08-16-2017, 09:47 PM
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INTRODUCTION
This assignment is basically designed to demonstrate the use of controllers in DC motor which consists of two stage ,electronic stage that is controlled by 8 bit microcontroller and second is the mechanical stage consisting of gear box which controls the motion of DC motor to provide a impulse to electronic stage which generates a resultant signal to control the parameters of controller.
FEEDBACK-CONTROL THEORY
Figure 1 shows the block diagram of a closed-loop system. In this configuration a portion of the information is fed back from the process and subtracted from the reference signal in order to calculate the error signal. This error signal is used by the PI to adjust the control input such that the process output can reach the given reference.
In this diagram, the process block refers to the physical system to be controlled. The controller block is an electronic device (a microcontroller) that calculates the necessary energy to modify the process such that the control objective can be reached. Usually, in a control scheme the controller precedes an actuator (for instance, a motor, turbine, valve, resistance, and so forth) so that the process can be manipulated. Finally, to close the loop, a measurement block is needed, which is often a sensor or transducer that provides a signal to automatically compare the actual state of the system variables with the desired objective.
Some of the motivation for using this configuration was to diminish the effects of parameter variations coming into the system, reduce the effects of disturbance inputs, improve the time transient responses of the process output, and to compensate for the steady-state error.9 Another advantage of this approach is that the effects of the "dead zone" in the motors can be reduced.
THE CONTROL PROBLEM
Our goal is to control the angular velocity of a DC gear motor by using a classical discrete-time PI-like controller. Figure 2 provides a block diagram of the sample data system. In the figure, r(kT) denotes the reference signal, u(t) is the control voltage applied to the motor, x(t) stands for the system output, y(kT) represents the discrete signal generated by the sensor (angular displacement), V(kT) is the output signal of the Velocity Sensor (VS), e(kT) is the error defined by the difference r(kT) V(kT), d(t) and n(t) are, respectively, the disturbance input to the plant and the noise in the sensor. Here (kT) is used to represent a discrete signal with a sample-time given by T.
The control algorithm works like this. First, a reference signal is given to the MICRO-CONTROLLER via a serial port. At this point the MICRO-CONTROLLER enables the VS to count the pulses per revolution provided by the motor's optical encoder. A few milliseconds later, the MICRO-CONTROLLER computes the V(kT), which is directly proportional to the motor's velocity. Using this signal, the MICRO-CONTROLLER then calculates the error signal e(kT) and the voltage u(kT) by means of the PI-like controller, which is the control input in discrete-time. Such a signal is then converted into analog form, u(t), by means of the DAC. The control input u(t) is current-amplified by the power stage and applied to the motor. This loop is repeated as many times as necessary until that the error signal e(kT) is near to zero. As the control objective is reached, the loop is terminated and the MICRO-CONTROLLER waits for a new reference.
Mechanical stage (gear box)
This block is composed of two mechanical stages, a planetary gear box assembled with the motor, and another external gear box formed by a pair of worm gears with reduction ratios of 159:1 and 625:1. The main function of these stages is to reduce the angular velocity of the motor and to translate the angular motion to linear motion as shown in Figure 2.
Creating the Motor-Control Model
To apply well-establish classical control theory, it's necessary to designate in advance the mathematical model of the system to be controlled with the purpose of simulating its dynamic behavior in open-loop as well as closed-loop modes. Otherwise, the designer may not have enough experience to tune the parameters of the PI controller, and its closed-loop performance could be poor or, in the worst case, unstable. Depending on the mechanical system, this may cause injuries to the system or to the user. For this reason, we recommend simulating the system's behavior before planning its physical implementation.
In general terms, a model is a set of differential equations that represents an approximation of the physical system's dynamics. One classic method to identify the model of simple systems is to excite it with a known input and measure the response. The inputs applied and the outputs measured depend on the nature of the system and the variables that the designer needs to control in the process. In applying these control techniques, we characterized our motor by applying voltages of 2.5V, 5V, 7.5V, and 9.47V over similar intervals of time to measure the motor's response to such inputs.