1 / 19

Evaluating Robustness of Embedded Model-Predictive Control Using Monte Carlo Simulation

Evaluating Robustness of Embedded Model-Predictive Control Using Monte Carlo Simulation. P. Vouzis 1 , M. V. Kothare 2 & M. Arnold 1 1 Computer Science 2 Chemical Engineering Lehigh University. 2006 AIChE Annual Meeting. d. Reference. u(k). y(k). Plant. MPC. u(k).

sezja
Download Presentation

Evaluating Robustness of Embedded Model-Predictive Control Using Monte Carlo Simulation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Evaluating Robustness of Embedded Model-Predictive Control Using Monte Carlo Simulation P. Vouzis1, M. V. Kothare2 & M. Arnold1 1Computer Science 2Chemical Engineering Lehigh University 2006 AIChE Annual Meeting

  2. d Reference u(k) y(k) Plant MPC u(k) Model Predictive Control (MPC) • Model Predictive Control • Use a predictive model of the plant • Step-wise decision with look ahead prediction • Flexibility on the control objectives past target future Projected outputs Manipulated variable u(k+l),l=0,1,…,m-1 k k+1 k+m-1 k+p-1 control horizon m prediction horizon p

  3. Need for Embedded MPC • MPC is proven technology for advanced optimal control in chemical process industry • Advantages • Can handle MIMO systems • Can handle constraints explicitly • Can handle uncertainties and disturbances • Can handle nonlinearities • Restricted to systems with slow dynamics • Requires dedicated computer Clear need/opportunity to embed MPC in hardware for high-speed size-constrained control problems

  4. Applications of Embedded MPC • Drug Delivery • Robotics • Microfluidic control

  5. PreviousWork • Parametric studies to relate precision to control performance – proposed ASIC design L. GBleris, M. V. Kothare, J. G. Garcia and M. G. Arnold, Towards Embedded Model Predictive Control for System-on-a-Chip Applications, Journal of Process Control, 2006. • Off-the-shelf processor implementation L. G. Bleris and M. V. Kothare,Implementation of Model Predictive Control for Glucose Regulation using a General Purpose Microprocessor, in 44th IEEE Conference on Decision and Control and European Control Conference, Seville, Spain, 2005. • Co-design architecture proposed – FPGA implementation P. D. Vouzis, L. G. Bleris, M. G. Arnold and M. V. Kothare, A System-on-a-Chip Implementation for Embedded Real-Time Model Predictive Control, to be submitted toIEEE Transactions on Control Systems Technology.

  6. Effects of Reduced Precision • Reduces the area requirements and power consumption • Decreased latency of the arithmetic circuits But… • Makes the system more susceptible to noise and accumulated arithmetic errors • Catastrophic cancellation and ill-conditioned matrices appear more frequently

  7. Logarithmic Number System (LNS) • In LNS a number X is represented by its logarithmic value: x=log(|X|) • Multiplication and division in LNS simplified: • log(X×Y)=log(X) + log(Y)=x+y • log(X/Y)=log(X) – log(Y)=x–y • …but addition and subtraction are more difficult: • log(X+Y)=max(x,y)+log(1+2|x–y|) • log(X–Y)=max(x,y)+log(1–2|x–y|) Storing the two functions is the most costly part for implementing the LNS

  8. Catastrophic cancellation a,b>0

  9. Ill-Conditioned Matrices • The condition number is associated with how numerically well-posed the problem is: Ax=b κ(A)=||A-1||·||A|| • Matrix inversion appears in optimization algorithms and ill-conditioning can be catastrophic, especially with reduced accuracy

  10. Monte Carlo Method • A simulation based approach that gives non-deterministic results • The solution is an average of multiple runs of the problem • Useful when analytical solutions on multidimensional problems can not be derived • Computationally intensive

  11. Monte Carlo Formulation • For each LNS multiplication an error is injected • e.g.: if the representation has 9 fractional bits and if t=9, then is a uniform distribution affecting the least significant bit

  12. Case Study: Antenna Rotation • Rotate the antenna so that it follows a moving object in the plane • –2 V < u< 2 V

  13. Error w.r.t. Optimization Iterations

  14. Error w.r.t. Optimization Iterations

  15. Error w.r.t. Optimization Iterations

  16. Variance or Error w.r.t. Optimization Iterations

  17. Worst-Case Error w.r.t. Optimization Iterations

  18. Conclusions • Appropriate selection of Monte Carlo iterations reduces the effects of error injection • Monte Carlo is less efficient in terms of performance • Monte Carlo properties can be utilized for: • detection of catastrophic cancellation • detection of ill-conditioned matrices

  19. Future Work • What if: • the noise has a different distribution (e.g. normal)? • the error bits are more than one? • the deterministic circuit has shorter wordlength?

More Related