Control system basics, block diagram and signal flow graph

Control system basics, block diagram and signal flow graph

1. Electrical Engineering Control Systems

2. Basic Definition of Control System System: - “ A system is a combination of different physical components which are connected in such a manner so that entire unit achieve certain objective ” Control: - “ It means to regulate or direct a system so that the desire objective is achieved ” Control System: - “ Control system is the arrangement of the different physical elements connected in such a manner so as to regulate, direct or command itself ” System Input Output System I/p Controller Controlled I/p Controlled O/p

3. Classification of Control System Control System Natural Man-mad Manual Automatic Open- loop Closed-loop Non-linear linear Non-linear linear Time-variant Time invariant Time-variant Time invariant

4. Open Loop and Close Loop Control System Close Loop Control System e(t) u(t) c(t) b(t) Reference r(t) Open Loop Control System r(t) c(t) u(t) r(t)= Reference i /p u(t)= Reference i /p e(t)= Error signal c(t)= Controlled o/p b(t)= Feedback Signal

5. Close Loop Control System Sr. No. Open Loop Control System Closed Loop Control System 1 The feedback element is absent. The feedback element is always present. 2 An error detector is not present. An error detector is always present. 3 It is a stable one. It may become unstable. 4 Easy to construct. Complicated construction. 5 It is economical. It is costly. 6 Having a small bandwidth. Having a large bandwidth. 7 It is inaccurate. It is accurate. 8 Less maintenance. More maintenance 9 It is unreliable. It is reliable. 10 Highly sensitive to parameter changes Less sensitive to parameter changes

6. Example: -Open Loop Control System Electric Hand Drier  – Hot air (output) comes out as long as you keep your hand under the machine, irrespective of how much your hand is dried. Automatic Washing Machine  – This machine runs according to the pre-set time irrespective of washing is completed or not. Bread Toaster  – This machine runs as per adjusted time irrespective of toasting is completed or not. Automatic Tea/Coffee Maker  – These machines also function for pre-adjusted time only. Timer Based Clothes Drier  – This machine dries wet clothes for pre-adjusted time, it does not matter how much the clothes are dried. Light Switch  – Lamps glow whenever the light switch is on irrespective of light is required or not. Volume on Stereo System  – Volume is adjusted manually irrespective of output volume level.

7. Example: -Close Loop Control System In servo voltage stabilizer , the voltage stabilization can be attained by giving output voltage feedback to the system In the  water level controller , the level of water can be decided by the input water The temperature in the AC can be adjusted depending on the temperature of the room. The motor speed can be controlled using a tachometer or current sensor, where the sensor detects the motor speed and sends feedback to the control system to change its speed. Some more examples of these systems include thermostat heater, solar system. missile launcher, auto engine, automatic toaster, water control system using a turbine. Automatic electric iron can be controlled automatically by the heating element’s temperature in the iron.

8. Transfer Function A transfer function represents the relationship between the output signal of a control system and input signal, for all possible input values. In engineering, a transfer function (also known as system function or network function) of an electronic or  control system   component  is a  mathematical function  which  theoretically models  the device's output for each possible input. Transfer function is the ratio of the Laplace transform of the output to Laplace transform of the input under the assumption of zero initial condition.     G(S) C(S) R(S)  

9. Properties of Transfer Function The transfer function of a system is the Laplace transform of its impulse response for zero initial conditions. The transfer function can be determine from system input-output pair by taking ration of Laplace of output to Laplace of input. The system differential equation can be obtained from transfer function by replacing s-variable with linear differential operator D defined by D= . The transfer function is independent of the inputs to the system. The system poles/zeros can be found out from transfer function. Stability can be determined from the characteristics equation. The transfer function is define only for linear time invariant systems. It is not defined for non-linear system.  

10. Disadvantages of Transfer Function Transfer function is valid only for linear Time Invariant systems. It does not take into account the initial condition. It does not gives any idea about how the present output is progressing. No idea about physical structure of the system is immediately known.

11. Laplace Transform

12. Inverse Laplace Transform

13. Block Diagram Reduction Rules Block diagram: - Block diagram is a pictorial representation of the cause-and-effect relationship between input and output of the system. Summing point: - More than one signal can be added or subtracted at summing point. Take off point: - point from which a signal is taken for the feedback purpose is called take off point. Forward path: - The direction of flow of signal is from input to output. Feedback path: - The direction of flow of signal is from Output to input.

14. Block Diagram Reduction Rules

15. Block Diagram Reduction Rules

16. Block Diagram Reduction Rules

17. Example: -1

18. Example: -1

19. Example: -1

20. Example: -2

21. Example: -2

22. Example: -3

23. Example: -3

24. Some important Signal flow graph terms Definition of SFG : “A signal flow graph is pictorial representation of a system, and it displays graphically, the transmission of signal in a system” It applied to time- invariant linear system.

25. Signal flow graph Mason’s Gain Equation: - Overall Transfer function = T.F. = i = Number of forward path = Gain of forward path = System determinant and can be calculated as follows = 1- ( sum of all individual loop gain including self loops) + ( sum of all gain products of two non – touching loops) - (sum of all gain products of three non – touching loops) + ------------------------ = The value of for the part of graph not touching to the forward path.  

26. Block Diagram to Signal Flow Graph

27. Signal Flow Graph to Block Diagram

28. Signal Flow Graph from equations         +  

29. Example: Signal flow graph

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