A process has the transfer function, K G(s) - ---='----- (lOs + 1)(5s + 1) where K has a nominal value of K = 1. PID controller settings are to be calculated using the Direct Synthesis approach with Tc = 5 min. Suppose that these controller constants are employed and that K changes unexpectedly from 1 to 1 + u. (a) For what values of u will the closed-loop system be stable? (b) Suppose that the PID controller constants are calculated using the nominal value of K = 1 but it is desired that the resulting closed-loop system be stable for lui :S 0.2. What is the smallest value of Tc that can be used? (c) What conclusions can be made concerning the effect that the choice of Tc has on the robustness of the closed-loop system to changes in steady-state gain K?
Class Notes 3/18 Question day 1. “Good as is discourse, silence is better, and shames it. The length of the discourse indicates the distance of thought betwixt the speaker and the hearer. If they were at a perfect understanding in any part, no words would be necessary thereon.” (157) 2. “There are no fixtures to men, if we appeal to consciousness. Every man supposes himself not to be fully understood; and if there is any truth in him, if he rests at last on the divine soul, I do not see how it can be otherwise.” (155) 3. “How often must we learn this lesson Men cease to interest us when we find their limitations. The only sin is limitation. As soon as you once come up with a man’s limitations, it is all over with him.” (155) 4. “Do not set the least value on what I do, or the least discredit on what I do not, as if I pretend to settle anything as true or false. I unsettle all things. No facts are to me sacred; none are profane; I simply experiment, an endless seeker, with no Past at my back.” (160) 5. “People wish to e settled: only as far as they are unsettled, is there any hope for them” (161) 6. “Dream delivers us to dream, and there is no end to illusion. Life is a train of moods like a string of beads, and , as we pass through them, they prove to be manycolored lenses which paint the world their own hue, and each shows only what lies in its focus” (229) Our thoughts 1. We don’t want to live with each other but we have to. No need to communicate because I can’t understand what is in your circle nor can you understand what is in mine. The more you speak the further you are from the person. If you are uncomfortable with someone you use language as filler. 2. We use communication to try and get in to someone’s circle, can never be in circle or completely understood. 3. Once you know the others limits they no longer interest you nor are they useful to you. Everyone has knowledge to offer you but that has limits, once the limit is reached you have no need for them. 4. Respond to emotion, not logic. No universal truths. Do not make fact of my argument; I’m just trying to appeal to emotion. Hopes we will run with it. 5. See antifoundationalism. Only as settled as we are not. Circle= solitude. We want to be settled but we can’t be settled because we can’t understand each other. Can’t live with others but have to. Emerson wants us to experiment. 6. Eye is the first circle; Horizon is second (perception). Perception pretty much. Every dream of experience you have provides you an interesting perspective that shapes & changes how you look at things. This is as far as we got. Hope this Helps.