Reference are Google open source and Application of Optimal Control Theory to the HEV Dynamic Process Based Control Method by ,Ou Jiajie * ,Li Lifu Institute of Mechanical and Automotive Engineering South China University of Technology Guangzhou, China oujiajiell@126.com

1. Application of Optimal Control
Theory to the HEV
Dynamic Process Control Method
-Godine Raja Sekhar

2. Overview
• Introduction
• Hybrid Electric Vehicle
• Drive system
• Optimal control theory
• Results
• Conclusion

3. Introduction
We know the growing importance of environmental friendly
Hybrid Electrical Vehicle( HEV)
In order to get benefits of using HEV we need to optimise the
consumption of fuel
Optimal working point of the engine and electric motor,
found using Dynamic Process Control Method (DPCM)
For this DPCM Optimal control theory is used for finding the
optimal working range

4. What is an HEV?
A vehicle that has two or more energy conversion
technologies combined with one or more energy
storage units
Hybrid electric vehicles (HEVs) combine the
benefits of gasoline engines and electric motors
HEVs run on fuel alone and do not plug in to an
electrical outlet to recharge the battery
So it becomes important to optimise the fuel
consumption to get benefits

5. HEV Objectives
Maximize fuel economy
Minimize fuel emissions
Reduce the conventional car weight
Maintain acceptable performance with a reasonable
cost

6. HEV Propulsion system

7. HEV Modes of operation
Motor
Transmission
IC Engine
Generator Battery
Wheel
Wheel
Motor
Transmission
IC Engine
Generator Battery
Wheel
Wheel
Motor
Transmission
IC Engine
Generator Battery
Wheel
Wheel
Scenario 2: Regenerative braking – Kinetic energy is converted to electric energy
Scenario 1: Low speed - Power is
provided only by battery
Scenario 3: High speed – Power is provided by IC
engine via generator, also charge battery

8. Control strategies
1. Back Ward Simulation Method (BWSM)
It is nothing but open loop system
2. Forward Simulation Method (FWSM)
Closed loop system, but ignores dynamic characteristics of
HEV
3. Dynamic Process Control Method (DPCM)
Closed loop system, and takes care of dynamic characteristics
of HEV.

9. Control theory
Since our system is multivariable and time varying
classical control theory can not be applied
For the reason we need to apply state system model
The state space approach helps the control system
to reach the required performance standard by
using state space Expression
Optimal control method based on modern
optimal control theory is common for lC engine
systems

10. The system's standard state space expression
X = AX +BU +Dξ
Y=CX
A --the System Matrix;
B--the Control Matrix;
C--the Output Matrix;
D--the disturbance matrix;
X --the state vector;
Y --the output vector;
U--the control vector;
ξ --the disturbance vector.

11. Optimal control theory
• How to choose the control to maximise economic
benefits from the resource
• Optimal control results in an optimal time trajectory of
the state
• We can define optimal use of natural resource for future
years and the following resource stock level
• If we deviate from the optimal control at any point in
time the economic benefits (Net Present Value) will
decrease

12. Objective function
• Q--the weighted matrix of the state variable;
• R--the weighted matrix of the control variable.
• X--the state vector;
• U--the control vector;
• R would be positive definite and symmetric matrix As
every component of control vector U should be restrained,
• Matrix Q would be positive semi-definite matrix as all
the components of state vector need not be retrained

13. Optimal control
• It is clear that control to be optimal, the objective
function to be minimal, is given by K
• Here P is constant matrix which satisfy Algebraic
Riccati Equation

14. DPCM program flowchart

15. Experiments
• Experiments were performed in practical
conditions as follows
• Case 1: Low-velocity-high acceleration city
driving condition
• Case 2: High-velocity-low-acceleration suburb
driving condition

16. Comparison of torque

17. Comparison of power

18. Comparison of fuel consumption

19. Comparison of charging curve

20. Conclusion
• Under control of DPCM, the EFC reaches 3.381L,
converting to 30.9332L per hundred km
• The largest distributed power of engine is 84.S3kw, while
power of electric motor is 60.1 93kw, both within
output of rated power source.
• Under control of DPCM, EFC reaches to 30.9332L per
hundred km, which is better than the 34.4 L/100 km
earlier research results

21. Thank you
• Any questions?