modelCascadeLevelControl

Cascade level control with PI controllers

Extends from Modelica.Icons.Example (Icon for runnable examples).

Information

Description

Level control with two PI controllers, connected with a cascade arrangement.
The considered system is a tank filled with water. The water level is the process variable to be controlled.
The system (see the figure below) is composed by a tank and one pipe connected to a linear valve that discharges the water in the atmosphere. The valve actuator is represented by a first order filter.
The control system is composed by the measurement part and the controller. The pressure sensor measures the absolute pressure
on the bottom of the tank.

The measured pressure is subtracted from the atmospheric pressure and then divided by the
gravity acceleration and the water density in order to obtain the water level.

  level = (p - p0)/(rho*g)

The PI controller, given the level measurement and the set point reference compute the control action. Such a control
action is the water mass flow rate flowing through the pipe. Such a mass flow rate becomes the set point reference for the second
PI that with its control action regulates the valve aperture

CS = 0 valve closed,
CS = 1 valve fully open

The tank is 2 m height, and the water level at t=0 is L = 1 m.
In the first phase the controller is asked to maintain the level at the initial value (SP = 1 m), at t = 1200 s the level set point
decrease as a step (SP = 0.5 m). The controller has to act on the valve in order to decrease the water level to the desired value.
A disturb represented by a water mass flow rate entering the tank, becomes different from zero at time t = 3600 s.

Set Point reference, water level

Set Point reference (the Control signal of the Level PI) and valve command

The simulation can be perfomed at an initial stage assuming that the controller is a continuous time one (Ts = 0) , that the math
operations are in double precision (FixedPoint = false). In such a phase it is possible to concentrate on the controller design.

Further stages

Once the controller has been designed and the parameters assigned, one should introduce more details in order to simulate a more realistic system. Please refers to the previous example ( LevelControl ) for more information.

Parameters

Type	Name	Default	Description
Process
Length	PipeL	1	Pipe length
Length	PipeD	0.0254	Pipe diameter
Length	Lstart	1	Initial water level
Length	H	2	Storage height
Area	A	1.5	Cross section storage area
Real	Tact	2	Actuator dynamics
Controller level
Real	Ts_l	0	Sampling time for the valve controller
Real	Kp_l	-200	Proportional gain
Real	Ti_l	100	Integral time
Boolean	AntiWindup_l	true	Flag that enables the antiwindup feature
Real	CSmin_l	-2	minimum value of the CS
Real	CSmax_l	2	maximum value of the CS
Real	CS_start_l	0	output initial value
Controller valve
Real	Ts_v	0	Sampling time for the valve controller
Real	Kp_v	50	Proportional gain
Real	Ti_v	2	Integral time
Real	CSmin_v	0	minimum value of the CS
Real	CSmax_v	1	maximum value of the CS
Real	CS_start_v	0	output initial value
Controller
Boolean	AntiWindup_v	true	Flag that enables the antiwindup feature
Conversion
Boolean	FixedPoint	false	Use FP operations for level measurement operations
Integer	Nbit	24	number of bit for FP operations
Real	scaleF_div	500	division scale factor
Real	scaleF_sub	20	subtraction scale factor

Components

Type	Name	Description
Controllers.PID	PI_Level	PI level controller
Modelica.Blocks.Sources.Step	disturb	inlet water disturb
Modelica.Blocks.Sources.Step	levelSetPoint	Set Point level
Modelica.Fluid.Vessels.OpenTank	tank	water tank
Modelica.Fluid.Valves.ValveLinear	valveLinear	outlet valve
Modelica.Fluid.Pipes.StaticPipe	pipe	outlet pipe
Modelica.Fluid.Sources.FixedBoundary	boundary	boundary pressure condition
Modelica.Fluid.Sources.MassFlowSource_T	Inlet	disturb water inlet
Modelica.Fluid.System	system
Modelica.Blocks.Continuous.FirstOrder	actuator	actuator dynamics
Modelica.Fluid.Sensors.Pressure	pSensor	pressure sensor
MathOperations.RealType.Div	div	water level
Modelica.Blocks.Sources.RealExpression	rho_times_g	density times the gravity acceleration
MathOperations.RealType.Sub	sub	hydrostatic pressure
Modelica.Blocks.Sources.RealExpression	p_amb	ambient pressure
Controllers.PID	PI_Valve
Modelica.Fluid.Sensors.MassFlowRate	flowRateSensor

Revisions

Industrial Control Systems (v 1.0.0) : April-May 2012