Two-Tank Level Control Experiment The purpose of this experiment is to determine the transfer function of each element in the control loop, to linearize the nonlinear ones, to determine the controller settings, and to compare t he results of the closed-loop system with theory and simulation. The two-tank system is designed so that most o f the parts of the control loop are either very close to linear or else have negligible dynamics, i.e., are very fast-acting. Each of the tanks may be considered linear in that the liquid height versus flow rate out has been made linear by use of special, sutro weirs. As you will see in the Controls class, the height in a tank c an usually be represented by a first-order differential equation, in this case linear, and therefore, it is an example of a first-order system. To st characterize the dynamics of a 1 -order process requires knowing the steady-state gain and the time constant. During the lab session, you are to obtain data in several ways to determine determine these parameters. Gains will be found by recording the input-output relationship for each element in the loop throughout the range of operation. Even in the case of a non-linear element (the valve), the input-output curve may be used to find the gain around the operating conditions. The time constants can be conveniently determined by recording the response of the tanks to step forcings. The time constants may also be found by the product of the resistance re sistance and capacitance of the tanks (τ = RC). Besides the actual parameters of individual elements, the entire process may be modeled using the popular “processreaction curve” method by determining the τ, ∆τ, and K parameters. The equipment associated with the experiment is as follows: a.
Two rectangular tanks fitted with electrical pressure transducers with serve as level transmitters. The flow out of the tanks tanks passes over specially specially designed weirs, called sutro sutro weirs, which give a relatively linear flow-to-height relationship.
b. An air-to-close control valve with a valve-stem positioner. c.
A rotameter to measure the controlled flow and one to measure the load.
d. A two-channel, panel-mounted recorder. e.
An electronic PID controller.
f.
A current-to-pneumatic transducer.
g.
Miscellaneous air regulators, valves, and gauges to aid in c ontrolling and monitoring the tanks. Also, there is an e lectrical patch panel for connecting transducers, recorders, and the controller. Note: the electrical control signals are standard standard 4 to 20 ma currents.
Prior to the Lab Session: 1. Read through all instructions before proceeding since much of the data can be obtained at the same time with proper planning.
st
During the 1 Lab Session: 1. Draw a block diagram which includes every e lement in the system. 2. Characterize the valve by plotting water flow out of the valve versus controlling pressure with the valve in both the auto and bypass conditions. 3. Measure the flow out of both tanks to determine the linearity of both weirs. 4. Obtain data to determine the time constants and gains of the two tanks by: a. measuring resistances and capacitances (a static method) b. measuring step responses under several conditions (a dynamic method) c. measuring the response to a delta function (a dynamic method) 5.
Gather the data necessary to determine the transfer function (i.e., gains) of each of the other elements in the control loop. This may be done at the same time as the resistances are being determined. For any non-linear elements, obtain enough data to allow for linearization.
6.
Obtain the responses to several step changes with the entire open-loop (sans controller). This can be done at the same time the step response to the first tank is being recorded.
Calculations: 1. Calculate the time constants by the two methods and compare results for all the data sets. 2. Plot data to determine the gains of all the elements in the system. Those that seem to be linear may be fitted by a straight line; non-linear elements should be plotted in enough detail to allow for graphical linearization. nd
3. Assuming pure 2 -order dynamics, you should be able to e stimate an appropriate value for nd proportional gain simply by knowing what kind of response (e.g., 2 order with a ¼ decay ratio) you want and what value of damping factor will produce it. 4. Using the Cohen-Coon technique, determine the controller settings for P, PI, and PID control. 5. Calculate the response of the controlled system to a particular step change in load for proportional control. 6. Calculate the response of the controlled system to a particular step change in the set point for PID control using the controller sett ings determined by the Cohen-Coon method. During the 2nd Lab Session: 1. Run experiments to compare with parts 5 and 6 of the calculations. Changes both up and down in both load and set point should be imposed on the control system for comparison with theory and simulation.
Procedure:
Characterizing the valve: 1. with the valve in auto position, record pressure vs. water flow rate from fully closed to fully open 2. with the valve in bypass position, record pressure vs. wate r flow rate from fully closed to fully open Characterizing the weirs: Record the flow rate which correlates to height on the weir by recording flow rate, tank 1 weir height, tank 2 weir height, tank 1 pin position, tank 2 pin position, and pressure. To calculate gain, you need to plot: a. height vs. position for both tanks b. pressure vs. flow c. flow vs. height Performing the step-responses: 1. perform five steps up and five steps down 2. record valve pressure, step flow, base flow, tank 1 weir height, tank 2 weir height, tank 1 pin position, tank 2 pin position, and the time required to return to steady-state Performing the delta function: 1. perform five delta functions by dumping a measured amount of water into tank 1 (when the system is at steady-state) 2. record valve pressure, step flow, base flow, tank 1 weir height, tank 2 weir height, tank 1 pin position, tank 2 pin position, and the time required to return to steady-state
