Control Systems- Theory-Introduction

• A Control system consists of subsystems and processes assembled for the purpose of controlling the outputs of the processes
• Configuration of Control systems: 
1. Open loop control systems                2. Closed loop control systems 

       Open loop control systems: 

• The elements of an open-loop control system can usually be divided into two parts: the controller and the controlled process, as shown by the block diagram.  

• An input signal, or command, r, is applied to the controller, whose output acts as the actuating signal u; the actuating signal then controls the controlled process so that the controlled variable y will perform according to some prescribed standards.
• In simple cases, the controller can be an amplifier, a mechanical linkage, a filter, or other control elements, depending on the nature of the system.
• The accuracy of an open control system depends on the calibration of the input. Any departure from pre-determined calibration affects the output.
• The open loop system is simple to construct and cheap.
• The open-loop systems are generally stable.
• The operation of open loop system is affected due to presence of non-linearities in its elements.

       Closed loop control systems:

• To obtain more accurate control, the controlled signal y should be fed back and compared with the reference input, and an actuating signal proportional to the difference of the input and the output must be sent through the system to correct the error. A system with one or more feedback paths such as that just described is called a closed-loop system. Example of closed-loop system shown in block diagram.
•  
  

• As error between the reference and output is continuously measured through  feedback, the closed loop system works more accurately.
• The closed loop system is complicated to construct and costly.
• The closed loop can become unstable under certain conditions.

        Feedback and its effects:

• Feedback is used to reduce the error between the reference input and the system output. However, the significance of the effects of feedback in control systems is more complex.
• Feedback exists whenever there is a closed sequence of cause and effect relationships.

       Effect of Feedback on overall gain:

• Feedback affects the gain G of a nonfeedback system by a factor of 1 + GH.
• In a practical control system, G and H are functions of frequency, so the magnitude of 1+GH may be greater than 1 in one frequency range but less than 1 in another. Therefore, feedback could increase the gain of system in one frequency range but decrease it in another.

         Effect of Feedback on stability:

• A system is unstable if its output is out of control.
• Feedback can cause a system that is originally stable to become unstable by introducing positive feedback. 
• Feedback can improve stability or be harmful to stability.

      Effect of Feedback on sensitivity:

• Consider G as a parameter that may vary. The sensitivity of the gain of the overall system M to the variation of G is defined as 

where ∂M denotes the percentage change in M due to incremental change in G;
  

• Feedback can increase or decrease the sensitivity of a system. 

       Effect of Feedback on Noise.

• The effect of feedback on noise and disturbance depends greatly on where these extraneous signals occur in the system.
• Feedback can reduce the effect of noise and disturbance on system performance.

       Feedback also can affect bandwidth, impedance, transient        responses, and frequency responses.

Objectives:
1. Which one of the following is an example of an open loop system?
  a. household refrigerator.
  b. Respiratory system of an animal
  c. Stabilization of an air pressure entering in to a mask.
  d. Execution of a program by a computer.
Ans: a.


2. For a standard feedback control loop, the sensitivity of the closed loop transfer function T to forward path gain G and feed back path gain H are respectively:


 a. 1/(1+GH)         -1/(1+GH)     
 b.-GH(1+GH)        -H(1+GH)
 c. G/(1+GH)           1/(1+GH)
d. 1/(1+GH)             -GH/(1+GH)
 Ans: d.


3. The presence of negative feedback in a control  system


a. increase accuracy and reduce bandwidth
b. reduce bandwidth and increases distortion
c. increases the effect of nonlinearities and reduces distortion
d. reduces distortion and increase bandwidth.


Ans: d.


4. Consider the following statements regarding negative feedback in a closed loop system:
     1. It increases sensitivity.
     2. It minimizes  the effect of disturbance.
     3. There is a possibility of instability.
     4. It improves the transient response.
Of these statements:
a. 1,3 and 4 correct.
b. 1,2 and 4 correct
c. 1,2 and 3 correct.
d. 2,3 and 4 correct.


Ans: d


5.  Which of the following are correct ?
The feedback affects the control system in the following ways:
1. Increases accuracy but reduces sensitivity of gain 
2. Increases bandwidth and reduces the effect of nonlinearity
3. Increases tendency towards oscillation or leads even to instability.


a. 1 and 2
b. 1 and 3
c. 2 and 3
d. 1,2 and 3


Ans : d.




Practice Objectives:

1. Consider the following statements in connection with feedback in control system:
1. With an increase in forward gain, the output value approaches the input value in the case of negative feedback closed-loop system.
2. A negative feedback closed loop system when subjected to an input of 5V with forward gain of 1 and a feedback gain of 1 gives output 4.999 V.
3. The transfer function is dependent only upon its internal structure and components, and is independent of the input applied to the system.
4. The overall gain of the block diagram shown is 10.


Which of the statements given above are
correct ?
a. Only 1 and 2
b. Only 2 and 3
c. Only 3 and 4
d. Only 1 and 3


2. Consider the following statements with regard to the bandwidth of a closed-loop system:
1. In systems where the low frequency magnitude is 0 dB h the Bode diagram,
the bandwidth is measured at the -3dB frequency.
2. The bandwidth of the closed loop control system is a measurement of the
range of fidelity of response of the system.
3. The speed of response to a step input is proportional to the bandwidth.
4. The system with the larger bandwidth provides slower step response and lower fidelity ramp response.
Which of the statements given above are correct?
a. 1, 2 and 3
b. 1, 2 and 4
c. 1, 3 and 4
d. 2, 3 and 4

3. Which of the following are the characteristics of closed- loop systems?

1. It does not compensate for disturbances
2. It reduces the sensitivity of plant parameter variations
3. It does not involve output measurements
4. It has the ability to control the system transient response
Select the correct answer using the codes given below:
a. 1 and 4
b. 2 and 4
c. 1 and 3
d. 2 and 3

 4. Match List I (Physical action or activity) with List II (Category of system) and
select the correct answer:

List I
A. Human respiration system
B. Pointing of an object with a finger
C. A man driving a car
D. A thermostatically controlled room heater

List II
1. Man-made control system
2. Natural including biological control system
3. Control system whose components are both manmade and natural
  
    A  B  C  D
a. 2  2   3  1
b. 3  1   2  1
c. 3  2   2  3
d. 2  1   3  3

5. Consider the systems shown in figure-I and figure-II. If the forward path gain is
reduced by 10% in each system, then the variation in C1 and C2 will be respectively





a. 10% and 10%
b. 2% and 10%
c. 5% and 1%
d. 10% and 1%