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# gfrancis

Francis equations for tracking

### Syntax

[L, M, T] = gfrancis(Plant, Model)

### Arguments

- Plant
a continuous time dynamical system in state-space representation.

- Model
a continuous time dynamical system in state-space representation.

- L,M,T
real matrices

### Description

Given the linear plant:

x'= F*x + G*u y = H*x + J*u

and the linear model

xm'= A*xm + B*um ym = C*xm + D*um

the goal is for the plant to track the model i.e. `e = y - ym ---> 0`

while keeping stable the state x(t) of the plant.
`u`

is given by feedforward and feedback

u = L*xm + M*um + K*(x-T*xm) = [K , L-K*T] *(x,xm) + M*um

The matrices T,L,M satisfy generalized Francis equations

F*T + G*L = T*A H*T + J*L = C G*M = T*B J*M = D

The matrix `K`

must be chosen as stabilizing the pair `(F,G)`

See example of use in directory `demos/tracking`

.

### Examples

### History

Version | Description |

5.4.0 | `Sl` is now checked for
continuous time linear dynamical system. This modification
has been introduced by this commit |

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