MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator (EVPS) group seminar on Oct. 19th, 2000 [presenter] Rong Zhang [advisor] Prof.. Andrew Alleyne [team partner] Eko Prasetiawan [project sponsor] Caterpillar ALLEYNE RESEARCH GROUP

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 2 Overview  1. Problem statement  2. Introduction to LQG/LTR control  3. EVPS LQG/LTR design  4. EVPS LQG/LTR performance  5. Conclusions

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 3 1. Problem statement  Introduction to the Earthmoving Vehicle Powertrain  An analogy between passenger vehicle powertrain and EVP  EVPS schematic and I/O list  Need for coordination  A tracking example 1. Problem statement  2. Introduction to LQG/LTR control  3. EVPS LQG/LTR design  4. EVPS LQG/LTR performance  5. Conclusions

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 4 An analogy Passenger Vehicle Prime mover: Usually Spark-Ignition type engine (gas) Torque Converter: Mechanical gearbox Resistance speed control: Brake Earthmoving Vehicle Prime mover: Usually Compression-Ignition type engine (diesel) Torque  pressure converter: Hydraulic pump Resistance speed control: Flow valve

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC EVPS schematic...

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 6 … and I/O list  A MIMO control system  Controlled outputs: load speeds (  3)

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 7 Need for coordination!  A tracking example Tracking references Node 1: A rising step Node 2: 0 Node 3: 0 Using only one input: Flow Valve 1...  n m1 (rpm)  n m2 (rpm)  n m3 (rpm )

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 8  5 control inputs without coordination... [Q] How to take actions at the right time, right direction and right amount? [A] Coordination needed !

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 9 2. Introduction to LQG/LTR control  Pole placement?  “Performance” vs. “Cost”  LQR controller -- “optimal” feedback law  LQR estimator -- “optimal” filter by Kalman  LQG controller design  Optimal controller + Optimal estimator  LQG/LTR controller design  Optimal + Optimal  Robustness 1. Problem statement 2. Introduction to LQG/LTR control  3. EVPS LQG/LTR design  4. EVPS LQG/LTR performance  5. Conclusions

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 10 Pole placement? [Q1] Where should the target poles be placed? Too slow? poor performance! Too fast? expensive controller and surprising power bill! [Q2] Is there an “optimal” controller balancing both Performance and Cost?  “Punishment philosophy” Poles will be here!

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 11 LQR controller In this method, pole locations are not designed directly. Instead, find a good u=-Kx that minimizes: Q and R are Performance Index or “Punishment Matrices” Want a quicker state convergence? make Q bigger to punish large states! Want to keep control efforts within saturation range or at a lower cost? make R bigger to punish overacting inputs! [Solution] Theoretical: ARE equation finds us a good K Practical: Matlab command ‘lqr’

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 12 LQR estimator Not all the states are available, how to construct them from y? An estimator Find a good L(u e =-LCe) that minimizes: If Q e and R e are determined by process and measurement noise level... A Kalman Filter! [Solution] Theoretical: ARE equation Practical: Matlab command ‘lqr’ ‘kalman’

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 13 LQG = LQR control + Kalman filter LQG/LTR = LQG + Robustness recovery  It’s a Optimal + Optimal design, but is it “optimal” in the sense of robustness? No!  Using a recovery procedure (r=0 to inf), to make the LQG closed-loop closer to that of the Target Loop: the ideal LQR loop with full-state feedback. [Solution] Theoretical: Loop Transfer Recovery procedure Practical: Matlab command ‘ltru’ ‘ltry’

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 14 Optimal + Optimal  Robustness LQR with Full-state feedback Singular Value Bode Plot Singular Value Bode Plot  LQG with measurements feedback r = 0 (no recovery)

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 15 Loop transfer recovery... r = 1 (small recovery)r = 10 5 (large recovery) Closer to the target loop Singular Value Bode Plot  Singular Value Bode Plot

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC EVPS LQG/LTR design  Plant Model (14 states) to Design Plant Model (17 states)  To insure 0 tracking errors to step inputs, the PM is augmented by 3 free integrators.  LQG design  Good “Punishment Matrices” are found and tested  LQG/LTR design  Robustness or the ideal LQR is recovered 1. Problem statement 2. Introduction to LQG/LTR control 3. EVPS LQG/LTR design  4. EVPS LQG/LTR performance  5. Conclusions

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 17 EVPS System Plant Model A 14x14 Design Plant Model A 17x17 Three 1/s’ added to insure 0 tracking error

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 18 LQG Controller LQG/LTR Controller

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC EVPS LQG/LTR performance  Simultaneous tracking Different nodes track different speed references The total flow demand changes  Disturbance rejection One of the 3 nodes is subject to a pressure disturbance The TOTAL flow demand does not change The distribution of pressures among the 3 nodes is changed 1. Problem statement 2. Introduction to LQG/LTR control 3. EVPS LQG/LTR design 4. EVPS LQG/LTR performance  5. Conclusions

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 20 Simultaneous speed-tracking  n m1 tracking +/- 100rpm reference  n m2 being regulated  n m3 tracking - 60rpm reference  n m1 (rpm)  n m2 (rpm)  n m3 (rpm ) Opposite directionSame direction

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 21 Pressures of simu-tracking  p d1 increased to push through more flow  p d2 unchanged to maintain the same flow  p d3 decreases to push through less flow  p d1 (MPa)  p d2 (MPa)  p d3 (MPa)

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 22 Control inputs of simu-tracking Throttle  when total flow demand  Pump  when total flow demand  Flow 1  when speed reference 1  Flow 2 compensates for pressure  resulted from total flow  Flow 3  when speed reference 3 

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 23 Pressure disturbance at node 1 Pressure step as disturbance is applied at node 1 only  p d1 (MPa)  p d2 (MPa)  p d3 (MPa) Neighbor node pressure doesn’t change significantly

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 24 Speeds of disturb. rejection  n m1 (rpm)  n m2 (rpm)  n m3 (rpm )  n m1 decreases when disturbance pressure squeezes out some flow; then regulated by the controller  n m2 increases by pressure disturbance squeezes in some flow from neighbor node; then regulated by the controller  n m3 increases by pressure disturbance squeezes in some flow from neighbor node; then regulated by the controller

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 25 Control inputs of disturb. rejection Throttle  compensates for small total pressure  Pump doesn’t need to change much Flow 1  to fight disturbance pressure Flow 2  compensates for upstream pressure  caused by load 1  Flow 3  compensates for upstream pressure  caused by load 1  total flow demand not changed!

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC Conclusions  An LQG/LTR MIMO controller is successfully designed and implemented  The system: 14 states, 9 measurements, 5 inputs  The design plant model with free integrators: 17 states  The LQG/LTR controller: 17 states, 9 inputs, 5 outputs  It has satisfying tracking and disturbance rejecting performance  It’s robustness and working range are subject to further validation  Model reduction technique will be used to simplify the controller 1. Problem statement 2. Introduction to LQG/LTR control 3. EVPS LQG/LTR design 4. EVPS LQG/LTR performance 5. Conclusions

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 27 References  M. Athans, "A tutorial on the LQG/LTR method," presented at American Control Conference, Seattle, WA, A quick start.  B. D. O. Anderson and J. B. Moore, Optimal Control, Linear Quadratic Methods. Eaglewood Cliffs, New Jersey: Prentice-Hall, A textbook.  J. C. Doyle and G. Stein, "Multivariable Feedback Design: Concepts for a Classical/Modern Synthesis," IEEE Trans. Automat. Contr., vol. AC-26, pp. 4-16, A classic.  A. Saberi, B. M. Chen, and P. Sannuti, Loop Transfer Recovery: Analysis and Design. London: Springer-Verlag, A monograph.  Matlab manual online “Robust Control Toolbox” at: robust.pdf A useful tool.

MIMO LQG/LTR Control for the Earthmoving Vehicle Powertrain Simulator ARG Rong Zhang ALLEYNE RESEARCH GROUP, M&IE/UIUC 28 An earthmoving vehicle powertrain Drive Hydr. Pump Hydr. Pump Steering Implement Engine Control