Introductory course on concepts used in predictive control. For more files and MATLAB suporting information go to: http://controleducation.group.shef.ac.uk/OER_index.htm

1. Predictive control Anthony Rossiter Department of Automatic Control and Systems Engineering University of Sheffield www.shef.ac.uk/acse © University of Sheffield 2009 This work is licensed under a Creative Commons Attribution 2.0 License .

6. Illustration Road CAR Horizon

8. Illustration of initial prediction

9. Illustration

10. Illustration

38. GPC may not always be good

40. Optimised predictions with different nu (1,2,  )

41. Optimised predictions one sample later Optimum at t Optimum at t+1

42. ny=50,nu=1,Wu=0.1 Input not close to optimum!

43. ny=50,nu=2,Wu=0.1 Input not close to closed-loop!

44. ny=5,nu=1,Wu=1 Input not close to optimum!

46. PFC approaches Ideal path (not actual)

87. Dual mode paradigm (or closed-loop prediction) Terminal region in which the control law u=-Kx satisfies constraints. Initial state trajectory nc moves maximum Terminal State In at most nc samples, predicted state moves into the terminal region while satisfying constraints.

88. Open and closed-loop prediction Model Future inputs Future outputs OPEN LOOP PREDICTION Model M K Future outputs r Decision variables CLOSED LOOP PREDICTION

91. Feasible regions for n c =1,2,3 nc=3 nc=2 nc=1

92. Terminal region variation with different feedback gains

101. Illustration of regions Each region has a different control law

102. Illustration of regions (b)