LMIs in Control/pages/LMI for Attitude Control of Nonrotating Missiles

LMI for Attitude Control of Nonrotating Missles, Pitch Channel

The dynamic model of a missile is very complicated and a simplified model is used. To do so, we consider a simplified attitude system model for the pitch channel in the system. We aim to achieve a non-rotating motion of missiles. It is worthwhile to note that the attitude control design for the pitch channel and the yaw/roll channel can be solved exactly in the same way while representing matrices of the system are different.


The SystemEdit

The state-space representation for the pitch channel can be written as follows:

 

where  ,   ,  , and   are the state variable, control input, output, and disturbance vectors, respectively. The paprameters  ,  ,  ,  ,  ,  , and   stand for the attack angle, pitch angular velocity, the elevator deflection, the input actuator deflection, the overload on the side direction, the sideslip angle, and the yaw angular velocity, respectively.

The DataEdit

In the aforementioned pitch channel system, the matrices   and   are given as:

 

 

 

 

where   and   are the system parameters. Moreover,   is the speed of the missle and  ,  , and   are the rotary inertia of the missle corresponding to the body coordinates.

The Optimization ProblemEdit

The optimization problem is to find a state feedback control law   such that:

1. The closed-loop system:

 

is stable.

2. The   norm of the transfer function:

 

is less than a positive scalar value,  . Thus:

 

The LMI: LMI for non-rotating missle attitude controlEdit

Using Theorem 8.1 in [1], the problem can be equivalently expressed in the following form:

 

Conclusion:Edit

As mentioned, the aim is to attenuate the disturbance on the performance of the missile. The parameter   is the disturbance attenuation level. When the matrices   and   are determined in the optimization problem, the controller gain matrix can be computed by:

 

ImplementationEdit

A link to Matlab codes for this problem in the Github repository:

https://github.com/asalimil/LMI-for-Non-rotating-Missle-Attitude-Control

Related LMIsEdit

LMI for Attitude Control of Nonrotating Missles, Yaw/Roll Channel

External LinksEdit

  • [1] - LMI in Control Systems Analysis, Design and Applications

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