CHAPTER #2
OVERVIEW:
A position control system converts a position input command to a position output response. Position control system finds widespread applications in antennas, robot arms, and computer disk drives. The radio telescope antenna is also an example of a system that uses position control systems. Positioning of an antenna has also a great importance in satellite communication, where it is very important that an antenna should continuously and automatically track position an antenna, for that correct reception becomes possible. An antenna position control system is shown below with a detailed layout.
The purpose of this system is to have the angle output of an antenna,?0(t),follow the input of the potentiometer ,?i(t).The input command is an angular displacement. The potentiometer converts the angular displacement into a voltage.Similarly; the output angular displacement is converted into a voltage by the potentiometer in the feedback path. The signal and power amplifiers boost the difference between the input and output voltages. This amplified actuating signal drives the plant. This system normally operates to drives the error zero. When the input and output match, the error will be zero, and the motor will not turn.Thus, the motor is driven when the output and the input do not match. The greater the difference between the input and the output, the larger the motor input voltage and the faster the motor will turn. The functional block diagram of antenna position control system is given below:
EXISTING CONTROLLERS:
In the closed-loop systems the input transducer converts the form of the input to the form used by the controller. An output transducer or sensor measures the output response and converts it into the form used by the controller. The input to the controller is error or actuating signal which is the difference of the input and output signals. The controller being the important part of any open-loop or closed-loop system drives the process or the plant. Hence the changes in the parameters of the controller can produce changes in the output of the plant.
Many controllers have been used to automate and control the position of an antenna, most familiar among them are:
And many more...
PID CONTROLLER:
The PID controller algorithm involves three separate parameters; the proportional, integral and derivative values. The proportional value determines the reaction to the current error, the integral value determines the reaction based on the sum of recent errors, and the derivative value determines the reaction based on the rate at which the error has been changing. Following figure show how PID controller works:
The transfer function of PID controller is given as:
G(s)=kp(1+1/Tis+Tds)
Where Kp is proportional gain, Ti is integral time constant and Td is the derivative time constant. The proportional control will have the effect of reducing the rise time but it does not eliminate the steady state error. An integral control will have the effect of eliminating the steady state error, but makes the transient response worse. The derivative term has the effect of increasing the stability of the system, reducing overshoot and improving transient response.
LIMITATIONS:
Although PID controller is most widely used controller but it has some limitations, due to which they can perform poor in some applications.
PID controllers, when used alone, can give poor performance when the PID loop gains must be reduced so that the control system does not overshoot, oscillate or hunt about the control set point value. The control system performance can be improved by combining the feedback (or closed-loop) control of a PID controller with feed-forward (or open-loop) control. Knowledge about the system (such as the desired acceleration and inertia) can be fed forward and combined with the PID output to improve the overall system performance. The feed-forward value alone can often provide the major portion of the controller output. The PID controller can be used primarily to respond to whatever difference or error remains between the set point (SP) and the actual value of the process variable (PV). Since the feed-forward output is not affected by the process feedback, it can never cause the control system to oscillate, thus improving the system response and stability. Another problem faced with the PID controller is that they are linear, thus there performance in the non-linear systems is variable. PIDs are enhanced through methods such as gain scheduling or fuzzy logic. Gain scheduling, in control theory is an approach to control the non-linear system that us family of linear controllers, each of which provides satisfactory control fro different operating point of the system. Issues can also rise from instrumentations connected to the controller. A high enough sampling rate, measurement precision and measurement accuracy is required to achieve adequate control performance. The problem with its derivative term is that small amounts of measurement or process noise can cause large amounts of change in the output.
STATE OBSERVER
Controller design relies upon access to the state variables for feedback through adjustable gains. However in some applications some of the state variable may not be available at all or it is too costly to measure them or send them to the controller.
If the state variables are not available because of system configuration or cost, then the other way is to estimate the states. Then these estimated states rather than the actual stares are fed to the controller. An observer or also called estimator is used to calculate state variable that are not accessible from the plant. The mathematical model of an observer is same as that of the plant. The design of the observer is separate from design of the controller. The design of observer consists of evaluating the constant vector L. in design methodology we first find the state equations for the error between the actual state vector and the estimated state vector. And then find the characteristic equation of the error system and evaluate the required L to meet a rapid transient response for the observer.
LIMITATIONS OF STATE OBSERVER CONTROLLER:
Like every other controller the linear state observer controller also has some limitations, some of them are given below:
