Lecture #1 16.31 Feedback Control Copyright c2001 by JJonathandHow D
Lecture #1 16.31 Feedback Control Copyright 2001 by Jonathan How. 1
Fall 2001 16.311-1 Introduction d(t) r(t) e(t) yt K(s Goal: Design a controller K(s so that the system has some desired characteristics. Typical objectives Stabilize the system( Stabilization) Regulate the system about some design point(Regulation Follow a given class of command signals(Tracking) Reduce the response to disturbances(Disturbance Rejection Typically think of closed-loop control > so we would analyze the closed-loop dynamics Open-loop control also possible(called"feedforward")-more prone to modeling errors since inputs not changed as a result of measured error Note that a typical control system includes the sensors, actuators and the control lay The sensors and actuators need not always be physical devices (e. g, economic systems) a good selection of the sensor and actuator can greatly simplify the control design process Course concentrates on the design of the control law given the rest of the system(although we will need to model the system)
Fall 2001 16.31 1—1 Introduction K(s) G(s) - 6 ? — u(t) r(t) e(t) y(t) d(t) • Goal: Design a controller K(s) so that the system has some desired characteristics. Typical objectives: — Stabilize the system (Stabilization) — Regulate the system about some design point (Regulation) — Follow a given class of command signals (Tracking) — Reduce the response to disturbances. (Disturbance Rejection) • Typically think of closed-loop control → so we would analyze the closed-loop dynamics. — Open-loop control also possible (called “feedforward”) — more prone to modeling errors since inputs not changed as a result of measured error. • Note that a typical control system includes the sensors, actuators, and the control law. — The sensors and actuators need not always be physical devices (e.g., economic systems). — A good selection of the sensor and actuator can greatly simplify the control design process. — Course concentrates on the design of the control law given the rest of the system (although we will need to model the system)
Fall 2001 6.311-2 Why Control? Easy question to answer for aerospace because many vehicles(space- craft, aircraft, rockets) and aerospace processes(propulsion ) need to be controlled just to function Example: the F-117 does not even fly without computer control and the x-29 is unstable
Fall 2001 16.31 1—2 Why Control? • Easy question to answer for aerospace because many vehicles (spacecraft, aircraft, rockets) and aerospace processes (propulsion) need to be controlled just to function — Example: the F-117 does not even fly without computer control, and the X-29 is unstable
Fall 2001 16.311-3 Feedback Control Approach Establish control objectives -Qualitative- dont use too much fuel Quantitative- settling time of step response <3 sec Typically requires that you understand the process(expected commands and disturbances)and the overall goals(bandwidths Often requires that you have a strong understanding of the phys ical dynamics of the system so that you do not "fight"them in appropriate(i. e, inefficient)ways . Select sensors actuators What aspects of the system are to be sensed and controlled? Consider sensor noise and linearity as key discriminator Cost, reliability, size Obtain model Analytic(FEM) or from measured data(system ID Evaluation model>reduce size/complexity>Design model Accuracy? Error model? ● Design controller Select technique(SISO, MIMO),(classical, state-space) Choose parameters(ROT, optimization Analyze closed-loop performance Meet objectives? Analysis, simulation, experimentation Ye→done,No→ iterate
Fall 2001 16.31 1—3 Feedback Control Approach • Establish control objectives — Qualitative — don’t use too much fuel — Quantitative — settling time of step response <3 sec — Typically requires that you understand the process (expected commands and disturbances) and the overall goals (bandwidths). — Often requires that you have a strong understanding of the physical dynamics of the system so that you do not “fight” them in appropriate (i.e., inefficient) ways. • Select sensors & actuators — What aspects of the system are to be sensed and controlled? — Consider sensor noise and linearity as key discriminators. — Cost, reliability, size, . . . • Obtain model — Analytic (FEM) or from measured data (system ID) — Evaluation model → reduce size/complexity → Design model — Accuracy? Error model? • Design controller — Select technique (SISO, MIMO), (classical, state-space) — Choose parameters (ROT, optimization) • Analyze closed-loop performance. Meet objectives? — Analysis, simulation, experimentation, . . . — Yes ⇒ done, No ⇒ iterate . .
Fall 2001 Example: Blimp control.31 1-4 Control objective Stabilization Red blimp tracks the motion of the green blimp ● Sensors GPS for positioning Compass for heading Gyros/GPS for roll attitude Actuators-electric motors(propellers) are very nonlinear · Dynamics rigid body" with strong apparent mass effect Roll modes · Modeling Analytic models with parameter identification to determine "mass Disturbances- wind
Fall 2001 16.31 1—4 Example: Blimp Control • Control objective — Stabilization — Red blimp tracks the motion of the green blimp • Sensors — GPS for positioning — Compass for heading — Gyros/GPS for roll attitude • Actuators — electric motors (propellers) are very nonlinear. • Dynamics — “rigid body” with strong apparent mass effect. — Roll modes. • Modeling — Analytic models with parameter identification to determine “mass”. • Disturbances — wind