EE249 Homework 4TA: Alessandro Pinto{[email protected]}November 2, 2003Goal of HW4 is to give you an example of hybrid system modeling. GeneralComments: there is not right/wrong answer to a question, I would ratherconsider your homework as solutions to design problems. I could argue thatyour solution is inefficient and you could argue the same about mine. Grade isestablished mostly on the rationale you follow to answer questions. Hence it isin your interest to justify all your statements. You can use any kind of sourcesas long as you reference them all.Homework are created by the TA from scratch. It is then reasonable that hemay forgot assumptions or make some that are not necessary. You can add orremove assumptions at you convenience as long as you justify your decisions.Problem description: We want to build a simplified model of an ele vator.As you may have noticed there is a specific pattern that the elevator follows togo from one floor to another. After you step in the elevator and the doors close,it starts increasing it’s speed until a cruise s peed is reached. When the distanceto the destination is smaller that a certain value, the speed decreases until alanding speed is reached and finally the elevator stops at the desired flo or.We can define few parameters. To reach the cruise speed the elevator moveswith a constant acceleration equal to a = 0.5g where g = 9.81m/s2. Thecruise speed is vc= 4km/h. The breaking distance (the distance needed by thecontrol algorithm to stop the elevator) is xb= 1m. Finally the landing speed isvl= 0.1m/s.The behavior of the elevator and control algorithm can be informally de-scribed as follows. The elevator waits a new command of the form¨’go to po-sition xT”’ (we assume by now that our elevator can only go up). During thisphase the acceleration and the speed are ¨x = 0, ˙x = 0. When the command isissued the system changes the state and goes to an acceleration state where thenew equations are ¨x = a. Two things may happen:• the cruise speed is reached: then the system has to go in the cruise statewhere the new e quation is ¨x = 0, namely constant speed.• the distance of the elevator from the target is less than or equal to thebraking distance and the speed is less then the cruise speed: then the1EE249 Spring 2003, Homework 4system has to go directly to the deceleration state. This means that thetarget position was so close to the starting position that the elevator didn’thave time to reach the cruise speed.If the distance to the destination becomes smaller than or equal to the brak-ing distance while the elevator is cruising, the elevator has to decelerate.When the speed drops down to the landing speed, the elevator has to movewith constant speed vluntil the target is reached (within a tolerance that youcan decide), and finally has to stop (ideally the speed can go to zero in zerotime, in practice this cannot happen).QUESTION 1: describe an hybrid model of the system that I have infor-mally explained.QUESTION 2: build such a model using HyVisual and plot position andspeed of the elevator to go from position 0.0 to position 10m.Acknowledgment I would like to acknowledge Claudio Pinello for helpingme in preparing this
View Full Document
Unlocking...