Automatic Control II: Summary and comments

Transcription

1 Automatic Control II: Summary and comments Hints for what is essential to understand the course, and to perform well at the exam. You should be able to distinguish between continuous-time (c-t) and discrete-time (d-t) systems! be acquainted with basic concepts and properties of linear systems (for both c-t & d-t): stability controllability & observability solution of the state equation etc... 1 / 8 hans.norlander@it.uu.se Summary

2 Summary and contents (cont.) You should know about system sampling, a.k.a. zero-order-hold (ZOH) sampling MIMO systems disturbance models: spectrums, spectral factorization white noise state space models; the standard form, covariance matrices from Lyapunov equations (c-t & d-t) Kalman filters in c-t & d-t: CARE/DARE P = covariance of estimation error innovations, innovations form the m-step predictor 2 / 8 hans.norlander@it.uu.se Summary

3 Summary and contents (cont.)... and about LQ & LQG (for c-t & d-t): CARE/DARE as design technique: the meaning of Q 1, Q 2, R 1, R 2 etc MPC: the basic principle the meaning and effect of the control horizon N the prediction horizon M the sampling period h other design parameters 3 / 8 hans.norlander@it.uu.se Summary

4 Aiding material At the exam you are allowed to bring and use Textbooks in automatic control, eg. Reglerteori Flervariabla och olinjära metoder (red) Reglerteknik Grundläggande teori (blue) Control Theory Multivariable and Nonlinear Methods (English vsn.) all by Glad & Ljung Mathematical handbooks (eg. β or Physics) Calculators Handwritten comments in textbooks are not forbidden Not allowed: Exercise manuals, problem collections, old exams and similar. 4 / 8 hans.norlander@it.uu.se Summary

5 Related courses Some relevant courses if you want to learn more about systems and control: Reglerteknik III (Automatic Control III) 5hp: given in per. 1 for F5Is & E5 (& STS5) enhanced understanding of MIMO systems what can be achieved by use of feedback? limitations and conflicts non-linear systems control design different approaches advanced design methods optimal control 5 / 8 hans.norlander@it.uu.se Summary

6 Related courses (cont.) Mathematical models are necessary for analysis, simulation and prediction of, as well as for control design for dynamical systems. Two courses where you learn about how mathematical models can be obtained are: Empirisk modellering (Empirical modeling) 10hp: given in per. 1 for ES5, STS5, W5 you learn how to construct models of dynamical systems eg. by use of experimental data learn by doing: examined (mainly) by project Systemidentifiering (System identification) 5hp: given in per. 4 for F4Is you learn how to construct models of dynamical systems from experimental data statistical methods are used for analysis of properties etc. 6 / 8 hans.norlander@it.uu.se Summary

7 assigned chapral surfaced for nced in a paper f Transfer Funceared as a pertomatic Control until 1983, in a ce on Decision rves, someone ust a version of tics for a long ed the value of t it should not about the diffition laws. They tegrated value ty function is e total amount l to zero for stal to some fixed vity magnitude, ensitivities less values are bad an open loop). sensitivity imequency is exerioration. For se because the Reglerteknik III 5hp Kursen ges i period 51 Hur bra kan man reglera? Kursen a mound is deposited gersomewhere fördjupad else. This factförståelse is most evident to the ditch digger, because he is right there to see it om happen. bl.a. In the same spirit, I can also illustrate the job of a more academic control designer with more abstract tools such as linear quadratic MIMO-system Gaussian (LQG), H, convex optimization, and the like, at his disposal. This designer guides a powerful ditch-digging machine by remote control from the safety of vad som är möjligt att uppnå (begränsningar och konflikter) his workstation (Figure 4). He sets parameters (weights) at his station to adjust the contours of the machine s digging blades to get just the right shape for the sensitivity function. He then lets the machine dig down as far as it can, and he saves the resulting compensator. Next, he fires up his automatic code generator to write the implementation code for the compensator, ready to run on his target microprocessor. Log Magnitude olinjära system Serious Design Frequency s.g mer om regulatordesign: olika ansatser (decentraliserad design, frikoppling...) mer sofistikerade designtekniker (t.ex. gör S(s) och T (s) så små som möjligt) optimal styrning Figure 3. Sensitivity reduction at low frequency unavoidably 7 / 8 hans.norlander@it.uu.se leads to sensitivity increase at higher frequencies. Summary

8 Empirisk modellering 10hp Kursen ges i period 51 Var kommer modellen ifrån? Både analys och regulatordesign förutsätter en bra modell. u? v Kursen erbjuder: n Teori för modellbygge med tonvikt på empirisk modellering. Gästföreläsare. Projektarbete: Empirisk modellering av några energirelaterade processer. y Bland annat ska modeller tas fram som beskriver dynamiken hos ett soluppvärmt hus, samt modeller som kan prediktera vindhastigheten vid ett vindkraftverk. 8 / 8 hans.norlander@it.uu.se Summary