I have a 4th order system. The system has 2 pairs of imaginary poles and I want to design a controller in order to track a desire trajectory without any error. Give me some advice on how to do it.
You need to use integrator backstepping design method, and it works if the system is minimum phase. Most of the reference papers on the subject deals with nonlinear systems. You maybe able to figure out the design method from our paper, which deals with nonlinear systems with unknown parameters. You may read the design for known parameter case to see if you can figure it out.
Article Adaptive Controller Design for Tracking and Disturbance Atte...
Using a continuous-time or discrete-time controller?
Either way, you could use a state-space controller with: internal state feedback, an observer to estimate the states and output feedback to remove the steady-state error. This allows you to arbitrarily place the poles to get the desired damping in the closed-loop response.
See
"Linear State-Space Control Systems" by Robert L. Williams II and Douglas A. Lawrence for the continuous case or
"Discrete-Time Control Systems" by Katsuhiko Ogata for the discrete case.
For this approach to be satisfactory, you will need to have a pretty good plant model (but that sounds like it might be the case), otherwise you will just waste a lot of time getting it to work, then end up just wishing you simply used a PID controller (with plenty of D for the marginally stable poles)
thanks for your help Mr Kennedy.but let me explain more about my system.the control architecture is in feedforward structure and i have chosen the feedforward path as the inverse of my system in order to have zero steady state error.now i want to design the controller to keep the poles of the cloosed loop system on the right side of imajinary coordinate(my current system(open loop) is stable )and also i want the system to track a desire trajectory how should i design the controller??? i dont know how to determine the place of desire poles in order to use root locus technique for designing the controller .can you suggest other techniques for designing?.if i have to use state space model and using modern control theory how should i determine the place of desire poles with respect to desire trajectory ????!!!!!!!!!!!!!!
Dear Sara,
You can try to use Ackermann’s formula for pole assignment.
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