A novel continuous time predictive control and generalized extended state observer (GESO) based acceleration tracking pitch autopilot design is proposed for a tail controlled, skid-to-turn tactical missile. As the dynamics of missile are significantly uncertain with mismatched uncertainty, GESO is employed to estimate the state and uncertainty in an integrated manner. The estimates are used to meet the requirement of state and to robustify the output tracking predictive controller designed for nominal system. Closed loop stability for the controller-observer structure is established. An important feature of the proposed design is that it does not require any specific information about the uncertainty. Also the predictive control design yields the feedback control gain and disturbance compensation gain simultaneously. Effectiveness of GESO in estimation of the states and uncertainties and in robustifying the predictive controller in the presence of parametric uncertainties, external disturbances, unmodeled dynamics, and measurement noise is illustrated by simulation.

Traditionally, missile autopilots are designed using linear control techniques wherein missile dynamics are linearized around certain number of operating points in the flight envelope. Subsequently, controllers are designed at the operating points and gain scheduling is employed to obtain desired performance in the complete flight envelope. To this end, linear control approaches have dominated missile autopilot design over the past several decades [

There exist certain issues in many of the controllers that require discussion. Firstly, the robustification approaches require some knowledge, in terms of either bound of uncertainties or some characteristics of the same. In either case, lack of exact information on this count may result in either a highly conservative design or poor robustness and performance. Secondly, controllers that are based on state feedback require availability of full state vector. In the case of pitch autopilot, the state vector consists of angle of attack, pitch rate, and the fin deflection. While the pitch rate and fin deflection are measured, the angle of attack is not normally available. This necessitates a separate design for an observer to estimate it [

In this paper, addressing the issues, acceleration tracking pitch autopilot design for a tail controlled, roll position stabilized, skid-to-turn missile that is robust to uncertainties and external disturbances is proposed. By considering missile acceleration as output, an output tracking formulation of the continuous time predictive control approach [

The remainder of the paper is organized as follows. Section

This work is concerned with pitch autopilot design for an aerodynamically tail controlled, roll position stabilized, skid-to-turn tactical missile. The objective is to force a missile to track a desired lateral acceleration command generated by the outer guidance loop. The design is expected to offer robust stability and performance over its operational flight envelope.

As is well known, the equations that represent the dynamics of a missile are usually highly nonlinear [

In this work, as considered in many designs, it is assumed that measurements of lateral acceleration,

The continuous time predictive control approach represents one viable approach for designing controllers for nonlinear systems. In this approach, first introduced by Lu [

Here, an output tracking formulation of the continuous time predictive control approach is used for the design of acceleration tracking control law. To this end, consider the system of (

As can be seen, the predictive controller (

One approach to robustify a given controller in the presence of uncertainties without requiring any knowledge of the same is through uncertainty and disturbance estimation [

While the standard ESO has offered viable solution to many practical problems as stated above, it needs dynamics in integral-chain system form with matched uncertainty. Extending the usefulness of the standard ESO for general systems, that is, for nonintegral-chain systems having mismatched uncertainty, a formulation of generalized ESO is proposed in [

As stated in the last section, the GESO extends the functionality and utility of the standard ESO for general systems. Consequent to its appearance in [

Now consider the dynamics of (

Using the GESO estimated states and disturbances in (

Functional block diagram of GESO based pitch autopilot.

Following [

As is obvious from (

Lastly, it may be noted that, in this work, the rate of change of uncertainties is assumed to be negligible. Although the assumption appears to be restrictive, in practice it holds true to a great extent. It can be seen from (

Simulations are carried out to verify the performance of the GESO in state and uncertainties estimation and tracking performance of the proposed design. To this end, the nominal values of the various aerodynamic parameters for a representative tail controlled missile flying at 500 m/s as taken from [

Performance in absence of uncertainties.

Next, simulations are carried out by introducing parametric uncertainties, unmodeled dynamics, measurement noise, and external disturbances. Parametric perturbations are introduced in aerodynamic derivatives except the one that appears in output channel (i.e., in ^{2} and 0.0667 deg/s, respectively [

Tracking performance of GESO based predictive controller.

Performance of GESO in state estimation.

Performance of GESO in uncertainty estimation.

Lastly, simulations are carried out by including parametric uncertainties of

Tracking performance of GESO based predictive controller with parametric perturbation in output channel.

Performance of GESO in state estimation with parametric perturbation in output channel.

Performance of GESO in uncertainty estimation with parametric perturbation in output channel.

In the simulation results presented in this section, it is important to note that the predictive controller of (

In this work, generalized extended state observer (GESO) robustified continuous time predictive control based acceleration tracking controller for pitch autopilot design of a cruciform, roll position stabilized, tail controlled tactical missile is proposed. The predictive control yields the feedback control gain and disturbance compensation gain simultaneously avoiding separate design procedures. Closed loop stability for the proposed design is established. The effectiveness of the GESO in estimation of the states and uncertainty and tracking of the commanded acceleration using the GESO based predictive controller is demonstrated through simulation. The results show that the GESO robustifies the predictive controller effectively leading to satisfactory tracking of the desired command in spite of the considered parametric uncertainties, unmodeled dynamics, external disturbance, and measurement noise. Lastly, as a further scope of research, the issue of uncertainty in output equation in GESO is highlighted.

The authors declare that they have no competing interests.