Introduction to control system
- 1. Unit 1. Introduction to Control System
- 2. Today we are going to learn and understand about System Control system Difference between system and control system Classifications of control system
- 3. System is a combination or an arrangement of different physical components which act together as a entire unit to achieve certain objectives INPUT SYSTEM PROPER OUTPUT May or may not be desired
- 4. INPUT OUTPUT Input is something entered into a machine or other system in order to produce the output. • The actual response obtained from a system is called output.
- 5. system is a combination or an arrangement of different physical components which act together as a entire unit to achieve certain objectives.
- 6. System + Control = Control System CONTROL SYSTEM DESIRED OUTPUT INPUT
- 7. This process of regulating the inputs or directing the system so that the desired objective is attained is called control
- 8. It is defined as an arrangement of different physical elements connected in such a manner so as to regulate, direct or command itself to achieve a certain objective.
- 10. ➢ A Fan without regulator can be a “SYSTEM” Because it can provide a proper output (airflow). ➢ But it cannot be a “Control System” Because it cannot provide desired output
- 12. ➢ A Fan with regulator can be a “CONTROL SYSTEM” Because it can provide a Desired output (Controlled airflow).
- 14. Asystem in which the control action is totally independent of the output of the system is called as open loop system. Controller Process Reference input Controlled output r(t) u(t) c(t) Fig.1 Block Diagram of Open loop Control System
- 15. 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. Fig.2
- 16. Automatic washing machine This machine runs according to the pre-set time irrespective of washing is completed or not. Fig.3
- 17. Bread toaster This machine as per adjusted time irrespective of toasting is completed or not. Fig.4
- 18. Automatic tea/coffee Vending Machine – These machines also function for pre adjusted time only. Fig.5
- 19. Fig.5
- 20. Fig.6
- 21. Asystem in which the control action is totally independent of the output of the system is called as open loop system
- 22. Simple in construction and design. Economical. Easy to maintain. Generally stable.
- 23. They are inaccurate They are unreliable Any change in output cannot be corrected automatically.
- 24. Control system which uses feedback signals to both control and adjust itself is called a Closed-loop System. The quantity of the output being measured is called the feedback signal.
- 25. Fig.7
- 26. Automatic Electric Iron- Heating elementsare controlled by output temperature of the iron. Fig.8
- 27. Fig.9
- 28. Closed loop control systems are more accurate even in the presence of non-linearity. Highly accurate as any error arising is corrected due to presence of feedback signal. Facilitates automation. This system is less affected by noise. Decision Making & Initiative Action is very fast
- 29. They are costlier. They are complicated to design. Required more maintenance. Feedback leads to oscillatory response. Overall gain is reduced due to presence of feedback. Stability is the major problem and more care is needed to design a stable closed loop system
- 30. Fig.10
- 31. Any closed loop system will have the following five elements Comparison element Control element Correction element Process element Measurement element
- 32. Consider a room heater used to maintain 24 centigrade temperature during a cold night. Fig.11
- 33. Controlled Variable – The room temperature. Reference Value – The required room temperature. We want to maintain 24 degree temperature in a room. Comparison Element- The person in the room comparing the measured value with required temperature. Error Signal- Difference between measured and required temperature. It may be positive or negative.
- 34. Control Unit – The person in the room. Correction Unit- The on-off switch present on the on the heating equipment. Process – The heating of the air by the heating equipment. Measuring Device – A thermometer.
- 36. Fig.11
- 37. The relationship between input & output of a system is given by the transfer function.
- 38. Transfer Function is defined as the ratio of Laplace transform of the output to the Laplace transform of the input under the assumption of zero initial conditions. Laplace transform of the output Laplace transform of the input
- 39. T o evaluate the performance of an automatic control system commonly used mathematical tool is Laplace Transform The Laplace transform of a function, f(t), is defined as F(s) -is the symbol for the Laplace transform, L is the Laplace transform operator f(t) is some function of time, t. L f (t) = F(s)
- 40. SYSTEM G(t) r(t) c(t) INPUT OUTTPU T SYSTEM G(s) r(s) c(s) INPUT OUTTPU T
- 41. 𝑮(𝒔)=𝑪(𝒔)/𝑹(𝑺) 𝒂𝒍𝒍 𝒕𝒉𝒆 𝒊𝒏𝒊𝒕𝒊𝒂𝒍 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏𝒔=𝟎
- 42. Amit Nevase 6/30/2016 System g(t) r(t) c(t) LT System G(s) R(s) C(s) For the system shown, c(t)= output r(t)= input g(t)= System function L{c(t)}= C(s) L{r(t)}= R(s) L{g(t)}= G(s) Therefore transfer function G(s) for above system is given by, G(s)= Laplace of output = C ( s ) R ( s ) Laplace of input 42
- 43. R-Input G-Open loop gain H-Feedback path gain C-Output r(s) G(s) H(s) C(s)
- 44. If the output or some part of the output is returned to the input side and utilized as part of the system input, then it is known as feedback. Feedback plays an important role in order to improve the performance of the control systems.
- 45. To counteract disturbance signals affecting the output.
- 46. To improve system performance in the presence of model uncertainty
- 47. There are two types of feedback systems Positive feedback Negative feedback
- 48. The set point and output values are added together by the controller as the feedback is “in-phase” with the input. The effect of positive (or regenerative) feedback is to “increase” the systems gain
- 49. cattle running in a village. It will lead to panic. Panic will cause more number of cattle to run. The output is contributing to the input in such a way that output further increases.
- 51. R(s) G(s) C(s) Output H(s) +- Error Signal E(s) Feedback Signal Input Error signal is given by; E(s) = R(s) + B(s) − − − − − (1) R(s) = E(s)− B(s) Gain of feedback network is given by; H(s) = B(s) C(s) B= H(s).C(s)−−−−−−(2) Gain for system G(s) = C(s) E(s) C(s) = G(s).E(s) − − − − − −(3) Substitute value of E(s) from eq. 1 to 3 C(s)=G(s).(R(s) +B(s)) C(s) =G(s).R(s) +G(s).B(s) −−−−−−(4) Substitute value of B(s) from eq. 2 to 4 C(s) = G(s) R(s) +G(s).H(s).C(s) G(s).R(s) = C(s) − G(s).H(s).C(s) G(s).R(s) = C(s)(1 − G(s).H(s)) Transfer function is given by; C(s) G(s) = R(s) 1 − G(s).H(s) T .F .= B(s)
- 52. In a negative feedback control system, the set point and output values are subtracted from each other as the feedback is “out-of-phase” with the original input. The effect of negative (or degenerative) feedback is to reduce the gain.
- 54. When we feel cold we shiver. Shivering increases body temperature. If body temperature increases then we sweat and decrease the body temperature. The positive and negative changes are reduced by adding or subtracting the feedback. Negative feedback reduces the error between the reference input, R(s) and system output.
- 55. E(S) C(S)* H
- 56. R(s) G(s) C(s) Output H(s) B(s) +- Error Signal E(s) Feedback Signal Input Error signal is given by; E(s) = R(s) − B(s) − − − − − (1) R(s) = E(s)+ B(s) Gain of feedback network is given by; H(s) = B(s) C(s) B= H(s).C(s)−−−−−−(2) Gain for system G(s) = C(s) E(s) C(s) = G(s).E(s) − − − − − −(3) Substitute value of E(s) from eq. 1 to 3 C(s)=G(s).(R(s) −B(s)) C(s) =G(s).R(s) −G(s).B(s) −−−−−−(4) Substitute value of B(s) from eq. 2 to 4 C(s) = G(s) R(s) − G(s).H(s).C(s) G(s).R(s) = C(s) + G(s).H(s).C(s) G(s).R(s) = C(s)(1 + G(s).H(s)) Transfer function is given by; C(s) G(s) = R(s) 1 + G(s).H(s) T .F .=
- 57. Basic Elements of Electrical based system are Resistor Inductor Capacitor
- 58. Consider an electrical circuit having the resistance R and the voltage applied across this circuit is V and the current flowing through resistor is i. V=IR I=V/R
- 59. Capacitors are device that can store an electrical charge when it connected to a voltage source. 𝑖 = 𝑑𝑞/𝑑𝑡 𝑞 = ∫ 𝑖*dt V = 1/C ∫ I𝑑𝑡
- 60. Inductors resist or oppose changes of current V= 𝐿 𝑑𝑖/𝑑𝑡 𝑖 = 1 /𝐿 ∫ V. 𝑑t
- 61. Inductance is the property of the coil due to which it resists any variation in the current passing through it. The current passing through the coil generates the field about it, the magnitude of the field depends on the strength of the current.
- 62. Consider the electrical Resistor having the resistance R Inductor having the inductance as L Capacitor having the capacitance as C. v
- 63. Apply KVL, so we will get the sum of the voltage in this loop is equal to zero V-VR-VL-VC =0 V=VR+VL+VC v =𝑅𝑖 + 𝐿 𝑑𝑖 /𝑑𝑡 + 1 /𝑐 ∫ 𝑖𝑑𝑡 V = 𝑅𝑖 + 𝐿 𝑑𝑖/𝑑𝑡 + 1/ 𝑐 ∫ 𝑖𝑑t ---------------2 Where 𝑖 = 𝑑𝑞/dt v = 𝑅 𝑑𝑞/𝑑𝑡 + 𝐿 𝑑²𝑞/𝑑𝑡² + 𝑞/𝑐---------3
- 64. v
- 65. Consider the electrical circuit having the parallel combination of the three elements resistor, inductor and capacitor
- 66. Apply KCL the circuit 𝑖(𝑡) = 𝑖𝑅 + 𝑖𝐿 + iC Where 𝑖𝑅 = V/R 𝑖𝐿 = 1/𝐿 ∫ V𝑑𝑡 𝑖𝐶 = 𝑐 .𝑑V/𝑑𝑡 𝑖(𝑡) = V/𝑅 + 1/𝐿 ∫ V𝑑𝑡 + 𝑐 𝑑V/𝑑t
- 67. Basic Elements of Electrical based system
- 69. To understand the behavior of systems, mathematical models are used. These mathematical models are equations which describe the relationship between the input and output of a system.
- 70. The mass of a body though distributed, we can assume that the entire mass is concentrated at one point called the CG of the body.
- 71. The elastic deformation of a body is represented by the ideal element known as spring. It stores energy during the variation of its shape due to elastic deformation resulting from the application of the force.
- 73. Dampers are used to minimize the vibrations to improve the dynamics of the system. Damper/Dash-pot is represented by,
- 76. Mechanical systems can be divided into two basic systems based on type of motion . (a) Translational systems. (b) Rotational systems
- 77. Translational motion is taking place along a straight line is known as Translational motion. • These systems are characterized by Displacement Linear velocity Linear acceleration
- 78. When a force ‘F’ is applied to a mechanical body of mass M displacement takes place then it is opposed by an opposing force 𝒇𝒎 due to mass. This opposing force is proportional to the acceleration of the body
- 80. If a force (f) is applied on spring K, then it is opposed by an opposing force due to elasticity of spring 𝒇𝒌. This opposing force is proportional to the displacement of the spring (x)
- 84. In physics, restraining of vibratory motion, such as mechanical oscillations, noise, and alternating electric currents, by dissipation of energy is known as damping force. Unless a child keeps pumping a swing, its motion dies down because of damping. A system may be so damped that it cannot vibrate.
- 85. A dashpot is a mechanical device, a damper which resists motion via viscous friction. The resulting force is proportional to the velocity, but acts in the opposite direction, slowing the motion and absorbing energy. It is commonly used in conjunction with a spring (which acts to resist displacement).
- 86. Damper /Dashpot Damper absorbs the velocity of a body. If a force (f) is applied on dashpot B, then it is opposed by an opposing force due to friction of the dashpot 𝒇𝒃. This opposing force is proportional to the velocity of the body
- 89. Rotational Mechanical System involves rotational motion (motion of an object about its own axis) Rotational motion in mechanical System
- 90. Mechanical System and basic Elements In the analysis of rotational mechanical system, three essential basic elements are •Moment of inertia (J) of mass •Stiffness constant (k) of the spring Rotational friction coefficient (B) of dash-pot
- 91. Mass (Rotation) in rotational mechanical system, moment of inertia stores kinetic energy. A torque is a force applied to a point on an object about the axis of rotation. The angular displacement Ɵ is equivalence of displacenet. The moment of inertia is represented by (J), angular displacement (Ɵ) and torque T.
- 93. Spring In rotational mechanical system, torsional spring stores potential energy. If a torque is applied on torsional spring K This opposing torque is proportional to the angular displacement of the torsional spring. Assume that the moment of inertia and friction are negligible
- 94. Spring represented in rotational motion, Comparing with F = Fk = K x in linear motion, For rotational motion we get T=Tk =kθ
- 96. Damper/Dash-pot Damping occurs whenever a body moves through a fluid. Dampers are used to minimize the vibrations to improve the dynamics of the system. These are different rotary dampers can be found in rotational motion of mechanical system
- 97. Damper/Dash-pot If a torque is applied on dashpot B, then it is opposed by an opposing torque due to the rotational friction of the dashpot. This opposing torque is proportional to the angular velocity of the body. Assume the moment of inertia and elasticity are negligible
- 102. We can represent mechanical systems in terms of equivalent electrical systems Force voltage analogy Force current analogy Torque voltage analogy Torque current analogy
- 103. The mathematical equations of translational mechanical system are compared with equations of the electrical system.
- 109. In force current analogy, the mathematical equations of the translational mechanical system are compared with the nodal equations of the electrical system.
- 110. All these electrical elements are connected in parallel.
- 112. In this analogy, the mathematical equations of the rotational mechanical system are compared with the nodal mesh equations of the electrical system