 ## Lecture Plan: IIAV3017 Advanced Control Engineering

 Week nr. Date Topic 34 22.08 Introduction, notation, state space models, solution of the state equation, discrete time state space models, controllability and observability.   Lecture notes Ch. 1. Files to run Ex 1.3 in the lecture notes, ctrb2ex.m, gram2.m Video Lecture: Lecture1a  Lecture1b 35 29.08 Zeroes and poles in multivariable systems. Multivariable frequency analysis.  Analysis based on both transfer matrix models and state space models. Example in lecture ex_zeroes.m Lecture notes Ch 1.8 Example 1.4 on page 15: main_ex1_4.m Lecture notes: Ch 1.8 and Ch  2 Video Lecture: Lecture2a  Lecture2b 36 5.09 Introduction to optimal control of linear dynamic systems with Linear Quadratic (LQ) criterions. Lecture notes Ch.. 3, Ch. 4.1 and Ch.  4.2 Video Lecture: Lecture 3a  Lecture3b  Lecture3c  Lecture3d 37 38 5.9-12.9 12.9-2019 Lecture notes Ch 3 and exercise 3. LQ-control and Sections 4.3 and 4.4.  Ex. 8.3-9.5 LQ and PD control. Section 4.6, systems with disturbances. LQ-control with integral action as an example. If time, solution of the Algebraic Riccati Equation (ARE) Section 4.5. Video Lecture: Lecture4 Video Lecture: Solving the ARE using Real Schur Decomposition of the Hamiltonian matrix F=[A -H;-Q -A^T]. Note -H in the F matrix in VideoRecord. 39-40 19.9-26.9 Sec. 4.6 Optimal systems with disturbances and Sec. 4.7 Optimal tracing systems. Video Lecture: Lecture5a  Lecture5b Video Lecture : Lecture5a  Lecture5b Optimal tracking systems, Sections 4.7 Details not syllabus, i.e only an overview. Lecture 19.09 Short intro! Discrete optimal control. Ch. 5.1 and 5.2 Video Lecture: Lecture6a  Lecture6b 39 26.9 Standard Discrete time LQ (DLQ) optimal control problem. Ch 5.2 Introduction to method for Discrete LQ optimal control with integral action Video Lecture: Lecture7 MATLAB m-file for the MIMO LQ-optimal controller with integral action: dlqdu_pi.m 40 3.10 DLQ problem Ch. 5.2. Discrete LQ optimal tracking control, Ch 5.3. MATLAB example: dlq_ex2_du.m 41 10.10 Discrete optimal control Lecture notes 5.3. mic-journal paper: LQ optimal control with integral action Video lectures 1): Lecture8a  Lecture8b 2): Lecture8 No classrom Lecture week 41 42 17.10 Discrete optimal control Ch. 5 Lecture notes Ch 5.2 and 5.3. LQG control Doyle paper   Video lecture Fall: Lecture9a  Lecture9b Work with: Task3 in Exercise 8. Solution proposal dlq_ex3_du.m 42-43 17.10-24.10 1) Standard discrete LQ opt control problem, Ch. 5.3. Josephs stable formulation of the discrete Riccati eq and solving the DARE dric_solv.m Test example main_ex_ric.m 2) LQ with integral action:  note. 3) Control of distillation column example. As in Example 5.3: m-file Software in d-col.zip main_kolreg_lq.m  Description of distillation column model used in Ex 5.3 with parameter numerical values 2620_001.pdf Se also Ex 8.1 for a distillation column modeling example. Function dread.m used in main_kolreg_lq.m 43-44 24.10-31.10 Weighting control deviations. Paper:  Discrete LQ optimal control with integral action (pdf-fil uten figurer) LQ optimal control with integral action (mic-paper). MATLAB scripts for the examples in the paper: dlq_ex4_du.m, dlq_ex3_du.m, dread.m (low level function used) Solution to given exercise: main_2x2_ex.m Function to compute the optimal control: dlq_du.m dlqdu_pi Testing Alternative 1. x=x+y and Alternative 2 x(i+1)=x(i)+y: main_test_alt1.m main_test_alt2.m Mandatory Exercise: Task Mandatory Exercise 44 31.10 Lecture notes Sec 5.4. Weighting control deviations. Sec 5.6 Solution of DARE, generalized eigenvalue problem. Ch 8 Time delay. Examples tau=1, tau=2 delays. Ex implementing delay model in Ch 8.2.1  ex1_delay_ssmodel.m lecture notes Example 5.2 m-files: main_dlq_rdu.m   main_dlq_rdu2.m Integral action: paper IMC tuning rules etc. (Lecture notes) (Lecture notes2) 45 7.11 Lecture 12a Estimator and Regulator duality, Ch. 11.1-11.2 Lecture 12b The Separation principle, Ch. 11.3 Lecture 12c The LQG controller, Ch. 11.4 1) Control and state estimation. Kalman-filter. Lecture notes Sec 10. 2) Exam 2010 Task 1 amd Task 2 3) Handwritten solutions to some old Final exam tasks (in norwegian)(2641_0001.pdf) 46 14.11 Summing up lecture. Main Topics: System theory, from Ch.1 and 2. LQ optimal control of linear continuous and discrete time systems, Ch. 4 and 5 (mostly Ch4.2+Ch5.2). Item 1-4 in Main Topics. Control and state estimation. Kalman-filter. Lecture notes Sec 11. Exam tasks. Robustness in LQ and LQG systems. Ch. 13 and 12. (short info) Uncented Kalman Filter (UKF note) (for info, not syllabus). LQ and PI control with time delay. (Paper for info) (for info, not syllabus)). New paper on LQ optimal control with integral action:http://www.mic-journal.no/PDF/2012/MIC-2012-2-1.pdf Video record: Fall 17 20.11.17 47 28.11.2021 Final Exam on Campus Email: david.di.ruscio@usn.no