The PID Controller (Algorithm)
RESULTS AND DISCUSSION:
As we have mentioned earlier, that different types of controllers are used to control the position of an antenna. One among them as previously mentioned is PID controller.
The PID controller (algorithm) is the most popular feedback controller used within the process industries. It has been successfully used for over 50 years. It is robust easily understood algorithm that can provide excellent control performance despite the varied dynamic characteristics of process plant. In designing the PID controller, tuning of the controller is the main point of focus, so that the desired transient and steady-state responses could be obtained. The process of selecting the controller parameters to meet given performance specifications is known as controller tuning.
TUNING OF PID:
Ziegler & Nichols suggested rules for tuning PID controllers, i.e: to set values of Kp, Ti and Td based on experimental step responses. In fact, Ziegler &Nichols tuning rules give an educated guess for the parameter values and provide a starting point for the tuning rather than giving the final settings for Kp, Ti and Td in a single shot.
ZIEGLER-NICHOLS RULES FOR TUNING PID:
Ziegler and Nichols proposed rules for determining the value of proportional gain Kp, integral time Ti and derivative time Td based on the transient response characteristics of a given plant. Such determination of the parameters of PID controllers or tuning of the PID controllers can be made by the engineers on-site by experiments on the plant. Many other methods have also been proposed to do so.
There are two methods called Ziegler-Nichols tuning rules: the first method and the second method.
In the first method, we obtain experimentally the response of the plant to a unit step input as shown in the figure below. If the plant involves neither integrator(s) nor dominant complex conjugate poles, then such a step response curve may look S-shaped curve as shown below. This method applies if the response to a step input exhibits an S-shaped curve. Such step response curves may be generated experimentally or from a dynamic simulation of a plant.
The S-shaped curve may be characterized by two constants, delay time L and time constant T.The delay time and the time constant are determined by drawing a tangent line at the inflection point of the S-shaped curve and determining the intersections of the tangent line with the time axis and line c(t)=K.
In the second method, we first set Ti=8 Td=0.Using the proportional control action only, increase Kp from 0 to the critical value Kcr at which the output exhibits sustained oscillations.
The figure is given on next page; figure 2.1 shows closed-loop system with a proportional controller and figure 2.2 is showing the sustained oscillations.
If the output does not exhibit sustained oscillations for whatever value Kp may take, then this method does not apply. Thus the critical gain Kcr and the corresponding period Pcr are experimentally determined. Ziegler and Nichols suggested that we set the values of the parameters Kp, Ti and Td according to the table shown below:
As we know that in designing 3 major objectives are very important to be taken care of:
- Transient response
- Steady-state error
- Achieving stability
The above curve response of PID shows satisfactory results, the transient response has an overshoot and then goes down and remains constant.
Next, we train the network by using neural network's training algorithm TRAINLM. The inputs taken are the proportional, integral and derivative of the error signal. The hidden layer of the MLP architecture has 8 neurons and there is one neuron at its output. The diagram on the next page is the simulation of the system.