# SpringSemester

### Experiments in the Spring Semester

On this page you will find short descriptions of every experiment we offer. You can also download the manuals and necessary files for your homework preparation from here.

Registration: Please register for experiments on the D-ITET online registration website.

#### 2.2 Self Erecting Inverted Pendulumg - LQR

Self Erecting Inverted Pendulum - LQR

In this experiment, a pendulum is mounted on a cart. The pendulum shall be controlled to stay in its unstable equilibrium, i.e. the upright position. You will design an LQR controller to achieve this goal. Additionally, you will implement a destabilizing controller that will make the pendulum swing up from its stable downward position. Finally, the two controllers will be combined to yield a self-erecting pendulum.

###### Homework

Preparation time approx 2.5 hrs, see Manual.

#### 2.6 Helicopter II - Lead/Lag

You will control the two coupled axes of a helicopter model. First the model of the plant is calculated and then linearized. Using Matlab and Simulink, you will design a compensation controller (Lead/Lag), which can then be tested on the real system.

###### Homework

Preparation time approx 2.5 hrs, see Manual.

###### Place

The quad-tank system is a relatively simple MIMO (multi-input, multi-output) system. MIMO systems are inherently more difficult to control than systems with only one input / output. In this experiment, you will learn some fundamental techniques to control a MIMO system, like coupled- and decoupled designs or LQR / LQG state-space controllers.

###### Prerequisites
• Basics in MIMO control
• Minimum/Non-minimum phase plants
• PI control
• LQR control
###### Homework

Preparation time approx 2.5 hrs, see Manual.

#### 3.7A Flexible Shaft A - System Analysis & PI

Flexible Shaft A - System Analysis & PI

This experiment emphasizes the properties of so-called flexible structures. These are mechanical systems that allow to be modeled as a system of many masses interlinked by springs. Examples are robots, huge satellite dishes, power trains and so on. The experiment itself consists of a shaft with two inertia wheels that are connected by a spring. A drive motor accelerates the shaft whereas a load motor is used to simulate a load torque. The student starts with a system analysis of this setup and investigates typical resonance and anti-resonance behavior which also get interpreted in terms of pole/zero configurations. Afterwards, a PI controller get designed to control the speed of the shaft.

###### Prerequisites
• PID Controller (RS1 § 4,12; week 4 and 8)
###### Homework

Preparation time approx 2 hrs, see Manual.

#### 3.7B Flexible Shaft B - Loop Shaping & LQR

Flexible Shaft B - Loop Shaping & LQR

This experiment is the continuation of experiment 3.7A. Here, students design two more feedback controllers to control the speed of the flexible shaft. The first controller is obtained from a loop shaping procedure. The second controller consists of a state-feedback LQ controller with integral action and an appropriate observer. Please note that the experiment 3.7A has to be done prior to this one.

###### Prerequisites
• Experiment 3.7A completed
• LQR (RS1 § 17.9; week 13)
###### Homework

Preparation time approx 2 hrs, see Manual.