Model predictive control of a miniaturized linear single-piston cryocooler

Abstract

Remote Sensing Satellites use IR (Infra-Red) detectors for imaging in 1 um to 15 um bands. Most of these detectors are operated at cryogenic temperatures to extract the low-level signal from the background noise. Stirling cycle based miniature active linear cryocoolers are now being widely used for cooling these IR detectors to cryogenic temperatures. The Cryocooler Control Electronics (CCE) used for driving the cryocoolers, often uses a proportional-Integral-Derivative (PID) controller for controlling the cold tip temperature. Besides, the CCE for most space-borne missions uses a Feed-Forward (FF) control to reduce the vibration export coming from the movement of compressor pistons. The stringent cold-tip temperature stability and vibration control requirements pose a challenge to traditional cryocooler controllers, motivating to investigate and design more appropriate control structure and well-tuned well-performing controllers. This paper presents a novel scheme of simultaneous temperature and vibration control for a single-piston linear cryocooler based on an advanced Model Predictive Control (MPC) algorithm using multivariable (SIMO/MIMO) model of a miniature linear cryocooler. The MPC is one of the most popular advanced control algorithm which uses mathematical model of the underlying system or plant to predict the future response i.e. predicts future errors (in controlled variables) and uses constrained optimization to compute as decision variables a set of control actions (or manipulated variables) to minimize certain error-norm of controlled variables for specified horizon in future optimally respecting specified operational constraints. Because of its inherent capabilities to predict future errors using the multivariable model, and systematic handling of operational constraints, the proposed approach can provide better performance compared to existing cryocooler control approaches. Data-driven First Order Plus Dead Time (FOPDT) model of cryocooler has been developed and a low-cost speaker based actuator has been used for controlling the cryocooler vibration export. The paper presents the comparisons of simulated and measured control performance obtained using PI (SIMO case), PI + FF Control (MIMO case) and proposed MPC schemes (SIMO and MIMO cases) for the temperature and vibration control of a single-piston Stirling cryocooler. Significant improvement in the controller performance parameters such as Integral Absolute Error (ISE) and Integral Square Error (ISE) has been achieved with the MPC scheme. Besides, MPC is found to demonstrate significantly better performance in terms of satisfying the specific operational constraints, e.g. vibrations limits.