SLIDE 1 On the importance of tailored modeling data for model-based control
Xavier Bombois
CNRS Laboratoire Amp` ere (Ecole Centrale de Lyon)
IUAP study day - 28 November 2017
Xavier Bombois (CNRS) Identification for control IUAP study day 1 / 34
SLIDE 2 Introduction
Without models, no advanced engineering Without models, no satisfactory control systems Engineering systems become more and more complex A perfect model is an illusion Good news: for a given objective (e.g. control), only a few of the system properties are really relevant to be modeled Specification for an appropriate model for control: a model with little uncertainty for these relevant properties; large uncertainty allowed for all
Xavier Bombois (CNRS) Identification for control IUAP study day 2 / 34
SLIDE 3 Introduction
Without models, no advanced engineering Without models, no satisfactory control systems Engineering systems become more and more complex A perfect model is an illusion Good news: for a given objective (e.g. control), only a few of the system properties are really relevant to be modeled Specification for an appropriate model for control: a model with little uncertainty for these relevant properties; large uncertainty allowed for all
Xavier Bombois (CNRS) Identification for control IUAP study day 2 / 34
SLIDE 4 Introduction
Without models, no advanced engineering Without models, no satisfactory control systems Engineering systems become more and more complex A perfect model is an illusion Good news: for a given objective (e.g. control), only a few of the system properties are really relevant to be modeled Specification for an appropriate model for control: a model with little uncertainty for these relevant properties; large uncertainty allowed for all
Xavier Bombois (CNRS) Identification for control IUAP study day 2 / 34
SLIDE 5 Without data, no model Data are always required to determine/identify a model of a system Data obtained by applying an excitation signal at the input of the system and by measuring the effect of this excitation at the output The excitation signal perturbs the systems and leads to an economical cost
- particularly important when the system is a production unit
Objective: to obtain an appropriate model for control at a reasonable cost
Xavier Bombois (CNRS) Identification for control IUAP study day 3 / 34
SLIDE 6 Without data, no model Data are always required to determine/identify a model of a system Data obtained by applying an excitation signal at the input of the system and by measuring the effect of this excitation at the output The excitation signal perturbs the systems and leads to an economical cost
- particularly important when the system is a production unit
Objective: to obtain an appropriate model for control at a reasonable cost
Xavier Bombois (CNRS) Identification for control IUAP study day 3 / 34
SLIDE 7 Objective: to obtain an appropriate model for control at a reasonable cost Our solution: to design the excitation signal in an optimal way This signal must be optimized in order to uniquely capture those relevant system properties for control = ⇒ minimal economical cost leading nevertheless to an appropriate model for control
Xavier Bombois (CNRS) Identification for control IUAP study day 4 / 34
SLIDE 8 Objective: to obtain an appropriate model for control at a reasonable cost Our solution: to design the excitation signal in an optimal way This signal must be optimized in order to uniquely capture those relevant system properties for control = ⇒ minimal economical cost leading nevertheless to an appropriate model for control
Xavier Bombois (CNRS) Identification for control IUAP study day 4 / 34
SLIDE 9 Objective: to obtain an appropriate model for control at a reasonable cost Our solution: to design the excitation signal in an optimal way This signal must be optimized in order to uniquely capture those relevant system properties for control = ⇒ minimal economical cost leading nevertheless to an appropriate model for control
Xavier Bombois (CNRS) Identification for control IUAP study day 4 / 34
SLIDE 10 Combination Identification and Control
e.g. high level controller design for an industrial process
PROCESS
input= excitation
disturbances IDENTIFICATION EXPERIMENT
The excitation signal perturbs the system and lead to an economical cost - that can e.g. be measured by the power of the excitation signal
Xavier Bombois (CNRS) Identification for control IUAP study day 5 / 34
SLIDE 11 Combination Identification and Control
e.g. high level controller design for an industrial process
PROCESS
input= excitation
disturbances IDENTIFICATION EXPERIMENT
The excitation signal perturbs the system and lead to an economical cost - that can be e.g. measured by the power of the excitation signal
Xavier Bombois (CNRS) Identification for control IUAP study day 5 / 34
SLIDE 12 Combination Identification and Control
PROCESS
input= excitation
disturbances IDENTIFICATION EXPERIMENT
Identification Data → Uncertain model
Control Model → Controller
Performance evaluated a-priori by robustness analysis wrt. the model uncertainty
Xavier Bombois (CNRS) Identification for control IUAP study day 6 / 34
SLIDE 13 Combination Identification and Control
PROCESS
input= excitation
disturbances IDENTIFICATION EXPERIMENT
Identification Data → Uncertain model Control Model → Controller
Performance evaluated a-priori by robustness analysis wrt. the model uncertainty
Xavier Bombois (CNRS) Identification for control IUAP study day 6 / 34
SLIDE 14 Combination Identification and Control
PROCESS
input= excitation
disturbances IDENTIFICATION EXPERIMENT
Identification Data → Uncertain model Control Model → Controller
Performance evaluated a-priori by robustness analysis wrt. the model uncertainty
Xavier Bombois (CNRS) Identification for control IUAP study day 6 / 34
SLIDE 15 Combination Identification and Control
PROCESS
input= excitation
disturbances IDENTIFICATION EXPERIMENT
Identification Data → Uncertain model Control Model → Controller
PROCESS input
disturbances Controller MODEL-BASED CONTROL SYSTEM
Performance evaluated a-priori by robustness analysis wrt. the model uncertainty
Xavier Bombois (CNRS) Identification for control IUAP study day 6 / 34
SLIDE 16 Identification of an appropriate model for control: a complex problem
Identification and Robust Control: well established scientific fields (prediction error identification, H∞ control, µ-analyzis), but in a rather independent way An optimal combination of these two fields is a complex problem In other words, obtaining appropriate models for control via identification is a difficult task
Gevers, “Towards a joint design of identification and control?”, Essays on Control: Perspectives in the Theory and its Applications, 1993 Xavier Bombois (CNRS) Identification for control IUAP study day 7 / 34
SLIDE 17 Identification of an appropriate model for control
the uncertainty of the identified model plays a central role in the interaction identification-control
Xavier Bombois (CNRS) Identification for control IUAP study day 8 / 34
SLIDE 18 A bit of theory: uncertainty of an identified model
True system: y(t) = G(q, θ0)u(t) + H(q, θ0)e(t) Excitation signal u(t) = ⇒ Data: Z N = {u(t), y(t) t = 1...N} Estimation of θ0 ∈ Rk via prediction error identification: ˆ θN = arg min
θ N
- t=1
- H(q, θ)−1 (y(t) − G(q, θ)u(t))
2 ˆ θN ∼ N(θ0, Pθ) = ⇒ θ0 ∈ U = {θ | (θ − ˆ θN)TP−1
θ (θ − ˆ
θN) < α} with a probability Pr(χ2(k) < α)
Xavier Bombois (CNRS) Identification for control IUAP study day 9 / 34
SLIDE 19 A bit of theory: uncertainty of an identified model
True system: y(t) = G(q, θ0)u(t) + H(q, θ0)e(t) Excitation signal u(t) = ⇒ Data: Z N = {u(t), y(t) t = 1...N} Estimation of θ0 ∈ Rk via prediction error identification: ˆ θN = arg min
θ N
- t=1
- H(q, θ)−1 (y(t) − G(q, θ)u(t))
2 ˆ θN ∼ N(θ0, Pθ) = ⇒ θ0 ∈ U = {θ | (θ − ˆ θN)TP−1
θ (θ − ˆ
θN) < α} with a probability Pr(χ2(k) < α)
Xavier Bombois (CNRS) Identification for control IUAP study day 9 / 34
SLIDE 20 A bit of theory: uncertainty of an identified model
True system: y(t) = G(q, θ0)u(t) + H(q, θ0)e(t) Excitation signal u(t) = ⇒ Data: Z N = {u(t), y(t) t = 1...N} Estimation of θ0 ∈ Rk via prediction error identification: ˆ θN = arg min
θ N
- t=1
- H(q, θ)−1 (y(t) − G(q, θ)u(t))
2 ˆ θN ∼ N(θ0, Pθ) = ⇒ θ0 ∈ U = {θ | (θ − ˆ θN)TP−1
θ (θ − ˆ
θN) < α} with a probability Pr(χ2(k) < α)
Xavier Bombois (CNRS) Identification for control IUAP study day 9 / 34
SLIDE 21 A bit of theory: uncertainty of an identified model
θ0 ∈ U = {θ | (θ − ˆ θN)TP−1
θ (θ − ˆ
θN) < χ}
.N
^ 0
.
Pθ = σ2
e
N 1 2π π
−π
FuF ∗
u Φu(ω) + FeF ∗ e σ2 e dω
−1
Fu(z, θ0) = 1 H0 ∂G(z, θ) ∂θ
and Fe(z, θ0) = 1 H0 ∂H(z, θ) ∂θ
Xavier Bombois (CNRS) Identification for control IUAP study day 10 / 34
SLIDE 22 Identification of an appropriate model for control
the uncertainty of the identified model plays a central role in the interaction identification-control
Pθ = σ2
e
N 1 2π π
−π
FuF ∗
u Φu(ω) + FeF ∗ e σ2 e dω
−1
The uncertainty of the identified model strongly depends on the identification experiment (i.e. the excitation signal) excitation ց (i.e. cost ց) = ⇒ size of the uncertainty ր A too large uncertainty makes it impossible to design a satisfactory controller
Bombois et al., “Robustness analysis tools for an uncertainty set obtained by prediction error identification”, Automatica, 2001 Bombois et al., “Least costly identification for control”, Automatica, 2006 Xavier Bombois (CNRS) Identification for control IUAP study day 11 / 34
SLIDE 23 Identification of an appropriate model for control
the uncertainty of the identified model plays a central role in the interaction identification-control
Pθ = σ2
e
N 1 2π π
−π
FuF ∗
u Φu(ω) + FeF ∗ e σ2 e dω
−1
The uncertainty of the identified model strongly depends on the identification experiment (i.e. the excitation signal) excitation ց (i.e. cost ց) = ⇒ size of the uncertainty ր A too large uncertainty makes it impossible to design a satisfactory controller
Bombois et al., “Robustness analysis tools for an uncertainty set obtained by prediction error identification”, Automatica, 2001 Bombois et al., “Least costly identification for control”, Automatica, 2006 Xavier Bombois (CNRS) Identification for control IUAP study day 11 / 34
SLIDE 24 Identification of an appropriate model for control
the uncertainty of the identified model plays a central role in the interaction identification-control
Pθ = σ2
e
N 1 2π π
−π
FuF ∗
u Φu(ω) + FeF ∗ e σ2 e dω
−1
The uncertainty of the identified model strongly depends on the identification experiment (i.e. the excitation signal) excitation ց (i.e. cost ց) = ⇒ size of the uncertainty ր A too large uncertainty makes it impossible to design a satisfactory controller
Bombois et al., “Robustness analysis tools for an uncertainty set obtained by prediction error identification”, Automatica, 2001 Bombois et al., “Least costly identification for control”, Automatica, 2006 Xavier Bombois (CNRS) Identification for control IUAP study day 11 / 34
SLIDE 25 Our paradigm for the optimal design of the identification experiment for control
Bombois et al., “Least costly identification for control”, Automatica, 2006
Design of the least costly identification experiment leading to a model uncertainty which is sufficiently small to enable satisfactory robust controller design Ideal compromise between the cost of the identification and the size of the uncertainty
Xavier Bombois (CNRS) Identification for control IUAP study day 12 / 34
SLIDE 26 Our paradigm for the optimal design of the identification experiment for control
Bombois et al., “Least costly identification for control”, Automatica, 2006
Design of the least costly identification experiment leading to a model uncertainty which is sufficiently small to enable satisfactory robust controller design Ideal compromise between the cost of the identification and the size of the uncertainty
Xavier Bombois (CNRS) Identification for control IUAP study day 12 / 34
SLIDE 27 Admissible uncertainty for control
Suppose that we have designed a controller C based on an identified model G(z, ˆ θN) C will be applied on the true system G(z, θ0) Question: Is the performance of the closed-loop system [C G(z, θ0)] satisfactory? θ0 is unknown, but lies in U Reformulated question: Is the performance of the closed-loop system [C G(z, θ)] satisfactory for all θ ∈ U?
Xavier Bombois (CNRS) Identification for control IUAP study day 13 / 34
SLIDE 28 Admissible uncertainty for control
Suppose that we have designed a controller C based on an identified model G(z, ˆ θN) C will be applied on the true system G(z, θ0) Question: Is the performance of the closed-loop system [C G(z, θ0)] satisfactory? θ0 is unknown, but lies in U Reformulated question: Is the performance of the closed-loop system [C G(z, θ)] satisfactory for all θ ∈ U?
Xavier Bombois (CNRS) Identification for control IUAP study day 13 / 34
SLIDE 29 Admissible uncertainty for control
Suppose that we have designed a controller C based on an identified model G(z, ˆ θN) C will be applied on the true system G(z, θ0) Question: Is the performance of the closed-loop system [C G(z, θ0)] satisfactory? θ0 is unknown, but lies in U Reformulated question: Is the performance of the closed-loop system [C G(z, θ)] satisfactory for all θ ∈ U?
Xavier Bombois (CNRS) Identification for control IUAP study day 13 / 34
SLIDE 30 Admissible uncertainty for control
Suppose that we have designed a controller C based on an identified model G(z, ˆ θN) C will be applied on the true system G(z, θ0) Question: Is the performance of the closed-loop system [C G(z, θ0)] satisfactory? θ0 is unknown, but lies in U Reformulated question: Is the performance of the closed-loop system [C G(z, θ)] satisfactory for all θ ∈ U?
Xavier Bombois (CNRS) Identification for control IUAP study day 13 / 34
SLIDE 31 Admissible uncertainty for control
Robustness analysis: [C G(z, θ)] satisfactory ∀θ ∈ U if Pθ respects a certain LMI: LMI(ˆ θN, P−1
θ ) > 0
linear in P−1
θ
Xavier Bombois (CNRS) Identification for control IUAP study day 14 / 34
SLIDE 32 Admissible uncertainty for control
LMI(ˆ θN, P−1
θ ) > 0
This LMI verifies that U is ”smaller” than the largest admissible uncertainty Uadm
ADMISSIBLE UNCERTAINTY Uadm FOR CONTROL
U
Uadm REFLECTS THE IMPORTANT PROPERTIES FOR CONTROL Xavier Bombois (CNRS) Identification for control IUAP study day 15 / 34
SLIDE 33 Optimal excitation signal for control
The size Pθ of U depends on Φu(ω) i.e. on the power of u(t) and on its frequency distribution Concentrating the power in an optimal frequency band allows to obtain the relevant information with the smallest power
Xavier Bombois (CNRS) Identification for control IUAP study day 16 / 34
SLIDE 34 Optimal excitation signal for control
The size Pθ of U depends on Φu(ω) i.e. on the power of u(t) and on its frequency distribution Concentrating the power in an optimal frequency band allows to obtain the relevant information with the smallest power
P1 P2 < DF1 DF2
MODEL UNCERTAINTY
Xavier Bombois (CNRS) Identification for control IUAP study day 16 / 34
SLIDE 35 Optimal excitation signal for control
The size Pθ of U depends on Φu(ω) i.e. on the power of u(t) and on its frequency distribution Concentrating the power in an optimal frequency band allows to obtain the relevant information with the smallest power
P1=Popt P2 < DF1 DF2=DFopt
V
Xavier Bombois (CNRS) Identification for control IUAP study day 16 / 34
SLIDE 36 Some remarks on our paradigm
convex optimisation problem minΦu(ω) 1 2π ∞
−∞
Φu(ω) dω s.t. LMI(ˆ θN, P−1
θ ) > 0 ⇐
⇒ LMI(ˆ θN, Φu(ω)) > 0
P−1
θ
= N σ2
e
1 2π π
−π
FuF ∗
u Φu(ω) + FeF ∗ e σ2 e dω
- Chicken-and-egg problem: ˆ
θN is replaced by a first guess Other definition of the cost of an identification problem?? power of the perturbations induced by the excitation signal on the normal operations of the system experiment duration for a given perturbation
Xavier Bombois (CNRS) Identification for control IUAP study day 17 / 34
SLIDE 37 Some remarks on our paradigm
convex optimisation problem minΦu(ω) 1 2π ∞
−∞
Φu(ω) dω s.t. LMI(ˆ θN, P−1
θ ) > 0 ⇐
⇒ LMI(ˆ θN, Φu(ω)) > 0
P−1
θ
= N σ2
e
1 2π π
−π
FuF ∗
u Φu(ω) + FeF ∗ e σ2 e dω
- Chicken-and-egg problem: ˆ
θN is replaced by a first guess Other definition of the cost of an identification problem?? power of the perturbations induced by the excitation signal on the normal operations of the system experiment duration for a given perturbation
Xavier Bombois (CNRS) Identification for control IUAP study day 17 / 34
SLIDE 38 Some remarks on our paradigm
convex optimisation problem minΦu(ω) 1 2π ∞
−∞
Φu(ω) dω s.t. LMI(ˆ θN, P−1
θ ) > 0 ⇐
⇒ LMI(ˆ θN, Φu(ω)) > 0
P−1
θ
= N σ2
e
1 2π π
−π
FuF ∗
u Φu(ω) + FeF ∗ e σ2 e dω
- Chicken-and-egg problem: ˆ
θN is replaced by a first guess Other definition of the cost of an identification problem?? power of the perturbations induced by the excitation signal on the normal operations of the system experiment duration for a given perturbation
Xavier Bombois (CNRS) Identification for control IUAP study day 17 / 34
SLIDE 39 Some remarks on our paradigm
Possible extension: other applications of the identified model can also be considered (diagnosis, deconvolution, monitoring)
Xavier Bombois (CNRS) Identification for control IUAP study day 18 / 34
SLIDE 40 Using an optimal excitation: is that really necessary?
Consider the following resonating system that we will identify in closed loop with a to-be-improved controller
true system initial guess
Control objective: Sufficient rejection of disturbances in a certain frequency band
Xavier Bombois (CNRS) Identification for control IUAP study day 19 / 34
SLIDE 41 Using an optimal excitation: is that really necessary?
Yes, since it allows to reduce the output perturbation by a factor 2 These two experiments yield an admissible uncertainty U What does happen? The optimal signal does not excite the resonances, but distributes optimally the power at other frequencies.
Xavier Bombois (CNRS) Identification for control IUAP study day 20 / 34
SLIDE 42 Using an optimal excitation: is that really necessary?
Yes, since it allows to reduce the output perturbation by a factor 2 These two experiments yield an admissible uncertainty U What does happen? The optimal signal does not excite the resonances, but distributes optimally the power at other frequencies.
Xavier Bombois (CNRS) Identification for control IUAP study day 20 / 34
SLIDE 43 Using an optimal excitation: is that really necessary?
Let us use our approach for the following lab setup Control objective: tracking of the level of tanks 1 and 2 Excitation and control signals: voltage on pumps 1 and 2
Collaboration with M. Annegren, C. Larsson et H. Hjalmarsson (KTH Stockholm) Xavier Bombois (CNRS) Identification for control IUAP study day 21 / 34
SLIDE 44 Using an optimal excitation: is that really necessary?
Let us use our approach for the following lab setup Control objective: tracking of the level of tanks 1 and 2 Excitation and control signals: voltage on pumps 1 and 2
Pump 1 Pump 2 V alve 1 V alve 2 Tank 1 Tank 2 Tank 4 Tank 3
Collaboration with M. Annegren, C. Larsson et H. Hjalmarsson (KTH Stockholm) Xavier Bombois (CNRS) Identification for control IUAP study day 21 / 34
SLIDE 45 Let us identify the model required for the design of a MPC controller (tracking) with the optimal excitation signal for this control objective with a white noise having the same power i.e. the same cost (red) Small power for an experiment of 5 minutes
Xavier Bombois (CNRS) Identification for control IUAP study day 22 / 34
SLIDE 46 Let us identify the model required for the design of a MPC controller (tracking) with the optimal excitation signal for this control objective with a white noise having the same power i.e. the same cost (red) Small power for an experiment of 5 minutes
Xavier Bombois (CNRS) Identification for control IUAP study day 22 / 34
SLIDE 47 Let us identify the model required for the design of a MPC controller (tracking) with the optimal excitation signal for this control objective with a white noise having the same power i.e. the same cost (red) Let us perform 20 experiments and compare the performance of the MPC obtained with these two signals
Xavier Bombois (CNRS) Identification for control IUAP study day 22 / 34
SLIDE 48 Tracking performance of these MPC controllers obtained with signals of same power
Despite the small excitation, the performance is always appropriate with the optimal signal (black) It is more variable with the white noise of same power (red)
Xavier Bombois (CNRS) Identification for control IUAP study day 23 / 34
SLIDE 49 Tracking performance of these MPC controllers obtained with signals of same power
Despite the small excitation, the performance is always appropriate with the optimal signal (black) It is more variable with the white noise of same power (red)
Xavier Bombois (CNRS) Identification for control IUAP study day 23 / 34
SLIDE 50 Advantage of our paradigm
From theory to Practice
An efficient identification at a minimal cost These attractive features from an economic point-of-view have allowed to gather a consortium of academic and industrial partners for its application in industrial processes (EU-FP7 Autoprofit) to work with the Smart Transmission Systems Lab (KTH Stockholm) for its application in electrical transmission networks
Xavier Bombois (CNRS) Identification for control IUAP study day 24 / 34
SLIDE 51 Advantage of our paradigm
From theory to Practice
An efficient identification at a minimal cost These attractive features from an economic point-of-view have allowed to gather a consortium of academic and industrial partners for its application in industrial processes (EU-FP7 Autoprofit) to work with the Smart Transmission Systems Lab (KTH Stockholm) for its application in electrical transmission networks
Xavier Bombois (CNRS) Identification for control IUAP study day 24 / 34
SLIDE 52 Autoprofit
Global maintenance of industrial processes
Identification of chemical process = ⇒ modification of the production quality = ⇒ high cost Application on a flotation process (Boliden) and a refinery process (Sasol) Promising results published in Journal of Process Control
Xavier Bombois (CNRS) Identification for control IUAP study day 25 / 34
SLIDE 53 Estimation of oscillation modes in power systems
The network must be able to damp the electromechanical oscillations generated by incidents (short-cut) Ce coefficient d’amortissement peut varier au cours du temps et doit donc ˆ etre monitor´ e
Collaboration with V. Peric and L. Vanfretti (KTH Stockholm) Xavier Bombois (CNRS) Identification for control IUAP study day 26 / 34
SLIDE 54 Estimation of oscillation modes in power systems
The network must be able to damp the electromechanical oscillations generated by incidents (short-cut) The damping coefficient ζ can vary over time and must therefore be monitored
Collaboration with V. Peric and L. Vanfretti (KTH Stockholm) Xavier Bombois (CNRS) Identification for control IUAP study day 26 / 34
SLIDE 55 Estimation of oscillation modes in power systems
The network must be able to damp the electromechanical oscillations generated by incidents (short-cut) The damping coefficient ζ can vary over time and must therefore be monitored
Collaboration with V. Peric and L. Vanfretti (KTH Stockholm) Xavier Bombois (CNRS) Identification for control IUAP study day 26 / 34
SLIDE 56 Frequent monitoring of ζ: is it possible?
Collaboration with V. Peric and L. Vanfretti (KTH Stockholm) Xavier Bombois (CNRS) Identification for control IUAP study day 27 / 34
SLIDE 57 Frequent monitoring of ζ: is it possible?
MEASUREMENT EXCITATION
Measurements are possible via Phasor Measurement Unit Reactive power can be injected by modulating the reference of a FACTS
Collaboration with V. Peric and L. Vanfretti (KTH Stockholm) Xavier Bombois (CNRS) Identification for control IUAP study day 27 / 34
SLIDE 58 Frequent monitoring of ζ: is it possible?
MEASUREMENT EXCITATION POSSIBLE IDENTIFICATION OF z
Measurements are possible via Phasor Measurement Unit Reactive power can be injected by modulating the reference of a FACTS
Collaboration with V. Peric and L. Vanfretti (KTH Stockholm) Xavier Bombois (CNRS) Identification for control IUAP study day 27 / 34
SLIDE 59 Optimal experiment to identify ζ
Our paradigm allows to design an experiment guaranteeing a-priori a certain accuracy for the estimate of ζ the minimal perturbations in the network KTH Nordic Grid Simulator: the injected power is only 6 MVA for an experiment length of 10 minutes (≈ power of a TGV) This power must be compared to the power of 40000 MW going through the network Improvements with respect to tests consisting in a transient analysis after the application of an artificial incident (ringdown): huge perturbation an identification using only the ambient noise: low accuracy
Xavier Bombois (CNRS) Identification for control IUAP study day 28 / 34
SLIDE 60 Optimal experiment to identify ζ
Our paradigm allows to design an experiment guaranteeing a-priori a certain accuracy for the estimate of ζ the minimal perturbations in the network KTH Nordic Grid Simulator: the injected power is only 6 MVA for an experiment length of 10 minutes (≈ power of a TGV) This power must be compared to the power of 40000 MW going through the network Improvements with respect to tests consisting in a transient analysis after the application of an artificial incident (ringdown): huge perturbation an identification using only the ambient noise: low accuracy
Xavier Bombois (CNRS) Identification for control IUAP study day 28 / 34
SLIDE 61 Optimal experiment to identify ζ
Our paradigm allows to design an experiment guaranteeing a-priori a certain accuracy for the estimate of ζ the minimal perturbations in the network KTH Nordic Grid Simulator: the injected power is only 6 MVA for an experiment length of 10 minutes (≈ power of a TGV) This power must be compared to the power of 40000 MW going through the network Improvements with respect to tests consisting in a transient analysis after the application of an artificial incident (ringdown): huge perturbation an identification using only the ambient noise: low accuracy
Xavier Bombois (CNRS) Identification for control IUAP study day 28 / 34
SLIDE 62 Identification of physical parameters
distributed parameter systems (PDE) nonlinear systems = ⇒ identification of physical parameters in a grey-box structure Objective for this identification var(θi) < βi ⇐ ⇒ eT
i Pθei < βi ⇐
⇒ βi eT
i
ei P−1
θ
Xavier Bombois (CNRS) Identification for control IUAP study day 29 / 34
SLIDE 63 Identification of physical parameters
distributed parameter systems (PDE) nonlinear systems = ⇒ identification of physical parameters in a grey-box structure Objective for this identification var(θi) < βi ⇐ ⇒ eT
i Pθei < βi ⇐
⇒ βi eT
i
ei P−1
θ
Xavier Bombois (CNRS) Identification for control IUAP study day 29 / 34
SLIDE 64 Identification of physical parameters: Why?
Cases of estimates with low accuracy (variance ր) are often reported The choice of the excitation signal may thus be even more critical for this type of models Example: Identification of the conductivity λ and of the diffusivity α
Collaboration with M. Potters (TU Delft) Xavier Bombois (CNRS) Identification for control IUAP study day 30 / 34
SLIDE 65 Identification of physical parameters: Why?
Cases of estimates with low accuracy (variance ր) are often reported The choice of the excitation signal may thus be even more critical for this type of models Example: Identification of the conductivity λ and of the diffusivity α
OPTIMAL SINUSOID WHITE NOISE (SAME COST) WHITE NOISE (COST 20 TIMES HIGHER) Collaboration with M. Potters (TU Delft) Xavier Bombois (CNRS) Identification for control IUAP study day 30 / 34
SLIDE 66 Application to an oil reservoir problem
Identification of porosity and permeability in oil reservoir samples
Collaboration: Max Potters (DCSC, TU Delft) and Jan Dirk Janssen (Petroleum Engineering, TU Delft) Xavier Bombois (CNRS) Identification for control IUAP study day 31 / 34
SLIDE 67 Current work: Optimal identification of nonlinear systems for control
Many of our results are limited to the LTI case, the original framework for robust control and identification An extension to the nonlinear case is necessary Indeed, taking into account the nonlinear effects will allow to further
An even more important impact is expected since the classical excitation signals will be inappropriate in many cases First step: the case of LPV systems
Collaboration with D. Ghosh, G. Scorletti, J. Huillery Xavier Bombois (CNRS) Identification for control IUAP study day 32 / 34
SLIDE 68 Current work: from local performance to global performance
Till now, the identification experiment is optimized to obtain a satisfactory performance in a given loop Control systems are more and more interconnected
CONTROLLED SYSTEM
How to take into account the global performance of the network in identification for control?
Collaboration avec A. Korniienko, H. Hjalmarsson Xavier Bombois (CNRS) Identification for control IUAP study day 33 / 34
SLIDE 69 Many thanks to M. Gevers, G. Scorletti, H. Hjalmarsson, P. Van den Hof, L. Vanfretti, M. Forgione, M. Potters, M. Annegren, C. Larsson, V. Peric, ...
Courtesy pictures: Mining technology (slide 25), Sasol (slide 25), isonomia.co.uk (slide 26), Rigzone (slides 29 and 31), Online tutoring (slides 29 and 30), USGS (slide 29), hydrochemistry.eu (slide 29) Xavier Bombois (CNRS) Identification for control IUAP study day 34 / 34
