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Disclaimer: This website contains copyrighted material, and its use is not always specifically authorized by the copyright owner. Take all necessary steps to ensure that the information you receive from the post is correct and verified.

1.
motivation

Flow control is required in many fields of applications such as,
energy, transportation, health and security. Though fluid flow has
high-dimensional, multi-layer physics and nonlinear system characteristics, it
can be approximated by some of the dominant low-dimensional system features. Since
performance of a model predictive controller (MPC) significantly depends on the
accuracy of its system prediction model, intractable complex systems pose
difficulty in designing such a controller which is otherwise efficient for the
particular application. The article [1] presents a DeepMPC controller where sensor-based observable
low-rank system states are used to generate a recurrent neural network (RNN)
based data-driven predictive system model for a real-time MPC implemented in fluid
flow control.

2.
Main Contributions

i. DeepMPC architecture is implemented for complex fluid flow system exhibiting broadband phenomena.

ii. Instead of using assumptions of full system states, the “surrogate” predictive system model uses only observable system states for future prediction. Thus, the method achieves a trade-off between accuracy and efficiency in capturing the essential physical system mechanisms.

iii. The proposed learning approach for the RNN utilizes limited past information from the sensors.

Figure 1: DeepMPC with surrogate RNN
prediction model presented in [1].

3.
METHOD

A.
DeepMPC

i. Finite Open loop control problem with quadratic cost. Penalties assigned on deviation from reference trajectory, control input and any variation in the control input. The last component among the three restricts sudden change in the control input.

ii. Surrogate system state prediction model, based on deep RNN architecture, is generated using control relevant observable sensor-based system states. For this flow control model, the states are lift and drag.

1.
RNN based predictive model
design:

a.
Decoder:

i. Performs actual prediction task

ii. N-cell for N time steps in the prediction horizon

b.
Encoder:

i. Predicts latent states and thereby accounts for long-term dynamics.

2.
RNN based MPC problem is solved
using gradient based optimization method.

3.
The gradient information with
respect to the control inputs is calculated using backpropagation-through-time.

iii. Training RNN:

1.
Offline three-stage training [2] with time-series data of observable system states.

2.
Training data, i.e., a
time-series data of the lift and the drag, is generated using random but
continuously variable control sequence of rotation force on cylinder(s).

4. Result Summarization

A.
Setup:

A detailed simulation model of the full
system is used instead of a real physical system. It is solved by OpenFOAM
solver using finite volume discretization.

B.
Experiments:

Objective:
The objective is to control the cylinder(s)
such that

Four flow (laminar regime) control models with different complexity
levels are considered:

i. One cylinder: Flow around a single cylinder

1.
RNN prediction evaluated on
exemplary control input sequence which showed accurate prediction for both lift
and drag except for a very small duration at the start of the experiment.

2.
Successful showcase of tracking
control of maintaining a schedules lift sequence for 20 sec with bounded
rotation control input.

3.
Reynolds number () is
assumed to be 100.

4.
Training dataset:

a.
Random rotation between -2 to
+2 chosen at every 0.5 sec. Thus, high input frequencies are avoided

b.
Intermediate control inputs are
computed using spline interpolation for every 0.1sec.

c.
A time-series with 110 000
datapoints are used for RNN training corresponding to 11 000sec.

ii. Fluidic Pinball: Control the flow around three cylinders, two of which can be rotated the third one is fixed, as shown in Figure 1.

Figure 2: System is controlled by rotating
cylinders 1 and 2 with respective angular velocities and [1].

1.
Objective is to follow three
given lift trajectories for each cylinder by rotating cylinders 1 and 2.

2.
considered as the base case, other two chaotic
cases with and are analyzed.

3.
Training dataset:

a.
Random rotation between -2 to
+2 chosen for each cylinder at every 0.5 sec.

b.
Intermediate control inputs are
computed using spline interpolation for every 0.005sec.

c.
Time series with 150 000, 200
000 and 800 000 are used for and respectively.

4.
In
order to improve performance for more chaotic systems with and , knowledge
regarding physical system characteristic is used by incorporating symmetric
input and corresponding lift data along the horizontal axis. This reduces the
tracking error by 50%.

5.
Robustness of the system is
tested by performing five identical experiments with , using
10%, 15% and 100% of symmetrized training data points. No trend is observed
with respect to the amount of training data.

Figure 3: DeepMPC lift tracking performance for laminar flow around rotating cylinders [1].

Figure 4: Re = 100 with online update [1].

6.
Finally,
online data is collected from the feedback loop at each time step and new data
collected over 25sec for each update. These 500 datapoints within each interval
is used to further train the RNN surrogate model. This has significantly
improved the performance of the DeepMPC as compared to (a) [1] in Figure 3.
Online update of the RNN system reduces both tracking error and control cost.

5.
SUGGESTED FUTURE WORK

The surrogate RNN prediction model proposed for the DeepMPC in this
article can be very usefully implemented for many practical engineering
problems where the complete system description is too complicated and poses
significant difficulty in solving related control problems. This method can be
used for system modelling with targeted observable states which predominantly
define respective system behaviour. This improve real-time implementation of
MPC for complex nonlinear systems.

REFERENCES:

[1] K. Bieker, S. Peitz, S. L. Brunton, J. K.-
arXiv preprint arXiv, and 2019, “Deep model predictive control with online
learning for complex physical systems,” 2012.

[2] I. Lenz, R. Knepper, and A. Saxena,
“DeepMPC: Learning Deep Latent Features for Model Predictive Control,” in Robotics:
Science and Systems XI, 2015.

REVIEW ON: Markov Chain Monte Carlo Simulation of Electric Vehicle Use for Network Integration Studies

Source: [1] Y. Wang, D. Infield, Markov Chain Monte Carlo simulation of electric vehicle use for network integration studies, International Journal of Electrical Power & Energy Systems, Vol.99, 2018, Pages 85-94

Disclaimer: This website contains copyrighted material, and its use is not always specifically authorized by the copyright owner. Take all necessary steps to ensure that the information you receive from the post is correct and verified.

1. Paper Motivation

As the penetration of electric vehicles (EVs) increases, their patterns of use need to be well understood for future system planning and operating purposes. Using high resolution data by 10 minutes, accurate driving patterns were generated by a Markov Chain Monte Carlo (MCMC) simulation. However, previous MCMC simulation works was not complete in the sense that model results were not subject to verification and uncertainty analysis for practical network assessment was not undertaken. The present paper includes both these important elements.

2. Methods

Method Name: Time-inhomogeneous Markov Chain Monte Carlo (MCMC)
simulation

Description: The EV movement was simulated using a discrete-state,
discrete-time Markov chain to define the states of all the EV at each time step
of T minutes. It was assumed that, at every unit of time, one and only one
event from a set of a finite number of events can occur to a given EV.

Four events were
considered: {D, H, W, C}, correspond to ‘driving’, ‘parking at home’, ‘parking
at workplace’, and ‘parking at commercial areas’ respectively

Proposed Markov
Chain Diagram:

Fig. 1. Markov
Chain diagram of possible vehicle state transitions at time t

From time step t-1
to t, the associated transition probability is given for each possible
transition at this specific time stamp. For instance, P^{t}_{H->D}
indicates the probability of the vehicle being ‘D’ at t given being ‘H’ at time
t-1.

3. Paper structure

1) Review Previous Markov Chain Simulation of Electric Vehicle →

2) Introduce the survey data,
the 2000 UK Time of Use Survey (TUS) data →

3) A matrix representation of the transition
diagram at time t, Tt, is shown by Eq. (1) →

An example of the
state transition matrix at 8:40 am (t = 29, t0=4am, 4am+29*10min=8:50am) is
shown in Eq. (2),

→ Verification of proposed MCMC method by convergence analysis.→

4) Distribution grid case study by OpenDSS software (Case
1 commercial, Case 2 residential).

Case 1: A University building at
Strathclyde, accommodates up to 300 workers, and has a nominal parking
availability for approximately 100 cars. This building is supplied by a
dedicated 1000 kVA transformer.

Case 2: low-voltage single-phase domestic
network that consists of 17 households.

Fig. 2. Case 2 Single
phase distribution network layout.

3.Paper Results

Results Description: 24 hour Load (KVA) profile in
grids, before and after EV connected.

Fig. 3. (Upper)Aggregate demand of workplace EV charging. And (Lower) averaged voltage profile for Household 17 with 99% CI under full EV penetrations.

Notes:

Case 1 : An office building, approximately 100 cars, 100% EV penetration level, that is, 100 out of 100 cars are EV. This building is supplied by a 1000 kVA transformer.

For Case 1, a 1000 kVA transformer would easily survive the extra EV load for both standard and fast charging cases. A more typical transformer for this building with rating of nearer 500 kVA would, however, fail to supply the EV related load in the fast charging scenario.

Case 2: low-voltage single-phase community consists of 17 households.

For Case2, EV penetration in this case causes a severe voltage violation of the network (with specified tolerance of [−0.06 +1.10] p.u.,

4. Summarization

1) Markov Chain Monte Carlo simulation, as
a numerical approach, can be used to generate
different electricity load profiles according to various EV charging
schemes.

2) The impact of the additional EV charging
loads on the local distribution network can be assessed by identifying the
expected value and associated uncertainty, as measured by the standard
deviation, for various grid operational metrics, such as thermal loading, voltage profiles, transformer loss of life, energy
losses, and harmonic distortion levels.

3) The uncertainty identification of these
different metrics requires large number of trials from MCMC simulation to achieve
convergence. These uncertainties could not be generated directly by sampling
from the original TUS dataset due to its size limitation.

4) Also, the same steps of MCMC approach,
as described in this work, can be applied to new data sets for extracting their
own inherent statistical characteristics.

5.
SUGGESTED FUTURE WORK

The EV movement was simulated using a discrete-state, discrete-time
Markov chain for four events {D, H, W, C}, correspond to ‘driving’, ‘parking at
home’, ‘parking at workplace’, and ‘parking at commercial areas’ respectively

The model can be extending to EV Charging
States, including V2G and G2V, and further implemented in reinforcement leaning
problems.

F: Uncertainty
analysis of detailed network impact.

✓: model feature is
included in a suitable manner.

✗: model feature not included.

—: not relevant.

References

[1] T.-K. Lee, Z. Bareket, T. Gordon, Z.S. FilipiStochastic modeling for studies of real-world PHEV usage: driving schedule and daily temporal distributions IEEE Trans Veh Technol, 61 (4) (May 2012), pp. 1493-1502

[2] F.J. Soares, J.P. Lopes, P.R. Almeida, C.L. Moreira, L. SecaA stochastic model to simulate electric vehicles motion and quantify the energy required from the grid PSCC, Stockholm, Sweden (2011)

[3] Iversen EB, Møller JK, Morales JM, Madsen H.
Inhomogeneous Markov models for describing driving patterns. IEEE Trans Power
Syst.

[4] A. Lojowska, D. Kurowicka, G. Papaefthymiou, L. van der Sluis Stochastic modeling of power demand due to EVs using copula IEEE Trans Power Syst, 27 (4) (2012), pp. 1960-1968

[5] A. Ashtari, E. Bibeau, S. Shahidinejad, T. MolinskiPEV charging profile prediction and analysis based on vehicle usage data IEEE Trans Smart Grid, 3 (1) (2012), pp. 341-350

[6] A.D. Hilshey, P.D. Hines, P. Rezaei, J.R. DowdsEstimating the impact of electric vehicle smart charging on distribution transformer aging IEEE Trans Smart Grid, 4 (2) (2013), pp. 905-913

[7] F. Rassaei, W.S. Soh, K.C. ChuaDemand response for residential electric vehicles with random usage patterns in smart grids IEEE Trans Sustain Energy, 6 (4) (2015), pp. 1367-1376

[8] Fluhr J, Ahlert KH, Weinhardt C. A
stochastic model for simulating the availability of electric vehicles for
services to the power grid. In: System Sciences (HICSS), 43rd Hawaii
International Conference on. IEEE; 2010. p. 1–10.

[9] S. Shafiee, M. Fotuhi-Firuzabad, M. RastegarInvestigating the impacts of plug-in hybrid electric vehicles on power distribution systems IEEE Trans Smart Grid, 4 (3) (2013), pp. 1351-1360

[10] Wang Y, Huang S, Infield D. Investigation
of the potential for electric vehicles to support the domestic peak load. In:
Electric Vehicle Conference (IEVC), IEEE. Dec. 2014. p. 1–8.

Disclaimer: This website contains copyrighted material, and its use is not always specifically authorized by the copyright owner. Take all necessary steps to ensure that the information you receive from the post is correct and verified.

1. Paper Motivation

Human intuitions in solving a problem are hard to replicate in robotics. For complex non-linear dynamics such as robotic food cutting, difficulties are faced in designing controllers specifically when the system dynamics vary temporally as well as with its surrounding environmental properties. In this article the authors have implemented deep learning to generate a recurrent conditional deep predictive model for a model predictive controller (MPC) used in robotic food cutting [1].
While MPC has already been proven efficient in solving control problems in various fields, the difficulty mostly lies in its implementation since it involves rigorous prediction optimization as each time step with considerably complex system model that sufficiently represents the dynamic system state transition with time in response to the control inputs. However, with rapid advancements in the field of machine learning, available system data can be exploited to design a simpler yet accurate system models that sufficiently approximates the system behaviours and generate reliable predictions for the MPC. In this article, the authors have showcased that deep architecture can help improve the performance of MPC and its real time implementation.

2. Main Contributions

DeepMPC: Online continuous-space real-time feedforward MPC using novel deep architecture which models system dynamics conditioned on learned latent system properties.

Novel multi-stage pre-training learning algorithm for recurrent network which avoids over fitting problem and the “exploding gradient” problem.

Multiplicative conditional interactions and temporal recurrence are used to model inter-material and time varying intra-material characteristics.

Instead of using temporally local information this model uses learned recurrent features to integrate long-term information and model unobserved system properties.

Implementation for real-time application. Fast inference with prediction horizon 1s = 100 samples, gradient evaluation at 1.2kHz.

3. Method

A.
Problem definition:

Figure 1: End-effector gripper with axes used in [1]

Figure 2: Block diagram of DeepMPC [1]

The objective is to cut the food items of different varieties, along
Z direction using a force applied along the end-effector X axis.

B.
Modelling of time-varying
nonlinear dynamics for the MPC prediction model with deep networks

i. Dynamic response features:

1.
Basic input features for the
deep predictive model incorporate both control inputs as well as system states
(output for the prediction model).

2.
To capture higher-order and
delayed-responses in the model time-blocks are used to train the model instead
of single timestep data.

ii. Conditional dynamic responses: to incorporate both short-term and long-term information in modelling local system dynamics three sets of features are considered,

1.
Current control inputs

2.
Past time block’s dynamic
response

3.
Latent features modelling
long-term observation.

iii. Long term recurrent latent features: transforming recurrent units (TRUs) are introduced that retains state information from previous observations by using

1.
Outputs from previous TRU.

2.
Short-term response features
from current and past time blocks.

C.
Learning and inference

i. Three step learning:

1.
Phase 1:Unsupervised pre training (similar to the sparse
auto-encoder algorithm) – to obtain a good initial estimation of latent
features and train the non-recurrent parameters of transforming recurrent unit
(TRU).

2.
Phase 2:Single step prediction training (2^{nd} pre training
stage) – trains to predict a single timestep in the future. Recurrent weights
from TRU are set to zero. Minimizes prediction error for initial set of
selection for model parameters i.e. weights. Generates the pre-trained set of
initial parameter values.

3.
Phase 3:Warm-latent recurrent training – set of initial parameters from
Phase 2 is used for initializing the recurrent prediction system which
generates system state predictions. The system is then optimized to minimize
the sum-squared prediction error for finite time horizon using algorithm
similar to backpropagation-through-time.

While
implementing online, the model is trained for warm start where the latent
system states are propagated for a few time blocks without any optimization or
prediction.

ii. Inference: The trained model is then recurrently used to predict future system states for a finite time horizon by using predicted system states, latent states and control inputs for subsequent time blocks. No online optimization is necessary for inference.

D.
Online MPC

i. Offline prediction process: As described earlier, model parameters from the deep predictive model are fed to the optimization process offline.

ii. Control process:

1.
Calculated end-effector (EE)
pose using forward kinematics.

2.
Stiffness control for restoring
forces along axes not controlled by MPC.

3.
Implements joint torques
received form the shared memory space as optimized MPC control signals.

4.
Updated the EE pose in the
shared memory space to be used by the optimization process.

iii. Optimization process:

1.
System model parameters: available
offline

2.
MPC cost function parameters: adjustable
online

a. penalizes the knife motion along the X and Z axis.

b. generates gradient w.r.t states which is subsequently used by the model to generate a gradient with respect to control inputs i.e. forces using the backpropagation through time.

3.
The
gradients with respect to forces are then optimized by a gradient descent-based
algorithm to generate the control signal which is used by the control process
from the shared memory space.

E.
Dataset

i. Large-scale dataset of 1488 material cuts for 20 different classes.

ii. Over 450 real-time robotic experiments.

4. RESULT SUMMARIZATION

A. Prediction experiments:

Baseline:

1. Linear state-space model, ARMAX model with weights on past states, K-nearest neighbour (5-NN) model.

As shown in Figure 2 [1], the proposed prediction model outperforms the baseline methods. It gives 95% confidence interval of prediction error.

Figure 3 [1]: Prediction error: Mean L2 distance (in mm) from predicted to ground-truth trajectory from 0.01s to 0.5s in the future [1].

B. Robotic experiments:

Baseline:

1. Class-generic stiffness controller

2. Class-specific stiffness controllers

3. An algorithm presented in [2] where class-specific material properties are mapped to haptic clusters.

Figure 4 [1]: Mean cutting rates, with bars showing normal standard deviation, for ten diverse materials Red bar uses the same controller for all materials, blue bar uses the same for each cluster given by [2], purple uses a tuned stiffness controller for each, and green is online MPC method proposed in [1].

This approach showed 46% improved accuracy as compared to a standard recurrent deep network. Related experimental videos and discussion can be found in http://deepmpc.cs.cornell.edu/ [1]

5. Suggested future work

The deep prediction model for MPC as proposed in this article can be useful for different non-linear applications for example, in building energy management where implementing MPC needs building specific prediction model. With deep predictive model for MPC, available seasonal forecast data, time-of-use and control data from existing control system can be used to model different types of buildings. Adaptive training of the deep predictive model can help in generalizing the MPC designing for building sector.

REFERENCES:

[1] I. Lenz, R. Knepper, and A. Saxena, “DeepMPC: Learning Deep Latent Features for Model Predictive Control,” in Robotics: Science and Systems XI, 2015. [2] M. C. Gemici and A. Saxena, “Learning haptic representation for manipulating deformable food objects,” in 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 638–645.