TAILIEUCHUNG - Sliding mode in automatic control systems

In industrial sector as well as military technology - especially in the improvement, modernization and manufacture of new weapons and technical equipment, the synthesis of high quality control systems is always an urgent demand. The assurance of quality for control systems operating under disturbance and uncertainty conditions of dynamic model requires the development of new control algorithms based on the modern control theory. | Nghiên cứu khoa học công nghệ SLIDING MODE IN AUTOMATIC CONTROL SYSTEMS Nguyen Vu1 Tran Ngoc Binh2 Ha Thi Thi2 Abstract In industrial sector as well as military technology - especially in the improvement modernization and manufacture of new weapons and technical equipment the synthesis of high quality control systems is always an urgent demand. The assurance of quality for control systems operating under disturbance and uncertainty conditions of dynamic model requires the development of new control algorithms based on the modern control theory. Along with other tools of modern control theory such as optimal control adaptive control linear robust control fuzzy control. sliding mode control is a relatively universal tool easy in technical realization and have high effectiveness in practice. This report presents sliding mode control features and its application for some classes in military technology. Keywords Sliding mode Sliding control Uncertain parameters Elastic backlash. 1. INTRODUCTION OF SLIDING CONTROL Consider a system described by the following dynamic equation x Ax Bu 1 where x e Rn A e Rn-n B e Rn-m u e Rm The idea of sliding mode is derived from transforming equation 1 into a set of equations 1 x. A x 2a 1 2 x2 A21 x A22 x B2 .u 2b . . x e Rn-m x e Rm where 221 -2 . x2 in 2a can be regarded as the virtual control signal of the system. To obtain the system stability state feedback control is used x2 -C1 x 3 where C1 e Rm- n-m . However because x2 is virtual control signal equation 3 can not be always exist. Then the equation 3 can be written as S C1 x Ix2 Cx 0 4 where S e Rm C e The problem is that in order to make the system in 1 stable control signal u_ needs satisfying condition 4 . Condition 4 occurs when 0 when m 1 5 When m 1 then S T Or ST. CAx CBu 0 when S 0. 6 By defining u - CB -1 CAx - CB -1 S 7 Tạp chí Nghiên cứu KH CN quân sự Số Đặc san ACMEC 07 - 2017 71 Điều khiển - Cơ điện tử - Truyền thông With sgn S sng S1 .sgn sm

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