Missile Autopilot Design Research Articles

Robust gain-scheduled missile autopilot design based on multifrequency extended state observers

This paper describes the design and implementation of a three-axis acceleration control autopilot for an asymmetric tail-controlled, skid-to-turn tactical missile. In an earlier flight test, degraded autopilot performance was attributed to multiple disturbances and uncertainties and the presence of hidden coupling terms, giving rise to a miss distance of greater than 20 m. To address these issues, the missile dynamics are decomposed into the angular rate dynamics as fast and the acceleration dynamics as slow subsystem using the singular perturbation theory to analyze a multi-time-scale property. Multifrequency extended state observers are then incorporated into the gain scheduling technique to attenuate disturbances, thus enhancing the control performance significantly. In the proposed engineering/practical design framework for missile autopilot, simple, conventional, and explicit tuning rules are provided. And the proposed control scheme can achieve input-to-state stability across the entire flight envelope under unknown but bounded disturbances. The advantages of the method over existing benchmark approaches are shown through nonlinear numerical simulations. This is supported by evidence from a new flight test result with a miss distance of only 2 m.

Robust missile autopilot design based on dynamic surface control

Since the dynamical system and control system of the missile are typically nonlinear, an effective acceleration tracking autopilot is designed using the dynamic surface control (DSC) technique in order to make the missile control system more robust despite the uncertainty of the dynamical parameters and the presence of disturbances. Firstly, the nonlinear mathematical model of the tail-controlled missile is decomposed into slow acceleration dynamics and fast pitch rate dynamics based on the naturally existing time scale separation. Secondly, the controller based on DSC is designed after obtaining the linear dynamics characteristics of the slow and fast subsystems. An extended state observer is used to detect the uncertainty of the system state variables and aerodynamic parameters to achieve the compensation of the control law. The closed-loop stability of the controller is derived and rigorously analyzed. Finally, the effectiveness and robustness of the design is verified by Monte Carlo simulation considering different initial conditions and parameter uptake. Simulation results illustrate that the missile autopilot based DSC controller achieves better performance and robustness than the other two well-known autopilots. The method proposed in this paper is applied to the design of a missile autopilot, and the results show that the acceleration tracking autopilot based on the DSC controller can ensure accurate tracking of the required commands and has better performance.

Switched Adaptive Resilient Control of Missile Autopilot Systems

This article proposes a switched adaptive resilient control method for missile autopilot systems subject to parametric uncertainties and unknown actuator failures. The nonlinear longitudinal dynamics of missiles are approximated by a piecewise linear system, based on which a computational effective adaptive fault-tolerant mechanism consisting of adaptive laws with a dwell-time constraint is developed. The merit of the proposed adaptive laws consists in integrating time-varying positive-definite matrices instead of constant ones, guaranteeing that the resulting Lyapunov function is decreasing at the switching instants. This decreasing property plays a crucial role in guaranteeing error-bounded tracking, by compensating for possible increase due to actuator failures. The stability guarantee and tracking performance are validated through simulations for missile autopilot design over a large range of operating conditions.

$${H}_{\infty }$$ Approach to Performance Analysis of Missile Control Systems with Proportional Navigation Guidance Laws

This paper presents a performance analysis of missile control systems considering nonlinear pursuit dynamics and proportional navigation guidance (PNG) laws. In order to analyze the system stability, missile dynamics are simplified as a linearized model which is often considered in missile autopilot design and the well-known $${{{H}}}_{\boldsymbol{\infty }}$$ approach is employed. A sufficient condition guaranteeing miss distance and the closed loop stability is proposed. The provided condition of missile system stability can be numerically easily verified by a linear matrix inequality (LMI).

Disturbance observer-based robust missile autopilot design with full-state constraints via adaptive dynamic programming

This paper aims to develop a robust optimal control method for longitudinal dynamics of missile systems with full-state constraints suffering from mismatched disturbances by using adaptive dynamic programming (ADP) technique. First, the constrained states are mapped by smooth functions, thus, the considered systems become nonlinear systems without state constraints subject to unknown approximation error. In order to estimate the unknown disturbances, a nonlinear disturbance observer (NDO) is designed. Based on the output of disturbance observer, an integral sliding mode controller (ISMC) is derived to counteract the effects of disturbances and unknown approximation error, thus ensuring the stability of nonlinear systems. Subsequently, the ADP technique is utilized to learn an adaptive optimal controller for the nominal systems, in which a critic network is constructed with a novel weight update law. By utilizing the Lyapunov's method, the stability of the closed-loop system and the convergence of the estimation weight for critic network are guaranteed. Finally, the feasibility and effectiveness of the proposed controller are demonstrated by using longitudinal dynamics of a missile.

An Optimal Missile Autopilot Design Model

This article describes how one optimal design method is given to the design of missile autopilots. This method profits from an exhaustive method. By this method, the design process of a missile autopilot is simplified, and the design efficiency is improved. In the design process of this method, the performance indexes of autopilot are translated into constraint conditions, and the response speed is translated to an objective function. Thus, the optimal design of missile autopilot is translated into the optimal design of a nonlinear system with multiple constraints. The optimization algorithm is found to be out of controller parameter combinations which can satisfy constrained conditions. Firstly, calculations of the corresponding objective function values. Second, by the extract the optimal combination which has the minimal objective function value.

A robust adaptive control approach to missile autopilot design

The huge developments in computational capabilities facilitate the design and implementation of adaptive and robust control. Furthermore, the great developments in nanotechnology and its availability in civilian level with less cost, weight, and size attract the researchers all over the world towards embedded systems especially the embedded flight control. One of the real applications are the guided missiles especially the anti-tank guided missile systems which are launched against the ground and short-range targets and is called command line of sight. The present work is concerned with improving the performance of an anti-tank guided missile system belonging to the first generation via adaptive synthesis of guidance systems. The online system identification is required to complete the cycle of adaptive autopilot design. This paper is devoted to designing an adaptive autopilot for the intended system using model reference and self-tuning regulator with justification against previous work and reference flight data concerning the performance requirements of time responses and flight path characteristics. The new design is implemented within the 6-DOF simulation from which the obtained results clarify its capability to stabilize the system in presence of unmodeled dynamics and satisfy the performance requirements with disturbance rejection and measurement noise attenuation. Also, the flight path is evaluated considering the HIL environment.

Robust autopilot design for STT missiles with multiple disturbances using twisting control

In this paper, a novel second-order sliding mode control (NSOSMC) scheme with finite time convergence is proposed for the autopilot design of skid-to-turn (STT) missiles considering coupling effects to track the desired maneuver commands. Firstly, the control system formulation is developed based on the mathematical model for nonlinear missile dynamics with system uncertainties and unknown multiple disturbances. Secondly, the NSOSMC scheme is developed by using a PID sliding mode surface with twisting control algorithm, which is to suppress the system uncertainties and unknown external disturbances, and to eliminate the chattering phenomenon. Then, the proposed NSOSMC law is proved to be finite time convergent to the origin. Finally, the effectiveness and robustness of the proposed NSOSMC scheme is verified through the numerical simulations with comparisons.

Longitudinal nonlinear adaptive autopilot design for missiles with control constraint

This paper develops a new nonlinear adaptive longitudinal autopilot for the control of missiles with control input constraint, in the presence of parametric uncertainties and external disturbance input. The objective here is to control the angle of attack of the missile. A saturating control law is derived for the trajectory control of the angle of attack. The control law includes an auxiliary dynamic system in the feedback loop, driven by control input error signal, caused by control saturation, to preserve stability in the closed-loop system. By the Lyapunov stability analysis, it is shown that in the closed-loop system, the system trajectories are uniformly ultimately bounded. Simulation results show that the designed autopilot with constrained input can accomplish accurate trajectory control if the control saturation period is short. It is also seen that although the tracking error increases with the saturation period, the angle of attack tends to zero, once the command input is set to zero. Furthermore this adaptive control system, including the control error signal feedback loop, performs better than the adaptive laws, designed earlier based on immersion and invariance principle, without control magnitude constraint.

Missile autopilot design based on robust LPV control

This paper proposes an effective algorithm to work out the linear parameter-varying (LPV) framework autopilot for the air defense missile so as to simultaneously guarantee the closed-loop system properties globally and locally, which evidently reduces the number of unknown variables and hence increases the computational efficiency. The notion of quadratic is inducted to meet the global properties, including the robust stability and robust performance, while the regional pole placement scheme together with the adoption of a model matching structure is involved to satisfy the dynamic performance, including limiting the fast poles. In order to reduce the conservatism, the full block multiplier is employed to depict the properties, with all specifications generalized in integral quadratic constraint frame and finally transformed into linear matrix inequalities for tractable solutions through convex optimization. Simulation results validate the performance of the designed robust LPV autopilot and the proposed framework control method integrating with the full block multiplier approach and the regional pole placement scheme, and demonstrate the efficiency of the algorithm. An efficient algorithm for the air defense missile is proposed to satisfy the required global stability and local dynamical properties by a varying controller according to the flight conditions, and shows sufficient promise in the computational efficiency and the real-time performance of the missile-borne computer system.

Sub-optimal Autopilot Design based on Dynamic Neural Unit Network for Tactical Missile

Dynamic Neural Unit (DNU) network based sub-optimal autopilot design for a tactical missile is investigated. An autopilot is expressed as two-loop nonlinear control phenomena and delivers an approximate solution to value function of State Dependent Riccati Equation (SDRE). The autopilot, not only tracks, stabilizes all the state vectors simultaneously but also, compensates the austere aerodynamic coupling and nonlinearities with an angle-of-attack. The body rates are transformed by outer-loop autopilot using state vectors command (total-angle-of-attack, bank angle), and fin deflections are transformed by inner-loop autopilot using state vectors command (body rates). Reduced cost computation is the novelty of the proposed autopilot. Outcomes are demonstrated using 6-DOF simulations and performance compared with sub-optimal Theta-D autopilot.

Design of an adaptive missile autopilot considering the boost phase using the SDRE method and neural networks

An adaptive autopilot to control a skid-to-turn missile during its boost phase is designed using the state-dependent Riccati equation (SDRE) method and neural networks (NN). To address the rapid changes in parameters during the boost phase, the translational and rotational motions of the missile are modeled with time-varying velocity and inertial parameters. The autopilot with a two-loop structure is designed to perform integrated roll-pitch-yaw control of the missile with cross-coupled dynamics; each loop has a baseline controller and an adaptive controller. The baseline controller is designed using the SDRE method for reference command tracking in a nominal environment, and the adaptive controller is designed based on NN to manage uncertainty during the boost phase. Stability analysis of the closed-loop system is performed, and the performance of the proposed autopilot is demonstrated by numerical simulation.

Augmented predictive functional control for missile autopilot design

In this paper, an augmented predictive functional control approach is investigated to design a missile autopilot system, which can be expressed as a linear model with state-dependent coefficient matrices. A novel performance index depending on the reference trajectory, the output prediction and the set-point is proposed to improve the closed-loop dynamic performance. An augmented predictive functional control strategy is designed based on the proposed index and the stability is proven by using the Z-transform. In order to demonstrate the performance of the proposed approach, numerical simulations comparing the predictive functional control in the missile autopilot system are performed. Finally, results from comprehensive simulations are presented to evaluate the proposed approach in the presence of input constraints and abrupt disturbances.

Robust backstepping control for a class of nonlinear systems using generalized disturbance observer

This paper presents a new composite robust controller for a class of uncertain nonlinear systems through backstepping method and disturbance observer (DOB) technique. By designing a generalized disturbance observer (GDOB), the mismatched/matched uncertainty is estimated and compensated at each backstepping step. By virtue of the proposed GDOB, the proposed controller only requires the lumped uncertainties are differentiable and the higher-order derivatives are bounded. With the help of GDOB, the high-gain backstepping controller is also avoided completely. Asymptotical stability of the closed-loop system is established using direct Lyapunov method. An illustrative example of missile autopilot design is given and simulations are carried out to validate the proposed method.

An enhanced velocity-based algorithm for safe implementations of gain-scheduled controllers

ABSTRACTThis paper presents an enhanced velocity-based algorithm to implement gain-scheduled controllers for nonlinear and parameter-dependent systems. A new scheme including pre- and post-filtering is proposed with the assumption that the time-derivative of the controller inputs is not available for feedback control. It is shown that the proposed control structure can preserve the input–output properties of the linearised closed-loop system in the neighbourhood of each equilibrium point, avoiding the emergence of the so-called hidden coupling terms. Moreover, it is guaranteed that this implementation will not introduce unobservable or uncontrollable unstable modes, and hence the internal stability will not be affected. A case study dealing with the design of a pitch-axis missile autopilot is carried out and the numerical simulation results confirm the validity of the proposed approach.

Roll-pitch-yaw autopilot design for nonlinear time-varying missile using partial state observer based global fast terminal sliding mode control

The acceleration autopilot design for skid-to-turn (STT) missile faces a great challenge owing to coupling effect among planes, variation of missile velocity and its parameters, inexistence of a complete state vector, and nonlinear aerodynamics. Moreover, the autopilot should be designed for the entire flight envelope where fast variations exist. In this paper, a design of integrated roll-pitch-yaw autopilot based on global fast terminal sliding mode control (GFTSMC) with a partial state nonlinear observer (PSNLO) for STT nonlinear time-varying missile model, is employed to address these issues. GFTSMC with a novel sliding surface is proposed to nullify the integral error and the singularity problem without application of the sign function. The proposed autopilot consisting of two-loop structure, controls STT maneuver and stabilizes the rolling with a PSNLO in order to estimate the immeasurable states as an output while its inputs are missile measurable states and control signals. The missile model considers the velocity variation, gravity effect and parameters’ variation. Furthermore, the environmental conditions’ dynamics are modeled. PSNLO stability and the closed loop system stability are studied. Finally, numerical simulation is established to evaluate the proposed autopilot performance and to compare it with existing approaches in the literature.

Hybrid Switched Gain-Scheduling Control for Missile Autopilot Design

This paper presents a new hybrid switched gain-scheduling control method for missile autopilot design via dynamic output feedback. For controller design purpose, the nonlinear missile plant model is first converted to a switched linear fractional transformation system. Then, the new hybrid switched gain-scheduling autopilot is designed, which consists of a switching dynamic output–feedback linear fractional transformation controller and a supervisor enforcing a controller state reset at each switching time instant. The proposed hybrid control scheme is shown to provide a systematic yet simple framework for missile autopilot design. Specifically, the control synthesis conditions that guarantee weighted stability performance are formulated in terms of a finite number of linear matrix inequalities, which can be solved effectively via convex optimization without parameter-space gridding. Furthermore, stringent controlled performance and strong robustness against parameter perturbations are achieved using this new control approach, whereas no parameter variation information is required for both controller synthesis and implementation. The advantages of the proposed design approach over existing methods will be shown through nonlinear simulations for the missile autopilot design over a wide range of operating conditions.

Robust output feedback tracking control for a class of perturbed systems using NDOB and nonlinear continuous predictive control

This paper presents a new robust output feedback tracking control scheme for a class of higher-order uncertain systems. Since traditional nonlinear continuous predictive control requires accurate system model as well as full system states to synthesize a controller, a composite control methodology is adopted in the proposed scheme. Specifically, the nonlinear disturbance observer (NDOB) is used to estimate the lumped uncertainty and the unmeasured system states in an integrated manner while the nonlinear continuous predictive control regulates the system states to track the desired reference signal asymptotically. Detailed stability analysis is also presented for the closed-loop nonlinear observer-controller structure through two steps. Then, the obtained results are applied to missile autopilot design to track the desired angle-of-attack signal. Finally, numerical simulations with some comparisons are provided to demonstrate the effectiveness of the proposed formulation.

Integrated Pitch-Yaw Acceleration Autopilot Design for Varying-Velocity Man Portable Missile

Integrated Pitch-Yaw Acceleration Autopilot Design for Varying-Velocity Man Portable Missile

Adaptive Backstepping Autopilot Design for Missiles of Fast Time-varying Velocity

An adaptive backstepping control scheme is proposed to design a missile autopilot during boost-phase. In the boost-phase, accurately controlled missiles experience fast velocity variations that make the missile dynamics be highly nonlinear. Missile parameters including the mass, the moment of inertia, and a center of gravity, which are usually considered as constants or slowly-varying, change very fast. The time-varying effects combined with nonlinear dynamics yield severe parametric uncertainties in missile dynamics. Therefore, the nonlinear dynamics as well as parametric uncertainty should be carefully treated in autopilot design. To deal with this problem, an adaptive nonlinear controller is designed based on backstepping procedure. Adaptation laws are properly designed so that robustness to the uncertainty as well as the closed-loop stability can be guaranteed using Lyapunov stability theorem. To demonstrate the performance of the proposed controller, numerical simulation is carried out.