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Introduction to Assignment 2 andDebuggerTSFS03 Lesson
Mahdi Morsali
Vehicular SystemsDepartment of Electrical EngineeringLinkoping University
April 03, 2017
1 Hand-in 2 Introduction2 DDP Algorithm Example3 Implementation4 Debugging in Matlab5 Summary
1 Hand-in 2 Introduction2 DDP Algorithm Example3 Implementation4 Debugging in Matlab5 Summary
Hand-in 2 Introduction
For a known drive cycle, how to optimally operate the electricmotor/combustion engine?
• Two hybrid architectures: parallel and series.
• Model the vehicles following the quasi-static approach.
• Solve the problem with Deterministic Dynamic Programming.
Hand-in Goals:
• Acquire knowledge and experience with DDP.
• Acquire knowledge about the properties and differences betweenparallel and series architectures.
TSFS03 Lesson Mahdi Morsali April 03, 2017 3 / 15
Hand-in 2 Introduction
For a known drive cycle, how to optimally operate the electricmotor/combustion engine?
• Two hybrid architectures: parallel and series.
• Model the vehicles following the quasi-static approach.
• Solve the problem with Deterministic Dynamic Programming.
Hand-in Goals:
• Acquire knowledge and experience with DDP.
• Acquire knowledge about the properties and differences betweenparallel and series architectures.
TSFS03 Lesson Mahdi Morsali April 03, 2017 3 / 15
Hand-in 2 Introduction
For a known drive cycle, how to optimally operate the electricmotor/combustion engine?
• Two hybrid architectures: parallel and series.
• Model the vehicles following the quasi-static approach.
• Solve the problem with Deterministic Dynamic Programming.
Hand-in Goals:
• Acquire knowledge and experience with DDP.
• Acquire knowledge about the properties and differences betweenparallel and series architectures.
TSFS03 Lesson Mahdi Morsali April 03, 2017 3 / 15
Hand-in 2 Introduction
For a known drive cycle, how to optimally operate the electricmotor/combustion engine?
• Two hybrid architectures: parallel and series.
• Model the vehicles following the quasi-static approach.
• Solve the problem with Deterministic Dynamic Programming.
Hand-in Goals:
• Acquire knowledge and experience with DDP.
• Acquire knowledge about the properties and differences betweenparallel and series architectures.
TSFS03 Lesson Mahdi Morsali April 03, 2017 3 / 15
Hand-in 2 Introduction
For a known drive cycle, how to optimally operate the electricmotor/combustion engine?
• Two hybrid architectures: parallel and series.
• Model the vehicles following the quasi-static approach.
• Solve the problem with Deterministic Dynamic Programming.
Hand-in Goals:
• Acquire knowledge and experience with DDP.
• Acquire knowledge about the properties and differences betweenparallel and series architectures.
TSFS03 Lesson Mahdi Morsali April 03, 2017 3 / 15
Hand-in 2 Introduction
For a known drive cycle, how to optimally operate the electricmotor/combustion engine?
• Two hybrid architectures: parallel and series.
• Model the vehicles following the quasi-static approach.
• Solve the problem with Deterministic Dynamic Programming.
Hand-in Goals:
• Acquire knowledge and experience with DDP.
• Acquire knowledge about the properties and differences betweenparallel and series architectures.
TSFS03 Lesson Mahdi Morsali April 03, 2017 3 / 15
1 Hand-in 2 Introduction2 DDP Algorithm Example3 Implementation4 Debugging in Matlab5 Summary
DDP Example
Graphical illustration of the solution procedure
0 1 2
1
2
3
2
1
0
x JN(xN)
tNN − 1
tbta
k =
TSFS03 Lesson Mahdi Morsali April 03, 2017 5 / 15
DDP Example
Graphical illustration of the solution procedure
0 1 2
1
2
3
2
1
0
0
2
4
2x JN(xN)
tNN − 1
tbta
k =
TSFS03 Lesson Mahdi Morsali April 03, 2017 5 / 15
DDP Example
Graphical illustration of the solution procedure
2
1
2
0
2
4
0 1 2
1
2
3
2
1
0
x
k =
ta tb
N − 1 tN
JN(xN)
TSFS03 Lesson Mahdi Morsali April 03, 2017 5 / 15
DDP Example
Graphical illustration of the solution procedure
2
1
0
2
0
2
4
0 1 2
1
2
3
2
1
0
x
k =
ta tb
N − 1 N t
JN(xN)
TSFS03 Lesson Mahdi Morsali April 03, 2017 5 / 15
DDP Example
Graphical illustration of the solution procedure
2
1
0
1
2
0
2
4
0 1 2
1
2
3
2
1
0
N
x
k =
ta tb
t
JN(xN)
N − 1
TSFS03 Lesson Mahdi Morsali April 03, 2017 5 / 15
DDP Example
Graphical illustration of the solution procedure
2
1
0
1
2
2
0
2
0 1 2
1
2
3
2
1
0
x
k =
ta tb
N − 1 tN
JN(xN)
TSFS03 Lesson Mahdi Morsali April 03, 2017 5 / 15
DDP Example
Graphical illustration of the solution procedure
2
1
0
1
2
3
2
0
0 1 2
1
2
3
2
1
0
x
k =
ta tb
N − 1 N t
JN(xN)
TSFS03 Lesson Mahdi Morsali April 03, 2017 5 / 15
DDP Example
Graphical illustration of the solution procedure
2
3
2
1
2
0
1
0 1 N2
1
2
3
2
1
0
0
2
4
x
k =
ta tb
N − 1 t
JN(xN)
TSFS03 Lesson Mahdi Morsali April 03, 2017 5 / 15
DDP Example
Graphical illustration of the solution procedure
2
3
2
1
2
0
1
0 1 N2
1
2
3
2
1
0
0
2
4
x
k =
ta tb
N − 1 t
JN(xN)
Matrix formulation benefits:
Each iteration compute all arcs using a vector/matrix
TSFS03 Lesson Mahdi Morsali April 03, 2017 5 / 15
1 Hand-in 2 Introduction2 DDP Algorithm Example3 Implementation4 Debugging in Matlab5 Summary
Algorithm Implementation
Generic DDP functions:
• dynProg1D.m – Solves a dynamic programming problem in onevariable
• dynProg2D.m – Solves a dynamic programming problem in twovariables
Problem specific scripts and functions that you need to complete:
• testHybrids.m – Template for setting up the problem
• parallelHybrid.m – Template for the parallel hybrid vehicle
• seriesHybrid.m – Template for the series hybrid vehicle
TSFS03 Lesson Mahdi Morsali April 03, 2017 7 / 15
Algorithm Implementation
Generic DDP functions:
• dynProg1D.m – Solves a dynamic programming problem in onevariable
• dynProg2D.m – Solves a dynamic programming problem in twovariables
Problem specific scripts and functions that you need to complete:
• testHybrids.m – Template for setting up the problem
• parallelHybrid.m – Template for the parallel hybrid vehicle
• seriesHybrid.m – Template for the series hybrid vehicle
TSFS03 Lesson Mahdi Morsali April 03, 2017 7 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
How to compute Arc CostsQuasi-static approach (backward power flow)
costVector = parallelHybrid(t vec,SOC start,SOC final)
• Calculate the whole bundle of arcs in one step.
• Add boundary and constraint checks.
• Be careful with: v = 0, Gear = 0 and sign convention.
Useful MATLAB commands:
• Computing time: tic, toc
• Create matrices: zeros, ones
• Modify matrices: meshgrid, repmat
• Element-wise operations: ./ or .*
• Logical indexing: m f(m f<0)
• Trick: P = T · ω · ηsign(T )
TSFS03 Lesson Mahdi Morsali April 03, 2017 8 / 15
Send parameters to parallelHybrid.mThe driving cycle used is set in testHybrids.m and is used inparallelHybrid.m. Two solutions to access T z, V z, and G z
1. Take the variables as inputs to dynProg1D and use them in thecall for parallelHybrid.m
2. Use global variables.
testHybrids.m:
global V_z
load EUDC_MAN
parallelHybrid.m:
global V_z
V z is available
Easier solution since the scripts are prepared to use global variables.
First global variable definition, then assign value.
Be cautious to not overwrite variables → Read only variables.
TSFS03 Lesson Mahdi Morsali April 03, 2017 9 / 15
Send parameters to parallelHybrid.mThe driving cycle used is set in testHybrids.m and is used inparallelHybrid.m. Two solutions to access T z, V z, and G z
1. Take the variables as inputs to dynProg1D and use them in thecall for parallelHybrid.m
2. Use global variables.
testHybrids.m:
global V_z
load EUDC_MAN
parallelHybrid.m:
global V_z
V z is available
Easier solution since the scripts are prepared to use global variables.
First global variable definition, then assign value.
Be cautious to not overwrite variables → Read only variables.
TSFS03 Lesson Mahdi Morsali April 03, 2017 9 / 15
Send parameters to parallelHybrid.mThe driving cycle used is set in testHybrids.m and is used inparallelHybrid.m. Two solutions to access T z, V z, and G z
1. Take the variables as inputs to dynProg1D and use them in thecall for parallelHybrid.m
2. Use global variables.
testHybrids.m:
global V_z
load EUDC_MAN
parallelHybrid.m:
global V_z
V z is available
Easier solution since the scripts are prepared to use global variables.
First global variable definition, then assign value.
Be cautious to not overwrite variables → Read only variables.
TSFS03 Lesson Mahdi Morsali April 03, 2017 9 / 15
Send parameters to parallelHybrid.mThe driving cycle used is set in testHybrids.m and is used inparallelHybrid.m. Two solutions to access T z, V z, and G z
1. Take the variables as inputs to dynProg1D and use them in thecall for parallelHybrid.m
2. Use global variables.
testHybrids.m:
global V_z
load EUDC_MAN
parallelHybrid.m:
global V_z
V z is available
Easier solution since the scripts are prepared to use global variables.
First global variable definition, then assign value.
Be cautious to not overwrite variables → Read only variables.
TSFS03 Lesson Mahdi Morsali April 03, 2017 9 / 15
Send parameters to parallelHybrid.mThe driving cycle used is set in testHybrids.m and is used inparallelHybrid.m. Two solutions to access T z, V z, and G z
1. Take the variables as inputs to dynProg1D and use them in thecall for parallelHybrid.m
2. Use global variables.
testHybrids.m:
global V_z
load EUDC_MAN
parallelHybrid.m:
global V_z
V z is available
Easier solution since the scripts are prepared to use global variables.
First global variable definition, then assign value.
Be cautious to not overwrite variables → Read only variables.
TSFS03 Lesson Mahdi Morsali April 03, 2017 9 / 15
Send parameters to parallelHybrid.mThe driving cycle used is set in testHybrids.m and is used inparallelHybrid.m. Two solutions to access T z, V z, and G z
1. Take the variables as inputs to dynProg1D and use them in thecall for parallelHybrid.m
2. Use global variables.
testHybrids.m:
global V_z
load EUDC_MAN
parallelHybrid.m:
global V_z
V z is available
Easier solution since the scripts are prepared to use global variables.
First global variable definition, then assign value.
Be cautious to not overwrite variables → Read only variables.
TSFS03 Lesson Mahdi Morsali April 03, 2017 9 / 15
Solution Postprocess
How to retrieve the solution after calculating the cost to go matrixis not trivial.
Helpful things to check:
• Start with the parallel hybrid.
• Check what are the outputs from dynProg1D.m anddynProg2D.m
• How are the costs stored in the DDP algorithm?
• How is the optimal path stored in the DDP algorithm?
TSFS03 Lesson Mahdi Morsali April 03, 2017 10 / 15
Solution Postprocess
How to retrieve the solution after calculating the cost to go matrixis not trivial.
Helpful things to check:
• Start with the parallel hybrid.
• Check what are the outputs from dynProg1D.m anddynProg2D.m
• How are the costs stored in the DDP algorithm?
• How is the optimal path stored in the DDP algorithm?
TSFS03 Lesson Mahdi Morsali April 03, 2017 10 / 15
1 Hand-in 2 Introduction2 DDP Algorithm Example3 Implementation4 Debugging in Matlab5 Summary
Debugging
• Is used to identify faults in the code
• It is possible to find and use the values of parameters andvariables inside functions (that use local workspace).
Matlab debugger
• Mouse click to the left in a m-file to add a debugger point.Possible to add conditional debugger point by right click (e.g.stop at a wanted index in a for loop).
• F10: Step forward (one line)
• F11: Step inside called function
• F5: Continue till next debugger point or till the end
TSFS03 Lesson Mahdi Morsali April 03, 2017 12 / 15
Debugging
• Is used to identify faults in the code
• It is possible to find and use the values of parameters andvariables inside functions (that use local workspace).
Matlab debugger
• Mouse click to the left in a m-file to add a debugger point.Possible to add conditional debugger point by right click (e.g.stop at a wanted index in a for loop).
• F10: Step forward (one line)
• F11: Step inside called function
• F5: Continue till next debugger point or till the end
TSFS03 Lesson Mahdi Morsali April 03, 2017 12 / 15
Example in Matlab
TSFS03 Lesson Mahdi Morsali April 03, 2017 13 / 15
1 Hand-in 2 Introduction2 DDP Algorithm Example3 Implementation4 Debugging in Matlab5 Summary
Summary
• Understand how DDP works and how returns the solution.
• Implement your hybrid models in paper first.
• Use your notes to implement your code with the giventemplates.
• Make use of the debugging tool to polish your code.
• Answer the questions and discuss your results in the Hand-inreport.
TSFS03 Lesson Mahdi Morsali April 03, 2017 15 / 15
Summary
• Understand how DDP works and how returns the solution.
• Implement your hybrid models in paper first.
• Use your notes to implement your code with the giventemplates.
• Make use of the debugging tool to polish your code.
• Answer the questions and discuss your results in the Hand-inreport.
TSFS03 Lesson Mahdi Morsali April 03, 2017 15 / 15
Summary
• Understand how DDP works and how returns the solution.
• Implement your hybrid models in paper first.
• Use your notes to implement your code with the giventemplates.
• Make use of the debugging tool to polish your code.
• Answer the questions and discuss your results in the Hand-inreport.
TSFS03 Lesson Mahdi Morsali April 03, 2017 15 / 15
Summary
• Understand how DDP works and how returns the solution.
• Implement your hybrid models in paper first.
• Use your notes to implement your code with the giventemplates.
• Make use of the debugging tool to polish your code.
• Answer the questions and discuss your results in the Hand-inreport.
TSFS03 Lesson Mahdi Morsali April 03, 2017 15 / 15
Summary
• Understand how DDP works and how returns the solution.
• Implement your hybrid models in paper first.
• Use your notes to implement your code with the giventemplates.
• Make use of the debugging tool to polish your code.
• Answer the questions and discuss your results in the Hand-inreport.
TSFS03 Lesson Mahdi Morsali April 03, 2017 15 / 15
