Ackermann’s formula

Calculate feedback gain matrix using Ackermann s formula K=acker(A,B,desiredpoles)... 

Pole placement design of state feedback systems. Application of the Ackermann s formula. 

There are other methods in pole-placement design. One of them is the Ackermann s formula. The derivation of Eq. (9-21) predicates that we have put (9-13) in the controllable canonical form. Ackermann s formula only requires that the system (9-13) be completely state controllable. If so, we can evaluate the state feedback gain as 1... 

Roughly, the Ackermann s formula arises from the application of the Cayley-Hamilton theorem... 

Check 1. The same result can be obtained with the MATLAB function acker () which uses the Ackermann s formula. The statements are ... 

To find the new state feedback gain is a matter of applying Eq. (9-29) and the Ackermann s formula. The hard part is to make an intelligent decision on the choice of closed-loop poles. Following the lead of Example 4.7B, we use root locus plots to help us. With the understanding that we have two open-loop poles at -4 and -5, a reasonable choice of the integral time constant is 1/3 min. With the open-loop zero at -3, the reactor system is always stable, and the dominant closed-loop pole is real and the reactor system will not suffer from excessive oscillation. 

With eigenvalues selected at -9, we have chosen the estimator to be faster than the state feedback, and all the errors are to decay exponentially. We ll make use of the Ackermann s formula in Eq. (9-39) for observer gains. The MATLAB statements are ... 

In this paper, the research subject is a 35-tonne electrical transmission underground mining articulated dump truck. And the hardware in the loop simulation is based on NI cRIO and PXI controller. The Ackermann s formula is used for solving the control law u. 

---