CS NOTES.pptx
- 1. ADDITIONAL THEORY FOR UNIT-2 (SECOND HALF SYLLABUS)
- 2. Stability of Control System The stability of a control system is defined as the ability of any system to provide a bounded output when a bounded input is applied to it. It is also referred as the system’s ability to reach the steady-state. Types of Stable System 1. Absolutely stable system: An absolutely stable system is the one that provides bounded output even for the variation in the parameters of the system. This means it is such a system whose output after reaching a steady-state does not show changes irrespective of the disturbances or variation in the system parameter values. The nature of poles for the absolutely stable condition must be real and negative The figure shown below represents the step response of an absolutely stable system:
- 3. 2. Conditionally stable system: A conditionally stable system gives bounded output for the only specific conditions of the system that is defined by the parameter of the system. Thus we can say here the system exhibits stability only under particular conditions. And if that particular condition is violated then the system generates unbounded output. 3. Marginally/ Critically stable system: A marginally stable system is the one that generates a signal which is oscillating with constant frequency and amplitude when a bounded input is provided to it. These oscillations are known as sustained oscillations. The figure here represents the step response of a marginally stable system:
- 5. Formation of Routh Array
- 7. Special Cases of Routh Array We may come across two types of situations, while forming the Routh table. It is difficult to complete the Routh table from these two situations. The two special cases are − 1. The first element of any row of the Routh array is zero. 2. All the elements of any row of the Routh array are zero. Difficulty-1. The first element of any row of the Routh array is zero. Step-1 If any row of the Routh array contains only the first element as zero and at least one of the remaining elements have non-zero value, then replace the first element with a small positive integer, ϵ. Step-2: Then continue the process of completing the Routh table. Step-3: Now, find the number of sign changes in the first column of the Routh table by substituting ϵ tends to zero. Step-4 : Verify the sufficient condition for the Routh-Hurwitz stability.
- 8. Difficulty-2: All the Elements of any row of the Routh array are zero Step-1 : Form the Routh array for the given characteristic polynomial. Step-2: Write the auxilary equation, A(s) of the row, which is just above the row of zeros. Step:-3: Differentiate the auxiliary equation, A(s) with respect to s. Fill the row of zeros with these coefficients. Step-4 : Verify the sufficient condition for the Routh-Hurwitz stability.
- 9. PROCEDURE FOR ROOT LOCUS –– Refer your Material ROOT LOCUS
- 10. Effect of addition of poles: i) Root locus shift towards right half of the s-plane ii) system stability relatively decreases iii) system becomes more oscillatory in nature iv) range of operating values of k, for stability of the system decreases Effect of addition of zeros i) Root locus shift towards left half of the s-plane ii) system stability relatively increases iii) system becomes less oscillatory in nature iv) Range of operating values of K, for stability of the system increases EFFECT OF ADDING POLES & ZEROS
- 11. ADDITIONAL THEORY FOR UNIT-3
- 12. Advantages of frequency response 1. It includes simple calculations. 2. The frequency response method is easy to implement in the designs of the control system. It also helps us to find the stability of the system. 3. It provides the stability analysis of the system without the need for any complex and time-consuming processes. 4. The effect of the noise disturbance can be easily analyzed. 5. The adjustment and performance of the closed loop system using the frequency response is easy as compared to the time domain. Dis-Advantages of frequency response 1. Loss of time-related information: 2. Limited for non-linear systems 3. Requires complex mathematical operations: 4. Limited for non-stationary signals:. Advantages & dis advantages of FREQUENCY RESPONSE
- 13. Advantages 1. It helps in identifying the stability of the system. 2. It helps in identifying phases and gaining margins with minimum calculation. 3. It can be used to calculate the system’s transfer function. 4. It can show the amplification and attenuation in the gain plot which is helpful in designing the filters. Disadvantages 1. It is only applicable to LTI (linear time-invariant) system. 2. It is not suitable for the system having extremely high or low frequencies. 3. It focuses on the frequency response without considering the transient time effect. Advantages & dis advantages of BODE PLOT
- 14. Advantages & dis advantages of POLAR PLOT
- 15. EXPLAIN PHASE MARGIN & GAIN MARGIN