Linear Optimal Control Systems by H. Kwakernaak and R. Sivan

In order to preserve the Control Systems literature, the Control Systems Society will make available without cost out of print books that had significant impact on the field.

Now isn't that just great !!! So why wait head over to this page and enjoy the book :D

transient response of non-linear systems

transient response of Finite Dimensional Linear Time Invariant (FDLTI) systems is determined by locations of the system poles, however for nonlinear systems there IS no concept of "poles of the system". in that case what really governs the transient response. what computable property/properties of a nonlinear system will be equivalent to "poles of a FDLTI system" ?

pid

i should feel ashamed in writing about this but i guess one has to confess his or her sins at one time or another.

the transfer function of a pid controller is NOT strictly proper

U(s) kd*s^2 + kp*s + ki
----- = -------------------- (1)
E(s) s

doesn't it create any problems ? all undergraduate control texts say that transfer functions are(should be?) strictly proper. there is something amiss here.

my guess is that since its physically impossible to construct a pure differentiator
( kd*s term ) its therefore impossible to physically construct a PID controller

degree of non-linearity

with reference to non-linear systems: is it fair rather meaningful to ask about the ``degree of non-linearity" of a system. all linear systems are linear, nothing big about it; however since the domain of nonlinear systems is vast, can the phrase/clause ``degree of non-linearity" be given some meaning?

step response

The system G(s) = (s+1)/( s*(s+3)*(s*s+4*s+8)) with poles at
0
-3.0000
-2.0000 + 2.0000i
-2.0000 - 2.0000i
and a zero at -1 has all stable poles, i.e. in the left hand of the s-plane . However the step response of the system is unstable !!!!

This is most probably due to the pole at the origin. The system then behaves as a double integrator. The impulse response of the plant does not decay to zero ! The plant is decidedly unstable.

This is food for thought , since before this I thought that the stability of the system could be determined my the location of poles alone. It now seems that its also important that whether the poles in question are open loop or closed loop !

pole zero cancellation

say a controllable system uses state feedback to cancel a zero in the lhs of s-plane. the system becomes unobservable. but does this cause ne probs. i think not. since at the start the system was controllable and observable(my assumption) what harm does it cause if now the system becomes unobservable. u need an observer only if u can't measure one or more state; so if u start with an observable and controllable system there is no problem in setting up a state feedback controller using an observer.