Application of first and higher order sliding mode control algorithms on control of nonminimum phase missile systems

Guided missile systems are one of the most important components in air warfare and it seems that they will continue to be, according to many predictions. Guided missiles that launched from land or air platforms are backbone of todays air defence. The requirements that expected to be satisfied by missile systems are getting more challenging every day, like any other weapon system. An important part of these requirements is related to missile guidance and control systems. Airborne targets are usually fast and highly maneuverable targets. Naturally, missiles systems are required to be fast and maneuverable enough to chase down these targets. In the near future, as the unmanned air vehicles become more common and advanced, maneuverability advantage of missiles over other air platforms will diminish and missiles will be subject of more challenging maneuverability requirements. Design of missile control systems is directly affected by changes in maneuverability requirements. Extreme maneuvers are accompanied with extreme angles of attack that missile dynamics is highly nonlinear and uncertain because of cross flow and turbulent air movement around the body. Besides that, to chase targets carrying out fast evasive movement missile systems should track commands that changes dramatically fast. Missile autopilot should response commanded inputs in very short time and be robust to system uncertainties. Increasing maneuverability and range requirement leads to some radical changes in missile design. Air breathing engines began to be used to propulsion of air-to-air missiles in recent years. This kind of propulsion systems brings limit to angle of attack and sideslip angle to ensure clean air inflow to engine air intakes. Missile body shapes differs from conventional axisymmetric cylindrical shape to reduce radar cross section. These facts, together with higher maneuverability demand, led to emergence of bank to turn air-to-air missile systems. Although bank to turn cruise missiles are in use for long time, for agile air-to-air missile systems bank to turn maneuvering is a new technology. If commanded acceleration from guidance unit is rapidly changing, bank to turn maneuvering becomes complicated and hard to implement such that while system is requested to carry high acceleration maneuvers and extremely fast roll movements simultaneously. In such maneuvers, effects of coupled dynamics would be severe and keeping the missile in control would be extremely hard. Because of these reasons control of bank to turn maneuvering agile missile systems are living and challenging topic today. In this thesis design of missile autopilots are carried out by using sliding mode control algorithms and performance of designed autopilots are examined. It may not be possible using sliding mode control algorithms in missile autopilot because of dynamic properties of the missile system. Missile guidance systems generate commands for autopilot to bring missile as close as possible to the target. Commands generated by guidance systems are in form of acceleration. The difficulty arises in this point. Tail controlled missiles are nonminimum phase systems if output of the system is acceleration. Nonminimum phase systems are not suitable for direct implementation of sliding mdoe control algorithms. In addition to this, there is a zeroth order relation between force component of input of the system, control surface deflection, and the output of the system. This means that any discontinuity will be observed directly in output of the system as discontinuous acceleration. As the sliding mode control based on the input discontinuity for robustness, implementation of sliding mode control to missile autopilot with acceleration as output cause concerns in many aspects. Output redefinition method that is proposed in this study is a method to solve problems in sliding mode application arises from nonminimum phase dynamics of the system. This method based on blending the output of an internal system model that is minimum phased and measured output of the real system so produced new output is almost minimum phased while converges to real output of the system. The internal model is a modified model of the system that force component of control surface deflection is cancelled. By this way, the internal model has no nonminimum phase dynamics. Difference between measured output and internal output is added to internal output after a smoothing process. With this smoothing process nonminimum phase features of the output is suppressed and the resultant output, which is called virtual output in the study, is nearly minimum phased that it is almost impossible to observe nonminimum phase features in it. Another advantage of the output redefinition method is filtering and smoothing the output signal that is used in control loop. There is noise, input based chattering in measured output, and filtering is a necessity. By using output redefinition, this filtering work is done and no extra filtering is needed. Once the system becomes suitable for implementing sliding mode control algorithms by using the output redefinition method, autopilot design process continued with using sliding mode control algorithms. In this study two different missile models is used. One of them is model of the HAVE DASH II missile, which was a prototype missile. This missile model is a multi input-multi output system and it has 6 degrees of freedom. As HAVE DASH II missile is a bank to turn missile so designed autopilot uses same maneuvering logic. First order sliding mode control method is used in autopilot design. Other missile model is Reichert missile. It is a hypothetical skid to turn missile system and used as a workbench in many studies related to missile guidance and control. This missile model is 3 degrees of freedom and resembles horizontal dynamics of the missile. It is a single input single output system so balance within control channels is not a concern for this system. Different higher order sliding mode control algorithms, namely second and third order quasi-continuous sliding mode control and second order super twisting algorithm are used in autopilot design process. For all autopilot designs for Reichert missile, variable gain technique is used to satisfy response time requirements. For both systems, various system uncertainties and external disturbances are defined. Simulations are run in MATLAB/Simulink environment. Performances of designed autopilots are examined for different combinations of system uncertainties and external disturbances.