Advanced Embedded Systems Design. Lecture 14 Implementation of a PID controller BAE 5030 - 003 Fall 2004 Instructor: Marvin Stone Biosystems and Agricultural Engineering Oklahoma State University. Goals for Class Today. Questions over reading / homework ( CAN Implementation )
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Lecture 14 Implementation of a PID controller
BAE 5030 - 003
Instructor: Marvin Stone
Biosystems and Agricultural Engineering
Oklahoma State University
Output (qout) is readily calculated as a function of:
Load (qin) and
Manipulation is a simple function of the controller TF and error.
One of the conventional models used to express a PID controller is:
A convenient way to implement this equation in a controller is as the derivative of manipulation known as the velocity form of the equation as shown below:
In a practical system this equation will work well and does not require any steady-state references, but eliminating the ti and td term completely results in:
This equation has no positional reference and error accumulation is a problem. Use velocity form only for PI or PID modes.
To begin the conversion of the PID equation to a difference equation, the equation is multiplied by dt.
Note that since M is a differential and ess is zero, this equation conveniently applies to the absolute variables as well as the deviation variables.
For small Dt, the equation can be approximated as:
The equation can be simplified with the assumption that Dt is constant:
Each of the differences (D) can be expressed as discrete values of each of the variables (m and e ) at the times 0, 1, and 2 as shown below:
Replacement of the differences (D) with the discrete
variables ( m ande ) results in:
Note that Dt is assumed to be a constant. If Dt varies, the equations should be derived with that in mind.
This equation can be solved for the current manipulation, m2, in terms of values known at time t2: m1,e2, e1, and e0.
The other parameters in the equation are constants.
Where C1,C2, and C3 are constants and the current manipulation is expressed in terms of known values, the current and past errors.
This equation may be translated directly into a computer language, for example:
m2 = m1 + k*(C1*e2 – C2*e1 + C3*e0);
Within a computer program, the current error
is calculated from the current measurement of
the controlled variable and the setpoint, for example:
e2 = T_setpoint – T_measured;
The current manipulation m2 is then computed using the previous controller equation, and finally, at the end of the time step, each of the variables is shifted forward for the next calculation.
For example in C, the code might look like:
measure_and_manipulate() //Call once per delta T
T_measured = measure_T(); //Get the measured temperature
e2 = T_setpoint – T_measured //Calculate the current error
m2 = m1 + k*(C1*e2 – C2*e1 + C3*e0); //Calculate the manipulation
set_manupilation(m2); //Output the manipulation
e0 = e1; //Shift the error and manipulation
e1 = e2; //forward one time step
Note that the time step Dt is controlled by the time required to execute the loop. C1,C2 and C3 are all functions of Dt. The equation will probably be executed as floats! (Or very special care must be taken with scaling.