Control Systems Lectures - Closed Loop Control — Transcript

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1. 0:00this lecture is on open loop versus
2. 0:02closed loop Control Systems a control
3. 0:05system is a mechanism that alters the
4. 0:07future Behavior or state of a system now
5. 0:11in order to be considered a control
6. 0:13system and not simply a change the state
7. 0:16system the behavior or the outcome must
8. 0:19tend towards a state that is desired
9. 0:22control theory is a branch of
10. 0:24mathematics that is concerned with the
11. 0:26strategy to select the appropriate input
12. 0:29or or to put it another way it deals
13. 0:32with how to go about generating that
14. 0:36outcome without control theory the
15. 0:39designer is relegated to selecting
16. 0:41appropriate actions through trial and
17. 0:45error now all Control Systems have two
18. 0:47basic parts the system to be controlled
19. 0:50usually called the plant and an input
20. 0:52into the plant the input acts on the
21. 0:55plant which responds over time to
22. 0:57produce a system output this type of
23. 1:00control system is called an open loop
24. 1:02system because the input does not depend
25. 1:04on the system
26. 1:06output open loop control systems are
27. 1:08typically reserved for simple processes
28. 1:11that have well-defined input output
29. 1:13behaviors for example a dishwasher is an
30. 1:16open loop control system the goal of a
31. 1:19dishwasher which is the plant is clean
32. 1:21dishes which is the output once the user
33. 1:24sets the wash time which controls the
34. 1:27time to clean the dishes the dishwasher
35. 1:30will run for that set time now this is
36. 1:33true regardless of the cleanliness of
37. 1:35the dishes if the dishes loaded were
38. 1:38clean to begin with the dishwasher would
39. 1:40still run for the prescribed time
40. 1:42further if you loaded the dishwasher
41. 1:44with 10 Plates Full of cake the set time
42. 1:47might not be enough to clean
43. 1:49them another common example of open loop
44. 1:52control is a sprinkler system for your
45. 1:56lawn in this control system the system
46. 1:59out outp put is the moisture content of
47. 2:01the
48. 2:03soil again the user sets the timer which
49. 2:06controls the amount of time to run the
50. 2:08sprinklers and while the sprinklers are
51. 2:10running the plant which is the grass in
52. 2:12this case is being
53. 2:14watered again an open loop sprinkler
54. 2:16system would still run even if it was
55. 2:18raining outside for a more complicated
56. 2:20example imagine trying to obtain a
57. 2:23constant speed in your car without the
58. 2:25benefit of the built-in automatic cruise
59. 2:28control to do this you a rod between the
60. 2:30front of your seat and the gas pedal to
61. 2:32depress it halfway down the output of
62. 2:35the control system is the speed of the
63. 2:37car and the input is the position of the
64. 2:40gas pedal again the car itself is the
65. 2:43plant the car begins to accelerate down
66. 2:46a flat road until the force supplied to
67. 2:48the system is balanced by the force of
68. 2:50friction at this point the car stops
69. 2:52accelerating and maintains a constant
70. 2:54speed but what happens when the car
71. 2:56encounters a hill or a valley without
72. 2:58varying the input
73. 3:00that is adjusting the gas pedal the car
74. 3:02will slow down or speed up and the
75. 3:04desired constant speed will not be
76. 3:06maintained this is the primary drawback
77. 3:08to open loop control the input to the
78. 3:10system has no way to compensate for
79. 3:12variations in the system now to account
80. 3:15for these changes you must vary the
81. 3:17input to your system with respect to the
82. 3:18output and this type of control system
83. 3:20is called a closed loop control
84. 3:23system now in addition to calling it
85. 3:25closed loop control this can also be
86. 3:27referred to as feedback control negative
87. 3:29feedback control or automatic control
88. 3:32for the time being we'll use these terms
89. 3:33interchangeably although there are
90. 3:35slight variations between some of them
91. 3:37that we won't address in this lecture in
92. 3:39Clos Loop control you measure the output
93. 3:41of the system with a sensor and compare
94. 3:43the result against a reference signal
95. 3:45often this is referred to as the desired
96. 3:47State or the commanded State an error
97. 3:50term is generated and then fed through a
98. 3:52controller where the error is converted
99. 3:54into a system input value when drawn in
100. 3:57block diagram form it's easy to see why
101. 3:59this is referred to as a control Loop
102. 4:01the negative part of the negative
103. 4:03feedback control term is based on the
104. 4:05comparator juncture where the feedback
105. 4:07is
106. 4:08subtracted so how does feedback control
107. 4:10work in practice well let's take the
108. 4:12case of the dishwasher there could be a
109. 4:14sensor that measures the cleanliness of
110. 4:17the plates the reference signal would be
111. 4:19some sort of desired cleanliness level
112. 4:21that would be set either by the
113. 4:22manufacturer or by the
114. 4:25user this desired cleanliness level
115. 4:28would be compared to the measured level
116. 4:32an error term would be generated which
117. 4:34would be fed through a controller which
118. 4:36would monitor wind to shut off the
119. 4:39dishwasher a sprinkler system could also
120. 4:42benefit from closed loop control the
121. 4:45sensor could be a device planted in the
122. 4:47soil that measures the moisture content
123. 4:49of the plant remember that in this case
124. 4:52the plant is both the grass and the soil
125. 4:56the reference signal would be a desired
126. 4:58soil moisture
127. 5:00content and again the error signal would
128. 5:03be generated which would then be fed
129. 5:05through a controller and the controller
130. 5:08would adjust the amount of time that the
131. 5:10sprinklers ran the sprinklers would then
132. 5:12run until the moisture level reached a
133. 5:15specified value and then they would be
134. 5:17shut
135. 5:20off for the car with cruise control
136. 5:23closed loop control would work something
137. 5:25like
138. 5:26this the sensor is a speedom
139. 5:30which measures the speed of the car the
140. 5:32reference speed would be the speed that
141. 5:34the car was going when the cruise
142. 5:36control was
143. 5:38set now assume that the car starts in a
144. 5:41steady state position on Flat Road and
145. 5:44what I mean by that is that the speed is
146. 5:46constant at your desired speed and also
147. 5:49that the gas pedal is depressed the
148. 5:51amount needed to generate that speed for
149. 5:54this example let's say that the desired
150. 5:56speed is 100 mph therefore the speedom
151. 5:59would also read 100 mph and since the
152. 6:02measured speed exactly matches the
153. 6:04reference speed the error term is zero
154. 6:07the gas pedal would stay exactly where
155. 6:08it is once the car encounters the hill
156. 6:11the speed starts to slow now the
157. 6:12reference speed is greater than the
158. 6:14measured speed and the error term
159. 6:15becomes positive which signals the
160. 6:17controller to speed up if the car
161. 6:20encounters a downhill the speed will
162. 6:21increase now the reference speed is less
163. 6:24than the measured speed and the error
164. 6:25term will be negative the beauty of the
165. 6:27feedback control system is that is
166. 6:29capable of reacting to changes to the
167. 6:31plant automatically by constantly
168. 6:33driving the error term to zero I want to
169. 6:36leave you with one more thought
170. 6:37regarding closed loop
171. 6:39control if we take a block diagram and
172. 6:42assign letters that abstractly represent
173. 6:44the various parts of a control system we
174. 6:47can gain new insight into how feedback
175. 6:49control is manipulating a system for
176. 6:52example if we label the reference signal
177. 6:54V and we call the controll or some
178. 6:57abstract process D through the plant G
179. 7:00which produces an output we'll call Y
180. 7:02which can be fed back through the sensor
181. 7:04H to generate an error turn e we can
182. 7:07then reduce this block diagram even
183. 7:10further for example we can multiply D
184. 7:12and G to combine into a single block to
185. 7:16reduce further however takes a small
186. 7:17amount of algebra the error signal is
187. 7:20the reference signal V minus the output
188. 7:23y times the sensor process H the output
189. 7:27Y is the error term time D * G
190. 7:30now solve this equation for E which will
191. 7:32give you y over
192. 7:34DG now you can set both equations equal
193. 7:37to each other and through a few more
194. 7:39algebraic steps you can solve for the
195. 7:42variable y with respect to
196. 7:46V and since Y is the output and V is the
197. 7:49input the rest of that equation is what
198. 7:52we refer to as a transfer function of
199. 7:54the
200. 7:56system in this case the transfer
201. 7:58function is d * G over 1 + d g h and for
202. 8:04those who are paying attention you'll
203. 8:05notice that I forgot to write the V at
204. 8:07the end of that equation
205. 8:09there we can now rewrite this back in
206. 8:12block diagram form these two block
207. 8:14diagram representations are equivalent
208. 8:16of each other now doesn't this new
209. 8:18process look a lot like an open loop
210. 8:19control system only with a modified
211. 8:21plant the feedback path has altered the
212. 8:24original plant to be something new and
213. 8:26furthermore the open loop behavior of
214. 8:27this new plant has the exact character
215. 8:29istics we wanted from the original plant
216. 8:31namely that it follows our input now
217. 8:34here's something to ponder until the
218. 8:35next video what are the limitations of
219. 8:38feedback control in other words can we
220. 8:41make any plant G behave like anything we
221. 8:45choose just by adding a feedback control
222. 8:48system which is made up of a controller
223. 8:50d and a sensor
224. 8:53H one other thing do you think in our
225. 8:56car example from up above that using
226. 8:59using feedback control we can turn a
227. 9:01pinto into a Ferrari just by applying
228. 9:04more
229. 9:05gas we'll discuss that in a future video