PID gains from transfer function


Thread Starter

Marco Doria


I am in the middle of my thesis project and I am trying to control all six degrees of freedom of a UAV. I have the 6 transfer functions but I am having trouble determining correct PID values for simulation in SIMULINK. A transfer function for x translation is 0.092/(s^2 +0.0275s) and they are all of this small magnitude. If anyone can guide me in the correct direction as I have tried the ZN method, root locus etc and nothing seems to work for me. I need an overshoot of max 20%.
Is there a way to determine PID gains from the root locus plots or is there a better way?

Thankyou so much

I would make two comments/suggestions:

1. The transfer function you provide (I suppose it is the plant transfer function) has an integrator. It complicates the use of the integral component of the PID controller because it would result in a double integration, which in turn would make the system unstable or dramatically reduce the stability margins. Therefore, only P-component of the controller can be used (the use of D-component is very questionable). This observation simplifies your task of the controller design but does not help to obtain a really good controller (if the design is carried out within the PID framework).

2. Your system is a servo system. Therefore, the approach to the controller (compensator) design should be different from that for the process control. Most probably the controller should be implemented as a lag-lead (or sometimes lead-lag) filter.

Igor Boiko
Might try Manfred Morari’s Internal Model Control prescription for PID controller design:

PID = C(1 + I/s + Ds)

Plant: K/(s(Ts+1))
C = (2e + T)/(K*e*e)
I = 1/(2e+T)
D = 2eT / (2e+T )

Chose e to give desired response…


I'm not sure you are asking the right question. The six transfer functions you speak of are not clearly defined. Normally, aerodynamic vehicle controls do something like: 1) Control pitch through the elevator. 2) Control roll through the ailerons. 3) Control speed through the throttle.

A 6-DOF simulation is probably not the right choice of instruments to do your first cut controller design with. Take a look at some books about airplane autopilot design and airframe dynamics and the problem may get easier than you now think. Good Luck.