27. Continuous Control

• A controlled system includes,

a basic system that does not achieve objectives by normal means: for our purposes a mathematical model a such a system is very important.

some objective for the operation of the system.

a controller that is matched to system, and tuned to meet the control objective.

• Objectives for control systems might include,

fast response

stability

energy efficiency

etc.

• The systems below are often directed by control systems.

 

• Some Notes:

Neither of these systems have controls.

They both have inputs, and outputs.

The output is not always something exiting the system. eg. the water tank height is the system state.

We can treat these systems with ‘black boxes’ with lumped parameters.

• All of the inputs and outputs are expressed as physical quantities (as will be seen later).

27.1 Controlling Continuous Systems

• We can use some type of feedback from the system to change the system input (this is called the control variable).

 

27.2 Controlling Discrete Systems

• In some cases we will be able to monitor continuous process variables, but only be able to change discrete actuators. This is common in heating systems, the system is either on/off, but temperature is monitored continuously.

• A common method is to use two setpoints with upper and lower bounds.

• Consider the example of a heating system in a room.

 

27.3 Control Systems

• Control systems use some output state of a system and a desired state to make control decisions.

• In general we use negative feedback systems because,

they typically become more stable

they become less sensitive to variation in component values

it makes systems more immune to noise

• Consider the system below, and how it is enhanced by the addition of a control system.

 

 

• Some of the things we do naturally (like the rules above) can be done with mathematics

• The basic equation for a PID controller is shown below. This function will try to compensate for error in a controlled system (the difference between desired and actual output values).

 

• The figure below shows a basic PID controller in block diagram form.

 

 

 

• The PID controller is the most common controller on the market.

27.3.1.1 - PID Control With a PLC

• The PID calculation is effectively a calculation in the PLC. One basic method of PID control is i) read voltage, ii) do PID calculation, iii) set output voltage. (Note: it is also common to get a self contained PID card for the PLC that deals with all inputs and outputs). The ladder logic below shows a PID control function.

 

27.4 Design Cases

• Design a controller that will heat an oven to 1200F +/- 30F for 3 hours after a start button is hit. The temperature is available as an analog voltage that is 1V at 500F and 3V at 1500F. Normal items such as E-stops should be added.

27.5 Problems

Problem 27.1 Can PID control solve problems of inaccuracy in a machine?