Lecture plan

IIA1117 Control Engineering: Control Theory

Week nr. Date Subject Tehme Topic
34 21.8. Syllabus: Lecture notes ch 1.1, 1.5, example 1.1.

Introduction, notations, dynamic models, state space models, system theory, state space and transfer function model analysis. Feedforward control and reasons for using feedback.

Introducing Exercise 1

Lecture contents: Lecture 1

Video Lecture 2018: Lecture1a  Lecture1b

Video Lecture (2017): Se link  (Unfortunately without sound !)

35 28.8
System theory and state space analysis. Poles and zeroes. Linearizing non-linear models. Lecture notes ch 1. Introduction to the PID controller, Ch. 4

Introducing Exercise 3

Lecture contents: Lecture 2

Video Lecture 2018: Lecture2a Lecture2b

Video Lecture 2016:  Ch.1.12 linearization+Exercise 3 Lecture2 Erratum: Notice that the A, B and C matrices should be as in Eq. (30) in oving_pid_reaktor.pdf

Video Lecture 2017: Lecture2a  Lecture2b
36 4.9 System teory and state space analysis. PI-controller.The  Skogestad method.. Lecture notes ch. 3, paper by Skogestad. Exercise 3, linearizing the chemical reactor model.

Lecture contentsLecture 3
Video Lectures:
3) Fall 2018: Lecture3a  Lecture3b  Lecture3c (PID params)
1) Fall 2016: Lecture 3
2) Fall 2017: Lecture3a  Lecture3b

MATLAB Example files:
Numerical linearization:
1) Calculate A: jacobi.m  fx_chemreac.m
2) Calculate both A and B: jacobi2.m  fx_chemreac2.m
>> % Linearized model in Exercise 3 may be calculated as
>> [A,B]=jacobi2('fx_chemreac2',0,[2.5;1],25)
3) Simulate step response of  chemical reactor model: main_reacsim.m
Notice: Calculate right hand side in dot(x)=f(x,u):  fx_chemreac.m
37 11.9 PID-controller: Skogestads method ch. 3.1 lecture notes. The half rule for model reduction.  Direct design ch. 7. Standard controllers (P, PI og PID)  Ch. 4. Discretization and implementation of  PI og PID controllers.

Lecture contents: Lecture 4
Video Lecture:
Fall 2018: Lecture4a  Lecture4b
Fall 2016: Lecture 4    Lecture 4b
Fall 2017: Lecture4a   Lecture4b

m-file for PI control of the  chemical reactor: main_reacsim_pid.m

Implementing a PI controller: ex1_pi.m

Inverse response example: main_invresp_ex.m

38-39 18.9-25.9 Ch. 4.3 Anti windup and constraints. Ch. 4.4 Bumpless transfer between manual and automatic control. Direct design of PI controllers, examples from ch.. 3, 4 og 5 in lecture notes.

m-file examples from Ch 4: ex1_pi_anti.m ex1_pi_bump.m

Video Lectures:

Fall 2018: Lecture5a  Lecture5b

Fall 2016:

1) anti windup+bumpless transfer Lecture5 
2) tuning PI controller ex.: Lecture5b + Lecture5c

Fall 2017: Lecture5a   Lecture5b

Example 3.3: 
In laplace plane, using approx to time delay: ex33_laplace2.m
In time domain, exact implementation of time delay: ex3b_half.m

If time: Controllability. Observability. Linear transformation av models, Ch. 1, lecture notes.

39-40  25.9-2.10 P and PI controllers for integrating plus time delay process, disturbance rejection and in particular disturbance at the input side.

Lecture Contents:
1) Lect notes Ch. 3.8+3.8.1.
2) Di Ruscio (2010) paper Ch. 4.1+4.2
Video Lectures:
3) Fall 2018: Lecture6a Lecture6b
1) Fall16:  Lecture6  Lecture6b
2) Fall17: Lecture6a  Lecture6b  Lecture6c

Info: New PI controller tuning method for integrating+time delay systems

1) Ch. 3.9.Retuning a PI controller for oscillating feedback loop, integrating+time delay process.
2) Exercise example: exercise_retune_pi.pdf ("Increase KP to avoid oscillations")
3) Integrating+time constant+delay plant, cascade control and PD controller.
4) Final Exam 2016. Task1 m-file

Video Letures:
Fall 2016 Lecture7
Fall 2017: Lecture7_fall17

4) Exercise 4: Canonical forms and controller design. Lecture notes ch 2. PD control and state feedback, examples.
41 9.10.  Video lecture: Introduction to frequency analysis.

1) Read Ch. 3-4 and the examples.
2) Work with Task 1 final Exam 2014.
3) Ch. 9.2+9.1



Introduction to frequency alalysis. Ch. 9

Work with example: main_ex_step1.m

Video Lecture:

Fall 2018:  Lecture8a  Lecture8b
Fall 2016:  Lecture8   (Theory from Ch. 9.2.)
                   Lecture8b (Work trough example.)
                   Lecture8c (Interpretation of GM and PM)
Fall2017: Lecture8a  Lecture8b

New PI controller tuning method for Integrating Plus Time Delay (IPTD) systems

43 23.10 PID-control, feedback systems, feed forward control.  Frequency analysis.

Lecture notes, Ch. 6  (feedback systems) ,  Ch. 8 (feed forward, ratio control) , Cascade control+ double int. ex., Ch. 9 (Frequency analysis)

Sensitivity index (Ms), Gain Margin (GM)  and Phase Margin (PM)

Video Lecture:

Fall2018: Lecture9
Fall2016: Lecture9    Lecture9b
Fall2017: Lecture9a  Lecture9b

Info: New PD/PID controller tuning method for Double Integrating Plus Time Delay (DIPTD) plants

44 30.10 Frequency analysis. Phase and gain margin. Bode's stability criterion. PID control with Ziegler Nichols method. Lecture notes.

Video 2018:   Lecture10

Video Lecture 2017:
Lecture10  + Lecture10b + Lecture10c

Lecture10 (The Bode stability criterion)
Lecture10b (the Ziegler Nichols method)
Lecture10c (Ex. 2: SIMC tuning for 1sr order+time delay plant)
MATLAB m-file for Ex.2 in Lecture10c  main_sim_1st_margins.m

45-46 6.11-13.11 1) Non-Minimum phase systems Ch. 9.6.
2) Bandwidt of a control system Ch. 9.7.

3) Margins using SIMC method, integrating pluss time delay process with PI controller. Task. Solution: task_1511.m

Video Lecture : (above items 1)+2)+3) )  Lecture 11

4) Velocity/deviation form of the PI controller.

From Laplace formulation to continuous time , to discrete time and to the velocity formulation. Partly repetition from Ch. 4 and leading to the result in Ch. 10.4 (10.4.1+10.4.2+10.4.3).

Video Lecture: Lecture11b (Velocity PID formulation)

5) Example of how to implement the PI velocity formulation: ex3b_half_pi_du.m for controlling a process model: y=h_p(s)(u+v) where h_p(s)=k*exp(-tau*s)/s with slope, k=1, and time delay, tau=1

6) New method for tuning PI controllers for integrating plus time delay systems: DiRuscio2010

Feedforward control.  Lecture notes.

State estimation, modal estimation and control. Notes. Exam task on black board. m-files to the notes: lpe.m, lpe2.m

46-47  13.11-20.11 The Smith Predictor

Video Lecture:
Fall 2016: Lecture12
Fall 2017: Lecture12_smith

Exercise: Example task. Solution proposal: main:solution_extask1.m Theory: Sensitivity index

Pade approximation to time delay. Stability analyzis. Feed forward control. Lecture notes, Ch 5 and 8.

D and PD controller for double integrator + time delay process. Example hp_double_int.m

47 20.11 Discrete control. Discrete PID-controller. Incremental form. Trapes method. Stability.  s-plane and z-plane. Ch. 10. Ratio control.

Exercise 10.

New method for tuning PI controllers for integrating plus time delay systems: DiRuscio2010

47 20.11  Smith-predictor, inverse response control, modified  Smith-predictor. System teory for discrete systems if time.

Handwritten block-diagram reduction of the Smith predictor. (lecture notes)

New PI controller tuning method for integrating+time delay systems

47 20.11 Multivariable control: RGA-analysis and decoupling.

Video Lectures:
Fall 2016:  Lecture13 (Pairing of variables in MIMO systems)
Fall 2017:  Lecture13 (Non-minimum phase system, bandwidth)

Summing up the syllabus:. PID-control, Skogestads method,  frequency analysis, Ziegler-Nichols method, Bodes stability criterion, stability analysis.


Teacher: Dr. ing., 1. amanuensis David Di Ruscio                             

  Edited by: david.di.ruscio@usn.no