Can't understand this PID code

Question

I am having trouble understanding some PID code on an FPGA that is posted on github, by David Paquette.

I will paste it in at the bottom of the post.

It looks very compact and neat, and I understand the concept behind it, but I don't understand why the Kp, Ki and Kd constants are negative numbers. Kp as -300 and Ki as -2 for example.

Suppose I have two questions regarding this:

1. Why the negative numbers? I am thinking it gives a broader spectrum to work with error values, as the output is capped at zero if the output calculates as a negative.

2. I am assuming the hardware requires integers of 100, i.e. whatever sensor or motor pwm frequency, but what would the reasoning be behind the 1000 and 10000 integer sizes for the variables?

----------------------------------------------------------------------------------
-- Company: 
-- Engineer: David Paquette
-- 
-- Create Date:    16:49:31 11/19/2015 
-- Design Name: 
-- Module Name:    PIDController - Behavioral 
-- Project Name: 
-- Target Devices: 
-- Tool versions: 
-- Description: 
--
-- Dependencies: 
--
-- Revision: 
-- Revision 0.01 - File Created
-- Additional Comments: 
--
----------------------------------------------------------------------------------
library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.numeric_std.all; 

-- Uncomment the following library declaration if using
-- arithmetic functions with Signed or Unsigned values
--use IEEE.NUMERIC_STD.ALL;

-- Uncomment the following library declaration if instantiating
-- any Xilinx primitives in this code.
--library UNISIM;
--use UNISIM.VComponents.all;

entity PIDController is
    Port (  samplingRateClock : in std_logic;
                reset : in std_logic;
                setpoint: in integer range 0 to 100;
                sensorFeedbackValue : in integer range 0 to 100;
                controlOutput : out integer range 0 to 100
        );
end PIDController;

architecture Behavioral of PIDController is
    signal controllerOutput : integer range 0 to 100:=0;
    constant kp : integer range -1000 to 0:=-300;
    constant ki : integer range -1000 to 0:=-2;
    constant kd : integer range -1000 to 0:=0;
begin
    process(samplingRateClock, reset)
        variable error :  integer range -1000 to 1000:=0;
        variable previousError : integer range -1000 to 1000:=0;
        variable errorSum:  integer range -100000 to 100000:=0;
        variable errorChange:  integer range -1000 to 1000:=0;
        variable output:  integer range -1000 to 1000:=0;
    begin
        if(reset='0') then
            error:=0;
            previousError:=0;
            errorSum:=0;
            errorChange:=0;
            output:=0;
            controllerOutput<= 0;
        elsif(samplingRateClock'event and samplingRateClock='1') then
            error := (setpoint - sensorFeedbackValue);
            errorSum    := errorSum + error;
            if(errorSum > 10000) then
                errorSum := 10000;
            elsif(errorSum < -10000) then
                errorSum := -10000;
            end if;
            errorChange := error - previousError;
            output := (kp*error + ki*errorSum + kd*errorChange)/100;
            previousError := error;
            if(output>100) then
                output := 100;
            elsif(output<0)then
                output:=0;
            end if;
            controllerOutput<= output;
        end if;
    end process;
    
    controlOutput<=controllerOutput;
    
end Behavioral;

```

Answer 1

I’m the author of the module and just came across this post.

All the comments made are pretty much correct. But if you want a full description of this PID module check out the document I wrote outlining its behavior: https://github.com/paquettedavid/FPGATemperaturePIDController/blob/master/Documentation/FinalProjectReportDavidPaquette.pdf

The PID module is described in section 8 (8.3 for the HDL overview). Hope this gives some clarity!