The feedback loop is designed to control a system (which is commonly called the plant, probably...

   

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The feedback loop is designed to control a system (which is commonly called the "plant", probably due to the influence of chemical engineers who also use feedback to control their processes). The plant (G) can be anything (a motor's rotation, a car's speed, an airplane's yaw rate). Keep in mind that in most cases, G itself cannot easily be changed immediately (that's why you build feedback loops around them to control them). When you're controlling (using a controller C) a plant, usually you want to track the reference r as good as you you can. In most cases you also have a disturbance d whose effect on the output y you want to reject (again as much as you can: if you can't eliminate it, you at least reduce it). In most cases you also have a sensor that has its own dynamics H, as well as a noise n that corrupts your measurement. Obviously, you also want to eliminate or suppress the effect of n on your output y. a) Derive the expression for y in terms of all the inputs to the system. Your answer should look like: y = F1*r + F2*d + F3*n, where F1, F2, F3 are combined expression of block diagrams b) Describe the qualitative conditions that are needed to achieve each goal separately. In other words, first ignore the d and the n and investigate what needs to happen to track r. And then do the same analysis for the other inputs. Remember, you want your output to track the r but you want the opposite for d and n. Also remember that you're not able to change G. You can't really change a specific H either but you can swap a sensor with another one which will effectively change the H. c) Now describe the conditions you need to achieve all goals at the same time. Do you see a dilemma? What is it? d) Bonus: How do you think this dilemma is dealt with? (this part is related to the concept of "frequency response" which we did not yet cover, hence it won't be graded, unless you have the right answer. When the solution is available you must read and learn the answer). d. System or "Plant" Controller + r C G Sensor + n H. + + The feedback loop is designed to control a system (which is commonly called the "plant", probably due to the influence of chemical engineers who also use feedback to control their processes). The plant (G) can be anything (a motor's rotation, a car's speed, an airplane's yaw rate). Keep in mind that in most cases, G itself cannot easily be changed immediately (that's why you build feedback loops around them to control them). When you're controlling (using a controller C) a plant, usually you want to track the reference r as good as you you can. In most cases you also have a disturbance d whose effect on the output y you want to reject (again as much as you can: if you can't eliminate it, you at least reduce it). In most cases you also have a sensor that has its own dynamics H, as well as a noise n that corrupts your measurement. Obviously, you also want to eliminate or suppress the effect of n on your output y. a) Derive the expression for y in terms of all the inputs to the system. Your answer should look like: y = F1*r + F2*d + F3*n, where F1, F2, F3 are combined expression of block diagrams b) Describe the qualitative conditions that are needed to achieve each goal separately. In other words, first ignore the d and the n and investigate what needs to happen to track r. And then do the same analysis for the other inputs. Remember, you want your output to track the r but you want the opposite for d and n. Also remember that you're not able to change G. You can't really change a specific H either but you can swap a sensor with another one which will effectively change the H. c) Now describe the conditions you need to achieve all goals at the same time. Do you see a dilemma? What is it? d) Bonus: How do you think this dilemma is dealt with? (this part is related to the concept of "frequency response" which we did not yet cover, hence it won't be graded, unless you have the right answer. When the solution is available you must read and learn the answer). d. System or "Plant" Controller + r C G Sensor + n H. + +