# Integration Project Systems and Control 2013 Group 1

## Group Members

 Name: Student id: Email: Abhishek Bareja please fill in a.bareja@student.tue.nl Ioannis Kokkinakis please fill in i.kokkinakis@student.tue.nl Vangelis Stamatopoulus please fill in e.stamatopoulos@student.tue.nl Donatella De Cesare please fill in d.de.cesare@student.tue.nl

## Planning

Week: Activities:
Feb 18 - Feb 24 ...
Feb 25 - Mar 3 ...

## Progress

#### Week 1

• Our first aim is to brush up on the technical knowledge required in the related areas.
• Literature study regarding the following aspects:

1. Robot: input-output variables of the given system, to study the matlab files provided, non-linearities, friction model, coupled phenomena in the system. 2. System Identification: to derive system model using two point method, to derive system model using three point method

• Lab activity_System identification/Frequency response measurements : Thursday 21/02, we will be in the lab collecting data.More precisely, given that no information is available to formulate a model from first principles, we have to revert to methods of System Identification using input/output behavior of the system. Hence, both open loop and closed loop frequency response measurements will be conducted on the robot. Initially we will take measurements using one input at a time, and then all four inputs together.As inputs we will use white noise and chirp signals.

In the open loop method, we will input a white noise of small power into the four controlled motors of the system and measure the corresponding output response. Using the frf of the input and output, we will find out the cross power spectral density on the input and the output using Matlab command cpsd.m. Then, we will calculate the auto power spectral density of the input using Matlab command psd.m (or spectrum.m). Then by using the formula H(f)=Syu(f)/Suu(f) we will arrive at the frf of the plant.This can be easily converted into a transfer function by using the Matlab command tfestimate.m. In the closed loop method, first a stabilizing controller will be build using SHAPE-IT for the calculated transfer function from the direct open loop method. Then closed loop measurements will be made where we inject white noise into the system and calculate the sensitivity and the process sensitivity. The plant frf is then calculated by using the above formula.

Once we have derived the model, response of the system in terms of bandwidth, time response, and stability margins will be noted. The same controller will then be plugged into the hardware to check if the response is same. A similar response would mean that the derived model of the plant is accurate.

#### Week 2

• More literature study regarding the following aspects:

1.Design Criteria/Specifications: bandwidth, steady state error, time response, sensitivity, modulus/phase margin 2. study about different types of controllers: feasibility of using a PID controller, feasibility of using an LQR controller, feasibility of using an H-inf. Controller , feasibility of using Adaptive control, feasibility of using Feedforward control, refresh memory on the use of ref3 and shapeit in matlab.

• Lab activity_Reference trajectory: The first task is to find out the desired and optimal reference trajectory. That is, the desired motion of the end effector where the Pizza will be placed. The reference trajectory is a plot of position, velocity and acceleration of end effector in x, y and z directions against time. The ref3 tool provided to us in the motion control course is an excellent way to plot a Matlab compatible reference trajectory. With the help of this tool we are able to generate a 3rd order polynomial for the reference trajectory. As the motor inputs directly correspond to the end effector horizontal, vertical and rotational displacements, we don’t need to find out the inverse kinematics. As the final time is undecided, a targeted time will be used, which will then be minimized after the controller has been designed, by using iterations. This minimum time will depend on the motor saturation voltages.