Abstract
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.
Highlights
The renewability of water resources is very environmentally friendly, and people have reached a consensus on vigorously developing hydropower, especially in China with its abundant water resources [1], [2]
When the values of the given parameters were substituted into Equation (28), the terminal sliding surface of the timedelay fractional-order hydraulic turbine regulating system (HTRS) can be obtained as si(t) = D0.98−1xi + D−1(50xi + ln0.2(|xi| + 1)sat(xi)), (i = 1, 2, 3, 4) . (51)
It can be seen that the time-delay fractional-order HTRS can be stabilized in a finite time
Summary
The renewability of water resources is very environmentally friendly, and people have reached a consensus on vigorously developing hydropower, especially in China with its abundant water resources [1], [2]. P. Chen et al.: Finite-Time Stability of a Time-Delay Fractional-Order HTRS The definition of the Caputo fractional derivative and gamma function and a method for solving systems with a time delay are given in Sect. MATHEMATICAL MODEL OF A TIME-DELAY FRACTIONAL-ORDER HTRS By modeling each part of the integer-order HTRS separately and integrating the transfer function according to each subsystem, the following mathematical model of the nonlinear
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