Dynamic and control subjest Assignment Example | Topics and Well Written Essays - 2500 words

Dynamic and control subjest - Assignment Example 'Controller' controls the system behaviour by providing the necessary excitation. 'Setpoint' is the desired result. 'Output' is the actual result. PID controller may be written in the equation form as: = + + (1) In this equation, all the symbols have the meanings explained earlier. Coming to the explanation in common words, with reference to Figure 1, we want the output Y of a process to be equal to or as close to the setpoint R as possible. Since the real systems are not ideal systems, usually some kind of control system is required to achieve this objective. In a PID controller, the output Y is compared with the setpoint R, the error e is calculated to be equal to R minus Y. Then the controller (a PID controller in this case) calculates u(t) from equation (1). This u(t) is an excitation signal to be passed to the 'process', with the objective of driving the 'output' Y as close to the 'setpoint' R as possible. For example, let us assume that we are required to control the temperatur e of the water coming out from a tap. Let us assume that we want the temperature of the water to be around 50 degree centigrade always. But let us assume that water is supplied to this tap by two separate water feeds. Let us assume that one of the water feed is always at around 30?C (cold water feed). Also, let us assume that the other water feed is always at around 70?C (hot water feed). We can see that to get the water from the tap at 50?C, we need to mix around 50% water from the hot water feed with the remaining 50% water from the cold water feed. This can be achieved by making the valve corresponding to the hot water feed 50% open (i.e., 50% closed) and at the same time, making the valve corresponding to the cold water feed 50% open (i.e., 50% closed). But, in a real system like this, one comes across several uncertainties like the temperature losses during the flow in the pipes due to radiation etc., which cannot be determined for certain since in this case, the radiation depe nds on the atmospheric temperature (or room temperature) also. Hence, when the valve corresponding to the hot water feed is 50% open and at the same time when the valve corresponding to the cold water feed is 50% open, the temperature of the water coming out from the tap may not be exactly equal to 50%. Let us assume that this temperature is 45?C. Now, in this problem, the setpoint R is 50?C while the output Y is 45?C. Now, according to Figure 1, R-Y= 5 ?C is calculated. This is the error e which is an input to the controller. Then the controller calculates 'u(t)' from Equation (1), this u(t) is in fact a signal which controls the valves. In this case, u(t) would instruct the valve corresponding to the hot water feed to open more than 50% (exact percentage would be known from u(t)). Opening the valve corresponding to the hot water feed x% would automatically mean opening the valve corresponding to the cold water feed (100-x)%. This ensures that the flow from the hot water feed is mo re than the flow from the cold water feed, which in turn forces the temperature of the water coming from the tap to go to 50?C. This way, the controller strives to make the temperature of the water coming out from the tap to be 50?C, and for a proper selection of the values for Kp, Ki and Kd, the controller usually performs its task satisfactorily. If the temperature of the tap water goes to 55?C for example, the error would