Säätö- ja systeemitekniikan kehittyneet menetelmät (477607S) Advanced control and systems engineering (477607S) 2018 Enso Ikonen säätö- ja systeemitekniikan professori professor of control and systems engineering Muista nämä: - käynnistä kysely: www.feedbackr.io sign in: (E.I@o.f/e...0) SSKM-1 start all käynnistä videokuvaus

DMC Exercise 1 (2h) Outline How are things going (5min) ? Any technical problems with lecture recordings? Book pdf ok? Did you follow all the lecture recordings 11.x-13.x? Did you make the exercises? Have you read the associated chapters? How have you found the course form from a pedagogical point of view? Recordings? Recap of week 1 lectures (10min) FSR + G + MPC horizons + DMC algorithm Homeworks ? (5min) pairs, consultation, report + presentation, evaluation HW Assignment 1 (5min) DMC exercise intro (10min) Rec 21-1 (intro to problem) DMC coding (45min) your Matlab implementation of DMC.. basis of HW1 & HW2 Rec 21-2 (sample coding solution) DMC simulations (10min) Rec 21-3 (simulations) Rec 21-4 (what’s next) guidelines for HW studies What’s next (1min)?

notation y(j|k) to emphasize ’prediction’ of y at instant j, when current instant is k free response forced response terms f depending on u(i) in the past, i<k Recap 1/6 FSR Write out individual predictions y(k|k) y(k+1|k) : y(k+n|k) use FSR terms depending on u(i) now, or in the future, i≥k

Recap 2/6 Dynamic matrix G free response response due to future control moves

Recap 3/6 Prediction and control horizons Prediction horizon p predict p-steps ahead may have p<n, p=n, p>n controller tuning parameter Control horizon c only c (first) control moves are considered in optimization no change in control afterwards tuning parameter Control horizon

Recap 4/6 Optimization Find a MV sequence that results in a (forced) response such that the plant output is close to desired future reference. future reference is often a setpoint Find GΔu+yp=ysp if p=c, a unique solution exists if c<p (usually), minimize a cost

Recap 5/6 DMC algorithm

Recap 6/6 DMC algorithm

HW guidelines & HW1 The aim of the homeworks is that the student i) familiarizes with the methods, and learns to code them in practice; ii) understands, can assess, and present the behaviour of the algorithms (via simulations, but all other analysis is also welcome). The works can be done alone or in pairs. The work is to be reported following the given schedule and presented in a seminar. There are few guided exercises/joint consultations before seminars; teacher is available for help during all consultation hours. The work (points) is assessed based on the written report and the presentation A short report is enough (apprx 2A4 pages without figs + figures) describing main observations; to be returned following the given schedule Presentation appx 10min + 5min for discussion; all authors should be present. If there are two authors, each will receive 75% of the points. If the work is done alone, the student will receive 100% of the points. The points are taken into account in the grade for the course. Irrespective, a minimum number of points must be obtained from an exam in order to pass the course. You are free to choose your target process. You may start with a first order process y(k+1) = ay(k)+bu(k) (a=0.5, b=0.2, or alike). Homework 1 Design a DMC controller. Examine and illustrate the behaviour of the controller/controlled systems in closed loop via simulations (3p.) Demonstrate control and prediction horizons, and other tuning parameters Demonstrate set point control and disturbance rejection Design a DMC controller for a higher order process or process with delay (3p) Compare the behaviour of DMC controller to PID control (2p) Max 5p/opiskelija/student Consultation available Mon 22 Jan SÄ114 at 14-16 Tue 23 Jan PR339 at 10-12 (Note change of schedule) Written report (pdf) email Thu 25 Jan by 12 seminar presentations Thu 25 Jan at 14-16

Exercises.. Outline a) Code the DMC algorithm. b) Simulate closed-loop behavior. c) Experiment tuning parameters (c, p, λ) d) Experiment second order process, etc. See Ex_DMC.m

DMC exercise: Code and simulate the DMC algorithm using Matlab % On-line y(1) = ... for k=1:100 % observe y(k) and d(k) d(k) = … % DMC control on-line: b(k) = ... delta_d(k) = ... ysp(k+1) = yp(:,k+1) = T*f+sd(1:p)*delta_d(k)+b(k) e(:,k+1) = ysp(k+1)-yp(:,k+1) delta_u(:,k) = H*e(:,k+1) u(k) = ... % prosess simulation: y(k) y(k+1)=PM(y(k), u(k), d(k)) f = M*f+su*delta_u(1,k)+sd*delta_d(k) % store info UYW(k,:) = [u(k) y(k) ysp(k)] end % illustrate simulation plot(UYW), xlabel(’k’), ylabel(’u, y, w’) DMC exercise: Code and simulate the DMC algorithm using Matlab % DMC exercise % Process PM: y_new=PM(y,u,d) PM = @(y,u,d) 0.5*y+0.2*u+d; % Step response models: n, su, sd n =..., u=... for i=1:n, y=PM(y,u,d); su(i,1)=y; end % Tuning parameters: lambda, p, c p=... % Off-line: G, M, T, H, f (1.7-10,12,14) G = ... H = inv(G’*G+lambda*I)*G’ f = zeros(n,1)

DMC simulations What’s next Consultation available Mon 22 Jan SÄ114 at 14-16 Tue 23 Jan PR339 at 10-12 (Note change of schedule) HW written report (pdf) email Thu 25 Jan by 12 to Enso.Ikonen@oulu.fi seminar presentations Thu 25 Jan at 14-16 Examine the behaviour of DMC in simulations, under various set point sequences parameter settings: p, c, λ plants of higher order with delay with non-minimum phase y(k+1)=0.5y(k)+0.2u(k-2), or y(k+1)=1.64y(k)-0.67y(k-1)-0.11u(k)+0.14u(k-1) disturbances plant-model mismatches Examine the algorithm variables most of them are quite explicit: su, sd, G, yp, f, …