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Ch5

Main content. The concept of stabilityThe Routh-Hurwitz stability criterionThe relative stability of feedback systemsDesign examples and MATLAB simulationSummary. Why investigate stability?. The issue of ensuring the stability of a closed-loop system is the most important to control system desig

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Ch5

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    1. Ch5 The Stability of Linear Feedback Systems

    2. Main content The concept of stability The Routh-Hurwitz stability criterion The relative stability of feedback systems Design examples and MATLAB simulation Summary

    3. Why investigate stability?

    4. 5.1 The concept of stability A stable system is a dynamic system with a bounded output to a bounded input (BIBO). absolute stability relative stability

    5. Examples and illustration Stability and super-maneuverability of modern fighter aircraft ( Figure or P398) Vibration control (sputnik 1 2 and bridge) Physical illustration (refer to Fig6.1)

    6. Stability for LTI system A necessary and sufficient condition for a feedback system to be stable is that all the poles of the system transfer function have negative real parts. Impulse response approach to zero when time lead to infinite.

    7. How to determine stability? The s-plane approach The frequency plane approach The time-domain approach

    8. 5.2 The Routh-Hurwitz criterion A necessary condition A necessary and sufficient condition

    9. Routh-Hurwitz criterion Routh array formulation Routh criterion:

    10. Four cases and examples Case 1: No element in first column is zero. Case 2: Zeros in the first column while some other elements of the row are nonzero. Case 3: Zeros in the first column and other elements of the row are also zero. Case 4: Repeated roots on the imaginary axis.

    11. 5.3 The relative stability The relative stability of a system can be defined as the property that is measured by the relative real part of each root or pair of roots. Axis shift and examples

    12. 5.4 Design example and MATLAB simulation Tracked vehicle turning control Disk drive read system

    13. Summary The concept of stability of feedback system The Routh criterion and its application The relative stability of feedback system

    14. Assignment E6.1 E6.4 E6.8 E6.13 P6.5 (a) P6.18 DP6.6

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