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Analyzing Errors in Controlled Turret System

Matthew Karlson, Heng Ban, Daniel G. Cole, Mai Abdelhakim, Jennifer Forsythe, John T. Fitzgibbons

TL;DR

This study addresses aiming errors in a controlled gun-turret system by building a linearized Newton-based model and evaluating PID and MPC controllers for azimuth $\theta$ and elevation $\alpha$ targets. It demonstrates that inertia parameter errors dominate accuracy degradation, that error statistics scale with reference aimpoints, and that delaying firing improves accuracy when time constraints are absent; measurement noise causes steady-state errors to mirror the noise distribution, while integral action is essential for tracking moving targets. The results provide an error-budget perspective for turret-fire-control design and suggest broader applicability to future AI-assisted aiming systems and more complete projectile dynamics. Overall, the work advances understanding of how model errors and sensor noise affect controlled turret accuracy and highlights the need for integral control in dynamic targeting scenarios.

Abstract

The purpose of this paper is to characterize aiming errors in controlled weapon systems given target location as input. To achieve this objective, we analyze the accuracy of a controlled weapon system model for stationary and moving targets under different error sources and firing times. First, we develop a mathematical model of a gun turret and use it to design two controllers, a Proportional-Integral-Derivative controller and a Model Predictive controller, which accept the target location input and move the turret to the centroid of the target in simulations. For stationary targets, we analyze the impact of errors in estimating the system's parameters and uncertainty in the aim point measurement. Our results indicate that turret movement is more sensitive to errors in the moment of inertia than the damping coefficient, which could lead to incorrect simulations of controlled turret system accuracy. The results also support the hypothesis that turret movement errors are larger over longer distances of gun turret movement and, assuming no time constraints, accuracy improves the longer one waits to fire; though this may not always be practical in a combat scenario. Additionally, we demonstrate that the integral control component is needed for high accuracy in moving target scenarios.

Analyzing Errors in Controlled Turret System

TL;DR

This study addresses aiming errors in a controlled gun-turret system by building a linearized Newton-based model and evaluating PID and MPC controllers for azimuth and elevation targets. It demonstrates that inertia parameter errors dominate accuracy degradation, that error statistics scale with reference aimpoints, and that delaying firing improves accuracy when time constraints are absent; measurement noise causes steady-state errors to mirror the noise distribution, while integral action is essential for tracking moving targets. The results provide an error-budget perspective for turret-fire-control design and suggest broader applicability to future AI-assisted aiming systems and more complete projectile dynamics. Overall, the work advances understanding of how model errors and sensor noise affect controlled turret accuracy and highlights the need for integral control in dynamic targeting scenarios.

Abstract

The purpose of this paper is to characterize aiming errors in controlled weapon systems given target location as input. To achieve this objective, we analyze the accuracy of a controlled weapon system model for stationary and moving targets under different error sources and firing times. First, we develop a mathematical model of a gun turret and use it to design two controllers, a Proportional-Integral-Derivative controller and a Model Predictive controller, which accept the target location input and move the turret to the centroid of the target in simulations. For stationary targets, we analyze the impact of errors in estimating the system's parameters and uncertainty in the aim point measurement. Our results indicate that turret movement is more sensitive to errors in the moment of inertia than the damping coefficient, which could lead to incorrect simulations of controlled turret system accuracy. The results also support the hypothesis that turret movement errors are larger over longer distances of gun turret movement and, assuming no time constraints, accuracy improves the longer one waits to fire; though this may not always be practical in a combat scenario. Additionally, we demonstrate that the integral control component is needed for high accuracy in moving target scenarios.
Paper Structure (22 sections, 41 equations, 6 figures, 9 tables)

This paper contains 22 sections, 41 equations, 6 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Gun Turret Model
  4. System Transfer Functions
  5. State-Space Representation
  6. PID Control
  7. Model Predictive Control
  8. Control System Objectives
  9. Results
  10. Experimental Setup
  11. Experiment 1 --- Effects of Parameter Errors on the Aiming Error
  12. Experiment 2 --- Effects of Aimpoint Uncertainty on the Aiming Error
  13. Experiment 3 --- Mean Aiming Error vs Firing Time
  14. Experiment 4 --- Model of Aimpoint Uncertainty and the Aiming Error
  15. Experiment 5 --- Moving Targets
  16. ...and 7 more sections

Figures (6)

  • Figure 1: Illustration of the gun turret system. The frame $\{x,y,z\}$ is fixed to the ground and the $z$-axis is coincident with the center of mass of the platform.
  • Figure 2: Error distributions under measurement noise with PID and MPC control for firing times of 3.0 -- 6.0 seconds. The results for PID are (\ref{['pidazimutherrornoiseft3456']}) and (\ref{['pidelevationerrornoiseft3456']}) and the results for MPC are (\ref{['mpcazimutherrornoiseft3456']}) and (\ref{['mpcelevationerrornoiseft3456']}). The noise is sampled from a normal distribution with 0mil mean and 0.1mil standard deviation. The total number of observations at each firing time is $10,000$.
  • Figure 3: Mean error as function of firing time in four different targeting scenarios for PID and MPC control. The results for PID are (\ref{['meanerrazimuthvsftpid']}) and (\ref{['meanerrelevationvsftpid']}) and the results MPC are (\ref{['meanerrazimuthvsftmpc']}) and (\ref{['meanerrelevationvsftmpc']}). In the case of measurement noise, the noise is sampled from a normal distribution with 0mil mean and 0.1mil standard deviation.
  • Figure 4: Error distributions for PID control normalized for probability density. The firing time is 10.0 seconds from stationary position. Target measurement noise is sampled from a normal distribution with 0mil mean and 1mil standard deviation. The red scatter plot is the theoretical probability density function obtained by evaluating \ref{['gaussianpdfe']} with the error data. The total number of observations is $10,000$.
  • Figure 5: Reference tracking output and errors for the azimuth and elevation with different PID controllers. The first column shows the azimuth with lead control, the second column shows the azimuth with PI+lead control, and the third column shows the elevation with PI+lead control.
  • ...and 1 more figures