Implementing PID on a microcontroller

BJ FurmanME 190 Mechatronics Engineering Design

11NOV2015

(adapted from: http://brettbeauregard.com/blog/2011/04/improving-the-beginners-pid-introduction/)

PID equation

Standard form

Parallel form

𝐾 𝑝=𝐾 𝐾 𝑖=𝐾𝑇 𝑖

𝐾 𝑑=𝐾𝑇 𝑑let

𝑂𝑢𝑡𝑝𝑢𝑡=𝐾 ¿

Figure from Matlab Help (Designing PID Controllers with the PID Tuner)

u=

u=

= r(t) – y(t)

Important considerations

o Sample Timeo Derivative Kicko On-The-Fly Tuning Changeso Reset Windup Mitigationo On/Off (Auto/Manual)o Initialization (bump-less transfer)o Controller Direction

(Way too) simple algorithm

Sample Time

o Need to call at a regular intervalo Use millis() or an interrupt

(cont.)

Sample Time, cont.

Derivative Kick

The problem

𝑂𝑢𝑡𝑝𝑢𝑡=𝐾 ¿

dttdy

dttde

dttdy

dttde

dttdy

dttdr

dttde

)()(

)(0

)(

constant is r(t) if

)()()(

Derivative Spikes

Derivative Kick, cont.

Derivative Kick, cont.

On-the-fly tuning changes

When things go ‘bump’…

On-the-fly tuning changes, cont.

Calculate the contribution for the integral term differently:

• Before

• After

On-the-fly tuning changes, cont.

Integrator windup

The problem

Integrator windup, cont.

Integrator windup, cont.(same as before)

Integrator windup, cont.

The result

On/Off (automatic or ‘manual’)

The problem

On/Off, cont.

On/Off, cont.(same as before)

Initialization

The problem

Initialization, cont.(same as before)

Initialization, cont.‘Bumpless’ transfer

Direction

The problem: should an increase in y (the output) lead to an increase or a decrease in the manipulating variable (u, the output of the controller)?

Direct acting (Kp, Ki, Kd should be positive) Reverse acting (Kp, Ki, Kd should be negative)

Direction, cont.

Direction, cont.(same as before)