Control of Uncertain Nonlinear Systems in the Presence of Input Saturation and External Disturbance , 2011, IEEE Transactions on Automatic Control.

[33]  Diyi Chen,et al.  Sensitivity analysis of a Pelton hydropower station based on a novel approach of turbine torque , 2017 .

[34]  Wenlong Fu,et al.  An adaptively fast fuzzy fractional order PID control for pumped storage hydro unit using improved gravitational search algorithm , 2016 .

[35]  Shengyuan Xu,et al.  Observer-Based Adaptive Neural Network Control for Nonlinear Stochastic Systems With Time Delay , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[36]  YangQuan Chen,et al.  Fractional-order exponential switching technique to enhance sliding mode control , 2017 .

[37]  Y. Chen,et al.  Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems , 2015 .

[38]  Nan Zhang,et al.  Load Frequency Control of a Novel Renewable Energy Integrated Micro-Grid Containing Pumped Hydropower Energy Storage , 2018, IEEE Access.

[39]  Yang Zheng,et al.  Adaptive condition predictive-fuzzy PID optimal control of start-up process for pumped storage unit at low head area , 2018, Energy Conversion and Management.