Implementation of an advanced controller strategy to emulate flare trajectories in a hardware-in-the-loop simulation environment

Abstract

This study investigates the implementation of a controller strategy to emulate flare trajectories on a Hardware-in-the-loop Simulation (HILS) platform. Flares are employed as countermeasures in aerial defence systems and the counter-countermeasures abilities of missiles against flares can be evaluated on a HILS platform. The HILS platform in this article consists of a flight motion simulator for missile seeker movement simulation and a target motion simulator. The target motion simulator is the gimbal system mounted on an arm which simulates the aircraft in motion with an ejected flare in trajectory. The gimbal system consists of two gimbals which are each controlled with a dc motor and provides the ability to emulate flare trajectory.

The focus of this study is on the control of the two gimbals in the gimbal system in order to emulate flare trajectory. The gimbal system consists of two gimbals which differ in size, a smaller inner gimbal is fitted inside the bigger outer gimbal. The inner gimbal can be fitted with a wafer that relays a light source to be viewed by a guided missile unit. The inner gimbal emulates horizontal movement and the outer gimbal emulates vertical movement. Each gimbal is actuated with its own dc motor. Current and position feedback are provided from each gimbal to a microprocessor. The microprocessor is inside the gimbal system and is used to control the two gimbals together to emulate flare trajectory. In this study both gimbals in the gimbal system are characterised during a process that involves implementation of a dc motor model with friction properties and other non-linear elements parametrised within the gimbal system. The characterised gimbals are then utilised for development of a control system.

The first step in the study is the investigation of flare dynamic models. A position set point in terms of flare trajectory is developed from the flare models. The position set point is converted for use in gimbal units. With the flare models, 1 m is represented with 5.3 mrad on the gimbals. The aim is to control both gimbals as accurately as possible. Accurate control is regarded as a moving Root Mean Square (mRMS) position error below 2.00 mrad in the gimbal system, or 0.377 m in the flare model. The second step is modelling each of the two gimbals with the aim of developing a controller for flare trajectory emulation. Controller development is the third and last step.

A non-linear simulation model is developed for each gimbal. The non-linear simulation model incorporates a dc motor characterisation process to determine gimbal system parameters. There are non-linear elements present within both gimbals, mostly attributed to friction in the mechanical system and the electrical harness connected to the outer gimbal. The non-linear elements are modelled with a parameter estimation process. In the parameter estimation process, only measurements from a certain range of input voltages is taken, due to the limited range of movement which is 330 mrad on the inner gimbal and 225 mrad on the outer gimbal. When the gimbals move too fast into limit switches, measurements are not possible. Therefore, only measurements within a certain range is taken into consideration for development of the simulation models. The mean fit of the non-linear simulation model on to the actual gimbal measurements is 94.17 % for the inner gimbal and 94.04 % for the outer gimbal.

The non-linear simulation models are reduced to simplified non-linear simulation models. The simplified non-linear simulation models each contain a non-linear gain function that approximates the non-linear elements which affects movement of the gimbals. The mean fit of the simplified non-linear simulation model on to the actual gimbal measurements is 91.86 % for the inner gimbal and 83.75 % for the outer gimbal. Lastly, linear simulation models are deduced from the simplified non-linear simulation models. The mean fit of the linear simulation model on to the actual gimbal measurements is 48.09 % for the inner gimbal and 72.48 % for the outer gimbal. Controllers are then developed based on these models.

Three controller strategies are evaluated. At first, linear controllers are developed for the linear models, and evaluated on the other models, as well as the actual gimbals. A different controller is developed for each gimbal. On the inner gimbal, a Proportional (P) controller is implemented. On the outer gimbal, a P controller with a designed control transfer function is developed. This transfer function is designed using Root Locus and Bode plot tools in Matlab. These linear controllers deliver the least satisfactory results.

The required performance criteria is a maximum mRMS position error of less than 2.00 mrad. On the inner gimbal linear control gives a maximum mRMS position error of 3:50 mrad, and the outer gimbal a maximum mRMS position error of 7:05 mrad is achieved.

Next, non-linear control elements are included with linear control action in the form of gain scheduling. The non-linear parameters present with each gimbal form the base of the gain scheduling control. Gain scheduling aims to compensate for the non-linear parameters. The gain scheduling function is determined with the defined input voltage range. This controller is designed on the simplified non-linear model, and evaluated on the non-linear model as well as the actual gimbal. For the inner gimbal, gain scheduling is implemented with Proportional-Derivative (PD) control action and does not provide much of an improvement. The maximum mRMS position error is 3.08 mrad. For the outer gimbal, gain scheduling is also implemented with PD control action and shows improvement over linear control. When the gain scheduling function is extended beyond the defined input voltage range, further improvements on the outer gimbal is observed. The maximum mRMS position error reduces to 4.70 mrad.

Lastly, a controller is developed on the non-linear model. It is also evaluated on the actual gimbal. This controller should perform the best, as it combines linear and non-linear control actions from the other models and compensates for their shortcomings. This compensation is in the form of feedforward control action, which increases response time of the controlling action. For the inner gimbal, feed-forward control is added with PD compensation which gives the best results, a maximum mRMS position error of 2.6 mrad. This does not meet the requirement of less than 2.00 mrad, but is still seen as good enough as the position error percentage increases from 0.6 % to 0.79 %, which is still close to the flare trajectory on a HILS platform. For the outer gimbal, feed-forward control is added to the PD compensator with an extended gain scheduling function. This provides the best result of all the controllers, and performs even better than the inner gimbal controller. On the outer gimbal, a maximum mRMS position error of 1.47 mrad is obtained, which satisfies the requirement of less than 2.00 mrad.

This study contributes to control systems by detailing the system identification process in order to develop a suitable controller for a gimbal system actuated with dc motors. Methods for controlling hardware with non-linear elements that influence its operation are analysed. It allows implementation of a mathematical model in hardware in order to provide additional capability for countermeasures evaluation. It contributes to the HILS environment with development of a flare trajectory. This gives the HILS platform the ability to evaluate counter-countermeasures on missiles.

Although a single flare trajectory result is shown in this study it has the ability to showcase more flare ejection scenarios by following the same procedure as outlined in the modelling section. For future work, different flare trajectories can be implemented and evaluated on the hardware.