Biomedical Control Systems - THE CONCEPT OF STABILITY & ROOT LOCUS TECHNIQUE (short Questions & Answers)
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The document discusses various concepts related to control systems stability, including definitions, conditions for stability, and methods of analysis like the Routh and Hurwitz criteria. It emphasizes the importance of ensuring bounded input results in bounded output and introduces techniques such as the root locus for determining system behavior. Key terms such as asymptotic stability, BIBO stability, and dominating poles are also defined.
Biomedical Control Systems - THE CONCEPT OF STABILITY & ROOT LOCUS TECHNIQUE (short Questions & Answers)
- 1. BIOMEDICAL ENGINEERING – BCS – UNIT III - SHORT QUESTIONS AND ANSWERS MATHANKUMAR.S, COORDINATOR/BME, V.M.K.V.E.C BIOMEDICAL CONTROL SYSTEMS UNIT – III: THE CONCEPT OF STABILITY & ROOT LOCUS TECHNIQUE PART-A 1. Define stable system. To get the desired output, system must pass through transient period. Transient response must vanish after some time to get the final value closer to the desired value. Such systems in which transient response dies out after some time is called stable systems. (or) A system is said to be stable, if every bounded input produces a bounded output. 2. What are the conditions for a linear time invariant system to be stable? A linear time- invariant system is stable if the following two conditions of system stability are satisfied. When the system is by a bounded input, the output is bounded. In the absence of the input, the output tends towards zero irrespective of initial conditions. 3. Define parameter variations. The parameters of any control system cannot be constant through its entire life. There are always changes in the parameters due to environmental changes and other disturbances. These changes are called parameter variations. 4. State routh criterion for stability. Routh’s criterion states that, the necessary and sufficient condition for the stability is that, all the elements in the first column of the Routh’s array be positive. If the condition is not met, the system is unstable, and the number of sign changes in the elements of the first column of Routh’s array corresponds to the number of roots of characteristic equation in the right half of the S-plane. 5. Define sensitivity of a control system. An effect in the system performance due to parameter variations can be studied mathematically defining the tern sensitivity of a control system. The change in particular variable due to parameter can be expressed in terms of sensitivity. 6. What do you mean by asymptotic stability? In the absence of the input, the output tends towards zero (the equilibrium state of the systems) irrespective of initial conditions. This stability is known as asymptotic stability.
- 2. BIOMEDICAL ENGINEERING – BCS – UNIT III - SHORT QUESTIONS AND ANSWERS MATHANKUMAR.S, COORDINATOR/BME, V.M.K.V.E.C 7. Define BIBO stability. A linear relaxed system is said to have BIBO stability if every bounded (finite) input results in a bounded (finite) output. 8. What do you mean by root locus technique? Root locus technique provides a graphical method of plotting the locus of the roots in the S-plane as a given system parameter, is varied over the complete range of values (may be from zero to infinity). The roots corresponding to a particular value of the system parameter can then be located on the locus or the value of the parameter for a desired root location can be determined from the locus. (or) Root locus technique is a powerful tool for adjusting the location of closed loop poles to achieve the desired system performance by varying one or more system parameters. It is a method of plotting the locus of the root of the characteristic equation in S-plane when the gain of the system is varied over the entire range. 9. Define critically or marginally stable system. A linear time invariant system is said to be critically or marginally stable, if for a bounded input, its output oscillates with constant frequency and amplitude. (or) A system said to be marginally stable system, if its response to a bounded input becomes a constant. 10. What is the necessary condition for stability? The necessary condition for the stability is that all the co-efficient of the characteristic polynomial be positive. 11. State Hurwitz criterion. The necessary and sufficient conditions to have all roots of the characteristic equation in left half of the s-plane is that, the sub-determinants DK, k = 1,2,…..,m obtained from Hurwitz’s determinant must be positive. 12. Define absolute stable. Absolutely stable with respect to a parameter of the system, if it is stable for all values of this parameter. 13. What do you mean by relative stability? Relative stability is a quantitative measure of how fast the transients die out in the system.
- 3. BIOMEDICAL ENGINEERING – BCS – UNIT III - SHORT QUESTIONS AND ANSWERS MATHANKUMAR.S, COORDINATOR/BME, V.M.K.V.E.C 14. Give an application of routh stability criterion. The Routh Stability criterion is frequently used for the determination of the condition of stability of linear feedback control systems. 15. What is auxiliary polynomial? In the construction of the Routh array, a row of all zero indicates the existence of an even polynomial as a factor of the given characteristic equation. In an even polynomial, the coefficients of auxiliary polynomial are given by the elements of the row just above the row of all zeros. 16. How will you find the root locus on real axis? To find the root locus on real axis, choose a test point on the real axis. If the total number of poles and zeros on the real axis to the right of this test point is odd number, then the test point lies on the root locus. If it is even number means, then the test point does not lie on the root locus. 17. When a system is said to be limitedly stable? For a bounded input signal, if the output has constant amplitude oscillations, then the system may be stable or unstable, under some limited constraints. Such a system is called limitedly stable system. 18. What is angle criterion of root locus? The angle criterion of root locus states that S =Sa will be a point on root locus if for that value of S, the argument or phase of G(S)H(S) is equal to an odd multiple of 180 19. How will you find the gain K at a point on the root locus? The gain K at a point S= Sa on root locus is given by K= (Product of length of vectors from open loop zero to the point Sa / Product of length of vectors from open loop poles to the point Sa.) 20. What are the dominating poles and zeros? The poles of a system give rise to the longest lasting term in the transient response of the system. Then those poles are called Dominating poles. The zero which is closer to the origin than all over zeros is known as dominating zero.