Nonlinear H(Infinity) Missile Longitudinal Autopilot Design with Theta-D Method

In this paper, a new nonlinear H 1 control technique, called μ¡D H 1 method, is employed to design a missile longitudinal autopilot. The μ ¡D H 1 design has the same structure as that of linear H 1 , except that the two Riccati equations that are part of the solution process are state dependent. The μ ¡D technique yields suboptimal solutions to nonlinear optimal control problems in the sense that it provides an approximate solution to the Hamilton-Jacobi-Bellman (HJB) equation. It is also shown that this method can be used to provide an approximate closed-form solution to the state dependent Riccati equation (SDRE) and consequently reduce the on-line computations associated with the nonlinear H 1 implementation. A missile longitudinal autopilot design demonstrates the capabilities of μ¡D method. This new nonlinear H 1 design also shows favorable results as compared with the linear H 1 design based on the linearized model

Nonlinear H Infinity Missile Longitudinal Autopilot Design with Θ-D Method

In this paper, a new nonlinear control synthesis technique, the theta- D method, is employed to design a missile longitudinal autopilot. The θ-D technique yields suboptimal solutions to nonlinear optimal control problems in the sense that it provides approximate solution to the Hamilton-Jacobi-Bellman (HJB) equation. Semi-global asymptotic stability can be achieved by manipulating the perturbation terms which are added to the cost function in developing a series solution. Furthermore, this method can be used to provide an approximate closed-form solution to the state dependent Riccati equation. The particular θ-D methodology adopted in this paper is referred to as θ-D H infinity design. The θ-D H infinity design has the same structure as that of linear H infinity, except that the two Riccati equations are state dependent. By using the θ-D technique, we would eliminate the need for online computations of Riccati equations as in the recently popular state dependent Riccati equation technique. A missile longitudinal autopilot design demonstrates the capabilities of θ-D method

Missile Longitudinal Autopilot Design Using a New Suboptimal Nonlinear Control Method

A missile longitudinal autopilot is designed using a new nonlinear control synthesis technique called the θ-D approximation. The particular θ-D methodology used is referred to as the θ-D H2 design. The technique can achieve suboptimal closed-form solutions to a class of nonlinear optimal control problems in the sense that it solves the Hamilton-Jacobi-Bellman equation approximately by adding perturbations to the cost function. An interesting feature of this method is that the expansion terms in the expression for suboptimal control are nothing but solutions to the state-dependent Riccati equations associated with this class of problems. The θ-D H2 design has the same structure as that of the linear H2 formulation, except that the two Riccati equations are state dependent. Numerical simulations are presented that demonstrate the potential of this technique for use in an autopilot design. These results are compared with the recently popular SDRE H2 method

Integrated Guidance and Control of Missiles with Θ-D Method

A new suboptimal control method is proposed in this study to effectively design an integrated guidance and control system for missiles. Optimal formulations allow designers to bring together concerns about guidance law performance and autopilot responses under one unified framework. They lead to a natural integration of these different functions. by modifying the appropriate cost functions, different responses, control saturations (autopilot related), miss distance (guidance related), etc., which are of primary concern to a missile system designer, can be easily studied. A new suboptimal control method, called the θ-D method, is employed to obtain an approximate closed-form solution to this nonlinear guidance problem based on approximations to the Hamilton-Jacobi-Bellman equation. Missile guidance law and autopilot design are formulated into a single unified state space framework. The cost function is chosen to reflect both guidance and control concerns. The ultimate control input is the missile fin deflections. A nonlinear six-degree-of-freedom (6-DOF) missile simulation is used to demonstrate the potential of this new integrated guidance and control approach

Analysis of the theta-D filter as applied to hit-to-kill interceptors and satellite orbit determination

When designing feedback control systems, there is often a need for estimation methods that provide system information that is not readily available via sensors placed within the system. In many cases a sensor that measures a particular system state either does not exist or is prohibitively expensive. In addition, all realistic systems contain some degree of nonlinearity. This thesis focuses on two such cases: missile guidance with bearings-only measurements and GPS satellite orbit determination. In each case, a new nonlinear filter, the [theta]-D method, is used and evaluated for its performance in providing the necessary estimation. To aid the filter in the bearings-only application, a guidance law is formulated that assists the filter in estimating the target location despite the lack of range measurement. An implementation procedure, called the Staggered Filter Concept, is also presented for implementing a continuous filter, such as the [theta]-D filter, with measurements taken at discrete intervals. This procedure is used to implement the orbit determination algorithm on the Missouri S&T Satellite Team M-SAT mission --Abstract, page iii

Nonlinear Optimal Tracking For Missile Gimbaled Seeker Using Finite-Horizon State Dependent Riccati Equation

The majority of homing guided missiles use gimbaled seekers. The equations describing seeker gimbal system are highly nonlinear. Accurate nonlinear control of the motion of the gimbaled seeker through the attached DC motors is required. In this paper, an online technique for finite-horizon nonlinear  racking problems is presented. The idea of the proposed technique is the change of variables that converts the nonlinear differential Riccati equation to a linear Lyapunov differential equation. The proposed technique is effective for wide range of operating points. Simulation results for a realistic gimbaled system with different engagement scenarios are given to illustrate the effectiveness of the proposed technique

An investigation study on model reference adaptive techniques as applied to attitude control system for launch vehicles Final report

Self adaptive control techniques for attitude control on Saturn 5 launch vehicle

Missile Longitudinal Dynamics Control Design Using Pole Placement and LQR Methods

In high-maneuvering missile systems, with severe restrictions on actuator energy requirements, it is desirable to achieve the required performance with least actuation effort. Linear Quadratic Regulator (LQR) has been in literature for long and has proven it’s mettle as an optimal controller in many benign aerospace applications and industrial applications where the response times of the plant, in most cases, are seen to be greater than 10 seconds. It can be observed in the literature that LQR control methodology has not been explored enough in the tactical missile applications where requirement of very fast airframe response times are desired, typically of the order of milliseconds. In the present research, the applicability of LQR method for one such agile missile control has been critically explored. In the present research work, longitudinal dynamic model of an agile missile flying at high angle of attack regime has been established and an optimal LQR control solution has been proposed to bring out the required performance demanding least control actuator energy. A novel scheme has been presented to further optimise the control effort, which is essential in this class of missile systems with space and energy constraints, by iteratively computing optimal magnitude state weighing matrix Q and control cost matrix R. Pole placement design techniques, though extensively used in aerospace industry because of ease of implementation and proven results, do not address optimality of the system performance. Hence, a comparative study has been carried out to verify the results of LQR against pole placement technique based controller. The efficacy of LQR based controller over pole placement design techniques is successfully established with minimum control energy requirement in this paper. Futuristic high maneuvering, agile missile control design with severe space and energy constraints stand to benefit incorporating the controller design scheme proposed in this paper.&nbsp