
Exercises in IIA1117 Control Theory 

A new exercise is given every
week.
Week 3435 Exercise 1
Solution 1
(state space analysis, matrix
theory) Some mfile solutions to subtasks in Exercise1b: ex1b_sol.m ex1b_sol2.m ex1b_sol3.m Sketch to solution of Exercise 1 Task 3 Note: Basic theory for solving the exercises is given in the lecture notes Ch. 1 Week 3536 Exercise 2 Solution 2(pdf) (modeling, state space analysis, simulation) main_losn2.m (MATLAB script with some solutions) Exercise 2b (Tuning controller for 1st order process. Simple method.) Solution to this exercise in mfile main_exercise2b.m Week 36, 37 and 38 Exercise 3 with sketch to a solution (pdf) (Design of PI/PID controllers for a chemical reactor) MATLAB script with some solutions (demo_reac_pid.m, dread.m) Enclosure to exercise 3 (pdf) (reactor model to be used in the exercise) MATLAB script for the enclosure (demo_reactor.m)
Week 3940 1) Work through Example 3.3 and Section 3.83.4, lecture notes. PI control of integrating+time delay process. mfile for simulations ex3b_half.m (exact time domain simulation, array method to implement time delay). ex33_laplace.m (Pade approximation for time delay and Laplace plane definitions using MATLAB functions, tf, series, feedback, step etc.) 2) Task 2 in Exercise 5 (below) is also a good choice. Week 40 1) Retuning an oscillating feedback loop, i.e., with an initial wrong tuning of an PIcontroller for an integrating plus time delay process and how to tune so that no oscillations occur. ex_retune_pi.pdf Some mfile hints, ex_KpTi.m 2) Exercise 4 (Controllability, PD control and state feedback.) Additional Example: Step response, half rule, PI control Example using MATLAB: ex2_half.m Week 41 Exercise 5 Solution 5 Solution task 1 in exercise 5 as the MATLAB script: main_losn7_1.m Contents: Identification of model from observed data, transformation from discrete to continuous model, design of PI controller based on the identified modell. Week 42 Partial task Friday 20/10, kl. 8.1510.15. Week 42 Exercise 6 Solution 6 ov6_1c.m ov6_1d.m Contents: Feedback systems. PI controller synthesis. Sketching the sensitivity function, S, and the complementary sensitivity function, T. Simulation of the closed loop system behaviour in the time domain. Week 4243. Margins and step response for PI controller tuning rules for an integrator plus time delay model with settings: 1) SIMC tuning rules. 2) Tuning rules deduced in lecture, Kp=1/(k*Tau_0) and Ti=2*Tau_0 where, Tau_0, is a specifed response time constant according to a unit relaive damping. Tau_0=4*tau gives SIMC tuning rules. Solution proposal. Week 4244 Exercise 7 Solution 7 losn7_oppg1.m Contents: Frequency analysis, computation of Gain Margin (GM) and Phase Margin (PM). Design of PI controller. Closed loop simulation. Comparison of PI controller parameters by the parameters fond by the Skogestad method in Exercise 6. Week 45 Exercise 8 Solution 8 losn_ov8.m ov678_pi.m dread.m Contents: Tuning of PI controller with the. ZieglerNichols method. Simulation of closed loop system and comparison of the PI controller settings found in Exercises 6 and 7. Week 46 Work with Exercise 9: Example task PI tuning 3rd order system. Notice how the velocity form of the PI controller is implemented: ex3b_half_pi_du.m Feed forward control: Exercise 9b Solution 9b Contents:: Design of an ideal feed forward controller. Approximations for transport delay and simulation. Week 47 Exercise 10 Solution 10 (pdffile) Solution10 (psfile) Week 48 Continue with exercise 10 or Exercise 11 below. Contents: Discretization of continuous process model and PID controller. Simulation of closed loop control system. Week 49 Exercise 11 Tips for task 1f) smithreg2002.m. SIMULINK may be used in this exercise.. Contents: Smith predictor for controlling systems with time delay. Interaction and pairing of variables., RGA analysis, Balchen indeks. 

