Control Theory · Automatic control
#01 Control Theory #01 - Introduction to Automatic Control Systems
Corrected solution notes. The audio is the original recording and may contain errors or incomplete phrases. Where they differ, use the corrected written solution.
Question
Corrected solution notes. The audio is the original recording and may contain errors or incomplete phrases. Where they differ, use the corrected written solution. Control Theory #01 - Introduction to Automatic Control Systems
Written solution and narration transcript(shows the full solution)
Below are all the lines written in the notebook together with the full narration transcript.
1. Automatic control
Corrected solution notes. The audio is the original recording and may contain errors or incomplete phrases. Where they differ, use the corrected written solution.Control studies how inputs influence the behavior of a dynamic system and how to make its output follow a chosen objective.Narration transcript
Hello, friends. Today, starting from this video, we're gonna give an introduction to automatic control systems or control theory, a course that goes by various names but is basically known as control. So first of all, here's where we need to start.
2. Plant and controller
A plant is the system being controlled. A controller chooses an input using the reference and available measurements.Dynamics describe how the system evolves with time and its state.Narration transcript
So what is control? This is what we call control. It deals with the behavior of automatic dynamic systems. In other words, we can say that dynamic systems, create a certain system and create a control mechanism, with automatic behavior of this system. Now, when we think about what is the dynamic system
3. Signals
Input, output and disturbance are different signals. Examples include position, speed, temperature, voltage and current.A signal is a quantity indexed by time; it may be constant or varying.Narration transcript
in the definition of this control, the dynamic system, if it is a dynamic system, is based on input and output signals. In all control operations, well, there is an input and, this input undergoes certain operations and then we get an output, as an output, friends. So what is the signal in this definition? This time we ask, what is the signal? Well, when we ask what is the signal, we can express it as a physical quantity that we call time varying, which usually varies with time. For example, the position vector, velocity vector, temperature, voltage, current and so on. These are the most basic definitions.
4. Models and memory
State stores the information needed to predict subsequent motion from present conditions and future inputs.Differential equations model many continuous-time systems. Transfer functions describe zero-state input/output behavior of LTI models.Narration transcript
Usually, dynamic systems have memory. This is another characteristic of dynamical systems that are in control. So how do we express dynamic systems? What matters is what I'll show you now. Dynamic systems. We can treat all these processes as differential equations. Well, of course, these transfer functions are also important for us. We illustrate with these. Well, if you take the dynamic system, one of the most important points for us is that we will do a lot of question solving and so on on these dynamic systems. Well, what we call a dynamic system is based on a very simple logic. Of course, what creates the complexity at this point is the internal structure of the dynamic system. In general, there is a dynamic system if you show the structure of a dynamic system as a dynamic system.
5. Keep the intended input
To compute the nominal forced response, retain the intended input and set the disturbance to its assumed nominal value. Omitting both generally changes the problem.For illustration: y'+y=u+d, y(0)=0. A unit input and zero disturbance give y(t)=1−exp(−t); zero input and zero disturbance give zero output.Narration transcript
We give an input to this dynamic system. This input combines with a certain disturbance, which is a signal that has a disturbing effect to produce a certain output from the dynamical system. Now, when we neglect the input signals and disturbance signals in our calculations, we can get an output signal as we expect. But after the disturbance signals come into play, we always get an output with a little bit more margin of error than we expect.
6. Feedback and disturbance
Negative feedback compares the measured output with the reference and adjusts the plant input.Appropriate design can reduce disturbance sensitivity. Stability and complete disturbance rejection depend on the controller and disturbance model; neither is automatic.Narration transcript
In fact, this is one of the biggest reasons why feedback circuits are usually created in these systems, because feedback is also about regulating the new input to the system by subtracting a certain margin of error and ensuring that the system receives the proper output. These feedback operations are one of the methods to eliminate these disturbance effects.
7. Review
Identify the plant, reference, input, output and disturbance before writing equations.State initial conditions and distinguish nominal response, zero-input response and disturbance response.Narration transcript
After this intro, friends, we'll continue examining these dynamic systems in the following questions. In this way, we've introduced our control lesson. Hope to meet you in another video about control in another video in the same way. Goodbye for now.
Source video: Control Theory #01 - Introduction to Automatic Control Systems (3:01)