CEC Conference, July 10, 2017 Comparison of different cryogenic control strategies via simulation applied to a superconducting magnet test bench at CERN M. PEZZETTI, Prof. Pasquale ARPAIA, Prof. Hervé COPPIER, Prof. Mario DI BERNARDO, Donato DE PAOLA, Agostino GUARINO, Benjamin LUZ PEDEMONTE CERN, 1211 Geneva 23, Switzerland Aknowledegments: the cryo operator team

INDEX Introduction Model synthesis and analysis Proposal Hi Lumi – LHC HFM Schema HFM Pre - cooling Model synthesis and analysis ECOSIM Switched Control Schema Cascade Control Schema Proposal Advanced Control Adaptive Cascade Controller Model Predictive Controller Controllers Comparison Conclusions structured

HFM Schema Biggest CRYOSTAT present at CERN

HFM Pre-cooling Pre – Cooling process: Supply line Actuators 300K 80K The way to reach the steady state temperature of 1.9 K is divided in three parts: Precooling from 300 K to 80 K, lead by GHe [10h – 200h, adjustable for each magnet]; Cooling from 80 K to 4.5K, lead by LHe [10h]; Cooling from 4.5 K to 1.9 K, lead pumping superfluid LHe [24h]. Pre – Cooling process: Supply line Actuators TWO VALVES Physical Constraints: Pipe Pressure < 3.5 - 4 bar Max Flow 50 to 90 g/s Difference of temperature on the magnet 50 K or lower.

Switched Control Schema Cold Valve(CV870) Warm Valve (CV871) PID 1 PID 4 PID 2 PID 5 PID 3 PID 6 3 different PIDs on each valve. The control signal is the minimum between PIDs outputs PRO: Intuitive Schema, a PID for each constraint for each valve. CONS : semi-automatic control need an intensive operation work!

Cascade Control Schema Current Controller PRO: Well organised strategy. PIDs cascade follows the logical steps of flow control with a smooth mix of cold and warm gaseous helium. CONS: Satisfaction of each constraints at the same time is guaranteed only in presence of nominal conditions. When this does not happens, some parameters exceed their limits.

EcosimPro EXPERIMENT SCHEMATIC Model tuned to fit real data taken from the field. EXPERIMENT Parameters Solver Tolerance SCHEMATIC EcosimPro is a Modelling and Simulation Software. Availability of a Cryogenic Library (CRYOLIB) developed at CERN. Chance to validate control schemas in silico. SIMULATIONS

Identification Strategy CV870 FT870 CV871 FT871 PT874 TT809a TT809b TT809d TT809e Our proposal is to identify a black box model of the plant in order to develop: A new Adaptive Cascade Controller A Model Predictive Controller Moreover, the controllers have to cool down the system in the most uniform way possible (ideally, following a ramp) even in presence of disturbances. The controllers must be user-friendly for the operators. TT800g At 80 K At 300 K

Adaptative Cascade Controller proposal Reference: Cool Down Nominal Time Constraints: Delta T Pressure Flow Pro: Uniform Cooling User Friendly Simple to implement Cons: (Chattering)

Inner Loop It works on the basis of a temperature error. Piping System Model is a Discrete Time System. (Discrete) PI tuned empirically (MATLAB tool). The loop is able to follow a descending ramp reference with no error. Spike on the Warm Valve opening due to the exceeding of physical limit. Temperature

External Loop Controller Constraint controllers give as output a signal between 0 and 1. Different strategies to choose the way they evaluate this output. Currently, the simplest choice has been tested. Performance oriented and Safety oriented solution could be tested.

Performances Simulation Details: Nominal Time: 7 Hours Delta T: 30K Flow: 90 g/s

MPC Proposal Uses the Piping System Model to calculate the present and anticipate n-step ahead future responses by modelling a prediction model. Optimizes the valves openings adopting a linearly constrained quadratic programming. It converges to the desired temperature set point by minimizing its tracking error, rate-of-change of the inputs.

MPC Block Schema

MPC Simulation Linear Discrete Time Piping System Model Temperature set point fixed from 300 K to 80 K. Optimizer block generates reference tracking error based on the prediction horizon.

Comparison results of the control models 1/2 Cryogenics parameters: 8 Hours, 30 K delta T, flow, 60 g/s, 2,5 bar pressure*. Working with the same operative conditions, ACC presents a faster response while MPC provides a smoother one. Choosing a different strategy for the ACC external controller, the performances could be enhanced, smoothing the response and reducing oscillations.

Comparison 2/2 Regarding Delta T, Figure 14 a, both controllers satisfy the constraint. ACC approaches the limit faster than MPC, but its response presents more oscillations than the other MPC evaluates the flow on the basis of a linearly constrained quadratic programming, increasing the cold flow and decreasing the warm one linearly. ACC has a different mixing strategy, in which the total flow decreases during time. Because of the strategy chosen in the external controller, oscillations arise when the Delta T approaches to its constraint.

Conclusions This study enhance the possibility to use advance control (user friendly!) in real installation at CERN. The difference between the proposed controllers is that ACC provides a faster response with some oscillations, while MPC is slower but smoother, both method will not need an operation supervision during cold down phase. ACC solution is more user friendly than MPC and it’s easier to implement but more difficult to use in a PLC environment.

Characteristic of the Valves and Pressure Fitting Electrical – Hydraulic Analogy

Piping system identification Open loop cycle Fit to Estimation Real Data Y= 57.16% Matlab identification toolbox Transfert function equation Closed loop Cycle Fit to Validation data: 81.22% Good dynamic replication RMS: 9.93K Estimation Method: Process Model 𝐺 𝑢 = 𝐾 𝑢 𝑒 − 𝑇 𝑑𝑢 𝑠 (1+ 𝑇 𝑝1𝑢 𝑠)(1+ 𝑇 𝑝2𝑢 𝑠) u=1,2

Cryostat Identification Fit to Estimation Real Data Y1= 98.52% Y2= 96.03% Y3= 98.28% Y4= 86.47% Fit to Data: 63.17% RMS: 11.09K Fit to Data: 50.45% RMS: 20.24K Estimation Method: Subspace Method for State Space Identification 4th order dx/dt=Ax+Bu y=Cx Fit to Data: 62.52% RMS: 11.33K Fit to Data: 57.26% RMS: 17.43K Good dynamic replication