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Control Systems - Part 5

Stability Hệ thống ổn định là một chủ đề quan trọng, bởi vì hệ thống không ổn định có thể không thực hiện một cách chính xác và thực tế có thể gây hại cho người dân. Có một số phương pháp khác nhau và các công cụ có thể được sử dụng để xác định sự ổn định của hệ thống, tùy thuộc vào cho dù bạn đang ở trong không gian nhà nước, lĩnh vực phức tạp. | Control Systems Print version - Wikibooks collection of open-content textbooks Page 123 of 209 Stability System stability is an important topic because unstable systems may not perform correctly and may actually be harmful to people. There are a number of different methods and tools that can be used to determine system stability depending on whether you are in the state-space or the complex domain. http en.wikibooks.org w index.php title ControlSystems Printversion printable yes 10 30 2006 Control Systems Print version - Wikibooks collection of open-content textbooks Page 124 of 209 Stability BIBO Stability When a system becomes unstable the output of the system approaches infinity or negative infinity which often poses a security problem for people in the immediate vicinity. Also systems which become unstable often incur a certain amount of physical damage which can become costly. This chapter will talk about system stability what it is and why it matters. A system is defined to be BIBO Stable if every bounded input to the system results in a bounded output. This means that so long as we don t input infinity to our system we won t get infinity output. Determining BIBO Stability We can prove mathematically that a system f is BIBO stable if an arbitrary input x is bounded by two finite but large arbitrary constants M and -M -Af T Af We apply the input x and the arbitrary boundries M and -M to the system to produce three outputs i z fM VM Ậf S-.V Af Now all three outputs should be finite for all possible values of M and x and they should satisfy the following relationship y-M yx VM If this condition is satisfied then the system is BIBO stable. Example Consider the system ft t 2 We can apply our test selecting an arbitrarily large finite constant M and an arbitrary input x such that -M x M. As M approaches infinity but does not reach infinity we can show that http en.wikibooks.org w index.php title ControlSystems Printversion printable yes 10 30 2006 Control Systems .