EE 3CL4: Introduction to Control Systems Lab 1: Introduction Tim Davidson Ext. 27352 davidson@mcmaster.ca Objective To establish safety protocols and to introduce the laboratory equipment. Assessment The assessment of this lab will occur within the time allocated for the lab. The first component is to complete the Department s laboratory safety quiz (see Section 2). If you do not successfully complete this quiz, you will not be able to proceed with this laboratory, nor the remaining laboratories. If you have already completed this quiz this term in another course, please check with the TAs to ensure that your completion has been registered. The second component is to demonstrate to the TAs that you have understood the specific safety information for the EE3CL4 labs (see Section 3). The third component is to demonstrate to the TAs that you have familiarized yourself with the equipment, by demonstrating components (chosen by the TA) of the familiarization exercises, and answering the TAs questions (see Section 4); The final component is the writing exercise discussed in Section 5. All components of the laboratory, including the writing exercise, must be completed and submitted before the end of the laboratory time. 1 Description of Laboratory Equipment In the laboratories in this course, we will deal with a closed-loop angular positioning system based around a DC motor. Such systems are often used to position heavy or difficult to move objects using a command tool that is easy to move, in which case they are often called servomechanisms. One example of a servomechanism is that involved in moving the control surfaces of an aircraft using a lever in the cockpit. The goal of this lab is to introduce the positioning system that will be used in all the laboratories in the course, and to establish the appropriate safety protocols. 1
Figure 1: Feedback system with y(t) = θ(t). In our models, the sensor will be assumed to have a constant gain over the frequencies of interest. (Figure 4.3 of Dorf and Bishop, Modern Control Systems, 11th edition, Prentice Hall, 2008.) A block diagram of the systems that we will develop in the laboratories is illustrated in Figure 1. The process that we wish to control is the motor and its associated electronics. We will use the function θ(t) to denote the output of the motor, rather than the function y(t) in Figure 1, because the output of the motor is a voltage that is proportional to its angular position. In our experiments, the bandwidth of the sensors that we will use is much wider than the signals that will pass through them, and hence they can be modelled as having a constant gain over all frequencies. The broad goal of the series of laboratories in this course will be to design controllers that ensure that the feedback system as a whole performs in desirable ways. As mentioned above, the process that we wish to control is the motor and its associated electronics. The input to the process is a control voltage, denoted x(t), and the output of the process is a voltage that is proportional to the angle of the motor shaft, denoted θ(t). A detailed description of the operation of the motor is provided in the appendix to these instructions; see the course web site. For the purposes of our EE 3CL4 labs, we will assume a linear model for the process. Using information about the structure of the motor and rotational Newtonian mechanics, the linear model for the operation of the motor can be described by the following differential equation: J d2 θ(t) dt 2 + b dθ(t) dt = K m x(t), (1) where J is the rotational inertia of the motor, b is the coefficient of viscous friction in the motor structure, and K m is the (internal) gain. Taking Laplace transforms of both sides of (1), for a system initially at rest, we obtain the transfer function of the process: s 2 JΘ(s) + sbθ(s) = K m X(s) (2) = G(s) = Θ(s) X(s) = A s(sτ m + 1), (3) where A = K m /b and τ m = J/b. In typical industrial applications, the gain A and the time constant τ m are unlikely to be known in advance. Therefore, in the second laboratory we will 2
develop experimental techniques by which A and τ m can be estimated. In the laboratories that follow that one, we will design controllers for the servomechanism that provide desirable performance characteristics. 2 Departmental Safety Information For the safety of everyone in the laboratory, it is critical that everyone is fluent in the Departmental laboratory safety procedures and in the specific procedures for the EE3CL4 laboratories. To that end, the first activity for the laboratory is to: Read and understand the Departmental laboratory safety information, which is available at the following url: http://www.ece.mcmaster.ca/ug_cours/lab_safety.html. Please ask the instructor or a TA if you have any questions or concerns. Complete the Departmental laboratory safety quiz, which is available at the above url. If you have already completed this quiz this term, please inform a TA, and they will confirm that the quiz has been completed. You will not be allowed to proceed with this or any other laboratory if you have not completed the safety quiz this term. 3 Specialized Safety Information Following the completion of the Departmental laboratory safety quiz, the TAs will lead the class through a safety information session that addresses the specific equipment that will be used in the laboratories. Each pair of students will be required to demonstrate that they understand the information that has been provided before they will be allowed to proceed with the laboratory. 4 Familiarize Yourself with the Equipment 4.1 Equipment list The laboratory equipment you will require for this laboratory consists of: i) Signal generator ii) Op-amp module: This module will be used to construct the controller for the servomechanism. iii) Servomechanism electronics unit (SEU): This unit contains the circuits which drive the motor and those which process the sensor output. As far as the control design is concerned, the process is the cascade of the SEU and the motor. Please note that 3
you must always set the motor switch to inhibit before turning the SEU on or off. iv) DC motor: Note that the flange indicates the angle of the shaft. v) Scope vi) Components for the op-amp module, including 10 kω resistors (orange) Flat conductors with banana plugs Cables with banana plug connectors vii) In future labs we will use other components, including 100 kω resistors (yellow), 1 MΩ resistors (green), various potentiometers, and capacitor banks. 4.2 Familiarization exercises (5 marks) To familiarize yourself with the equipment, perform the following simple tests. i) Set the motor switch on the SEU to inhibit, and set the resolution to one revolution. ii) Switch on the SEU. iii) Rotate the disk on top of the motor one revolution (with your finger) until the red uncal light goes off. You must do this every time you switch on the SEU. iv) Continue to rotate the disk and observe that the LEDs count upwards from 0 to 360. Observe that the range of the counter is 0 to 2399. v) Set the resolution to two revolutions and rotate the disk again. Observe that the LEDs count from 0 to 2399 as the angle goes from 0 to 720. vi) Set the resolution to one revolution. Pick a channel of the oscilloscope and set the scale to 5V/div and the coupling to DC. Connect the ground for that channel to the ground of the SEU and connect the probe for that channel to the angle output. vii) Rotate the disk again and observe that the output voltage goes from 10V to 10V. viii) Disconnect the probe from the angle output connect it to the rate output. ix) Rotate the disk with your finger in different directions and different speeds and observe the voltage output. You may wish to set the scale to 2V/div for this step. x) Leave the motor switch at inhibit, and connect the +12V supply on the SEU to the command input. Set the motor switch to enable and observe the direction and speed of rotation and the voltage of the rate output. 4
xi) Set the motor switch to inhibit. Connect the 12V supply on the SEU to the command input. Set the motor switch to enable and observe. xii) Set the motor switch to inhibit, and set the resolution to two revolutions. Disconnect the probe and its ground. These familiarization exercises will be assessed via a demonstration of successful completion of the exercises to the TAs, and through a question and answer session with a TA. 5 Laboratory Report The writing exercise associated with this laboratory is to write a one-page summary of the outcomes of the familiarization exercises that you have just completed. The target audience for the summary is one of your peers who was unable to attend the laboratory. The summary should be in sufficient detail that would enable this student to perform the next laboratory without having to go through the familiarization exercises. (That peer would have to complete the safety training before performing the next laboratory.) Each student shall submit two items: Outline (5 marks): The first item is a bullet-pointed list that acts as an outline for the final document. The purpose of this list is to guide the flow of ideas within the document. It is expected that the list will be modified several times before it reaches its final form. There is no need for the final list to be polished; evidence of the modifications can remain. One-page summary (5 marks): The second item is the final one-page summary. This should be written in regular prose. Ideas should flow logically from sentence to sentence, and from paragraph to paragraph. You should keep your target audience in mind as you write the summary. Each student must submit their own bullet-pointed list and one-page summary by the end of the laboratory time. 5