Exercises in IIA1117 Control Theory
| A new exercise is given every
Sketch to solution of Exercise 1 Task 3
Note: Basic theory for solving the exercises is given in the lecture notes Ch. 1
main_losn2.m (MATLAB script with some solutions)
Week 36, 37 and 38
Exercise 3 with sketch to a solution (pdf) (Design of PI/PID controllers for a chemical reactor)
Enclosure to exercise 3 (pdf) (reactor model to be used in the exercise)
MATLAB script for the enclosure (demo_reactor.m)
Week 39-40 1) Work through Example 3.3 and Section 3.8-3.4, lecture notes. PI control of integrating+time delay process. m-file 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 PI-controller for an integrating plus time delay process and how to tune so that no oscillations occur. ex_retune_pi.pdf Some m-file 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
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. 8.15-10.15.
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 42-43. 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.
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.
Contents: Tuning of PI controller with the. Ziegler-Nichols 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
Contents:: Design of an ideal feed forward controller. Approximations for transport delay and simulation.
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.
Contents: Smith predictor for controlling systems with time delay. Interaction and pairing of variables., RGA analysis, Balchen indeks.