What you should know for this experiment
Start by watching the introductory video for this experiment
Ensure you read about all the equipment that you will be using in the lab. Any transfer function that you have learnt about in class so far assumes one thing; that the system is linear and time invariant. While this somewhat simplifies calculations, it is rarely true in reality. This lab will investigate what may make the motor nonlinear and how these effects can be reduced to effectively create controllers for the system. In this experiment nonlinearities in the motor are investigated. There are two main reasons the motor is nonlinear. Firstly there is a large coefficient of static friction in the motor which is nonlinear in itself. Secondly the amplifier used to power the motor is a PWM, which inherently has some nonlinearities associated with it. The main effect of the nonlinearities are stiction at low velocities and a dead zone at low voltages, which you will notice in this lab. There are many ways to reduce the effects of this nonlinearity but the main one used in every control system is feedback. If the system behaved in a predictable way at all times there would be no need for feedback! Be sure to revise the mathematical model of a DC motor found in your lecture notes. The block diagram of the transfer function of a DC motor can be found below: In the above diagram, K_{m} is the static gain of the motor and
t_{m}
is the pole frequency or absolute value of the pole position of the motor. The
above model is a simplified model of the motor. In practice the motor with
velocity as output
is a second order system with two nonzero poles. However, since the poles are
far apart, one of them will be much more dominant and the other pole can be
ignored for feedback control in many applications. In this experiment, each motor parameter will be calculated and a transfer function will be generated for both speed and position output of the motor. The outputs will be in rad/sec and rad respectively. The usefulness of this practice of modelling from a mathematical perspective will also be investigated.
Visit the Control Tutorials at http://ctms.engin.umich.edu/ and study the theoretical part of DC Motor Speed: SYSTEM Analysis section by clicking on MOTOR SPEED at the top and ANALYSIS at the topleft under SYSTEM.
Visit the Control Tutorials at http://ctms.engin.umich.edu/ and study the theoretical part of DC Motor Position: SYSTEM Analysis section by clicking on MOTOR POSITION at the top and ANALYSIS at the topleft under SYSTEM.
Given a transfer function 100/(0.1s+1) determine its step response y(t). For t=0, 0.1, 0.2 and 0.3 determine y(t).
Using Matlab plot the step response of the following transfer function 1/(Ts+1), where T=1, 3, 5, 7 and 9, on a same graph using different colours.
A step response of a transfer function K/(Ts+1) is show in the following figure. Determine K and T in the transfer function.
