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I am trying to design a compensator to improve the yaw rate ($\dot{r}$) control performance of an aircraft. The lateral dynamics for this aircraft is given in steady space form as following:

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where A (4x4) and B(4x1) are both known. I am also given a set of closed loop and observer poles (6x1). I tried to construct a set of equations to incorporate the washout filter and rudder actuator ($\delta_{r}$) by creating the steady-space model for the aircraft, obtaining the transfer function, and finding the closed loop transfer function of the system including the rudder actuator and washout filter. In order to perform pole placement in MATLAB using the place() function I needed to have a state space model, so I used the tf2ss() to obtain the new state space model. However, the A matrix in this case was 11x11, but my system has only 6 states. Also, the rank of the observability matrix was 6. I am really confused on what I should do next to compute the compensator's transfer function.

The programming language I am using is MATLAB, so if you have any suggestions please include the MATLAB code.


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