# acker: Pole placement gain selection using Ackermann's formula In control: A Control Systems Toolbox

## Description

Computes the Pole placement gain selection using Ackermann's formula.

## Usage

 `1` ```acker(a, b, p) ```

## Arguments

 `a` State-matrix of a state-space system `b` Input-matrix of a state-space system `p` closed loop poles

## Details

K <- ACKER(A,B,P) calculates the feedback gain matrix K such that the single input system . x <- Ax + Bu

with a feedback law of u <- -Kx has closed loop poles at the values specified in vector P, i.e., P <- eigen(A - B * K).

This method is NOT numerically stable and a warning message is printed if the nonzero closed loop poles are greater than 10 in P.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```F <- rbind(c(0,1),c(0,0)) G <- rbind(0,1) H <- cbind(1,0); J <- 0 t <- 1 sys <- ss(F,G, H,J) A <- c2d(sys,t); j <- sqrt(as.complex(-1)); pc <- rbind(0.78+0.18*j, 0.78-0.18*j) K <- acker(A\$A, A\$B, pc) ```

### Example output

```Attaching package: ‘control’

The following object is masked from ‘package:stats’:

step

The following object is masked from ‘package:base’:

append

Warning message:
In acker(A\$A, A\$B, pc) : Pole locations are more than 10% in error.
```

control documentation built on May 1, 2019, 7:33 p.m.