Learning Control Applied to EHPV® PATRICK OPDENBOSCH Graduate Research Assistant Manufacturing Research Center  Room 259 Ph. (404) 894 3256 gte608g@mail.gatech.edu Frequently, presenters must deliver material of a technical nature to an audience unfamiliar with the topic or vocabulary. The material may be complex or heavy with detail. To present technical material effectively, use the following guidelines from Dale Carnegie Training®.   Consider the amount of time available and prepare to organize your material. Narrow your topic. Divide your presentation into clear segments. Follow a logical progression. Maintain your focus throughout. Close the presentation with a summary, repetition of the key steps, or a logical conclusion. Keep your audience in mind at all times. For example, be sure data is clear and information is relevant. Keep the level of detail and vocabulary appropriate for the audience. Use visuals to support key points or steps. Keep alert to the needs of your listeners, and you will have a more receptive audience. Georgia Institute of Technology George W. Woodruff School of Mechanical Engineering May 18, 2005

AGENDA OBJECTIVES INTRODUCTION LEARNING TOOL: NLPN CONTROL INVERSE MAPPING FEEDBACK CONTROL EXPERIMENTAL RESULTS FUTURE RESEARCH CONCLUSIONS In your opening, establish the relevancy of the topic to the audience. Give a brief preview of the presentation and establish value for the listeners. Take into account your audience’s interest and expertise in the topic when choosing your vocabulary, examples, and illustrations. Focus on the importance of the topic to your audience, and you will have more attentive listeners. May 18, 2005

OBJECTIVES May 18, 2005

EHPV LOCAL LEVEL CONTROL Develop a smarter and self-contained valve. Investigate algorithms for off-line and on-line learning of the input-output map. Develop robust trajectory learning controller Improve the valve’s performance Explore algorithms and applications via theory, simulation, and implementation on a Hardware-in-the-Loop simulator. May 18, 2005

EHPV HIGHER LEVEL CONTROL Compliance with INCOVA system performance requirements. Fault prognostics and diagnostics. May 18, 2005

INTRODUCTION May 18, 2005

BACKGROUND Hydraulic systems, in particular control valves, show nonlinear pressure-flow characteristics such as nonlinear gain, hysteresis, and saturation. Common control approaches used include: Linear methods: PID (modified), State Feedback (LQG) Nonlinear tools: gain scheduling, sliding mode, backstepping Advanced methods: Adaptive, robust control, Fuzzy, and Neural control Some of the challenges: energy savings, tracking, multidisciplinary systems, improved bandwidth, modeling and parameter estimation May 18, 2005

BACKGROUND Advanced approach: Learning control Learning control is used to improve future performance. Iterative and repetitive learning control action. Can be used to obtain direct and inverse input-output system’s mapping Tied to functional approximator: Neural network May 18, 2005

HUSCO’S HIERARCHICAL CONTROL Calculate desired speed, n US PATENT # 6,732,512 & 6,718,759 Calculate desired flow, Read port pressures, Ps PR PA PB Calculate equivalent KvEQ Determine Individual Kv KvB Hierarchical control: System controller, pressure controller, function controller In your opening, establish the relevancy of the topic to the audience. Give a brief preview of the presentation and establish value for the listeners. Take into account your audience’s interest and expertise in the topic when choosing your vocabulary, examples, and illustrations. Focus on the importance of the topic to your audience, and you will have more attentive listeners. KvA Determine input current to EHPV isol=f(Kv,DP,T) May 18, 2005

LOCAL (LOWER LEVEL) CONTROL INPUT-OUTPUT MAP: Currently obtained through offline calibration Specifically tailored for each individual valve Unable to reflect valve behavior after considerable continuous operation Flow conductance coefficient Kv as a function of input current and pressure differential In your opening, establish the relevancy of the topic to the audience. Give a brief preview of the presentation and establish value for the listeners. Take into account your audience’s interest and expertise in the topic when choosing your vocabulary, examples, and illustrations. Focus on the importance of the topic to your audience, and you will have more attentive listeners. May 18, 2005

LOCAL (LOWER LEVEL) CONTROL POSSIBLE SOLUTIONS: Online learning of the input-output map through suitable training criterion. Compatibility of adaptive look-up table with existing industrial trends Improve mapping that more accurately reflects valve behavior after considerable continuous operation Flow conductance coefficient Kv as a function of input current and pressure differential In your opening, establish the relevancy of the topic to the audience. Give a brief preview of the presentation and establish value for the listeners. Take into account your audience’s interest and expertise in the topic when choosing your vocabulary, examples, and illustrations. Focus on the importance of the topic to your audience, and you will have more attentive listeners. May 18, 2005

LOCAL (LOWER LEVEL) CONTROL POSSIBLE SOLUTIONS: Development of robust observer for the online estimation of the KV. Flow conductance coefficient Kv as a function of input current and pressure differential In your opening, establish the relevancy of the topic to the audience. Give a brief preview of the presentation and establish value for the listeners. Take into account your audience’s interest and expertise in the topic when choosing your vocabulary, examples, and illustrations. Focus on the importance of the topic to your audience, and you will have more attentive listeners. May 18, 2005

LEARNING TOOL: NLPN May 18, 2005

NODAL LINK PERCEPTRON NETWORK (NLPN) MAIN FEATURE Approximates nonlinear functions using a number of local adjustable functions. The NLPN is a three-layer perceptron network whose input is related to the output by: If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, e-mail, or the Internet. Develop each point adequately to communicate with your audience. NLPN structure The idea is to choose wi and fi so that May 18, 2005 More details found at: Sadegh, N. (1998) “A multilayer nodal link perceptron network with least squares training algorithm,” Int. J. Control, Vol.70, No. 3, 385-404.

TRAINING Once a basis function structure is chosen, train the network to learn the “weights”. LEAST SQUARES DELTA RULE HOW IT WORKS (1D EX) f1 f2 f3 May 18, 2005

COMMON BASIS FUNCTIONS Gaussian Triangular Hyperbolic A B C A B C A B C At most 2n components of F are nonzero. For multidimensional input space: For example, May 18, 2005

COMMON APPLICATIONS Offline curve fitting Filtering Actual Map NLPN approximation Approximation Error Filtering System identification & control Selmic, R. R., Lewis, F. L., (2000) “Identification of Nonlinear Systems Using RBF Neural Networks: Application to Multimodel Failure Detection,” Proceedings of the IEEE Conference on Decision and Control, v 4, 2001, p 3128-3133 Sanner, R. M., J. E. Slotine, (1991) “Stable Adaptive Control and Recursive Identification Using Radial Gaussian Networks,” Proceedings of the IEEE Conference on Decision and Control, v 3, 1991, p 2116-2123. Sadegh, N., (1993), “A Perceptron Network for Functional Identification and Control of Nonlinear Systems,” IEEE trans. N. Networks, Vol. 4, No. 6, 982-988 May 18, 2005

CONTROL May 18, 2005

INTERPOLATED AND INVERTED DATA INVERSE MAPPING DP isol Kv T EXPERIMENTAL DATA Kv DP isol T If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, e-mail, or the Internet. Develop each point adequately to communicate with your audience. INTERPOLATED AND INVERTED DATA May 18, 2005

EXPERIMENTAL ESTIMATION Steady state data was obtained from the Hydraulic circuit employed at the Hardware-In-the-Loop (HIL) Simulator Hardware-In-the Loop (HIL) Simulator Hydraulic circuit employed at the HIL EHPV mounted on the HIL. Quick connections for forward and reverse flow May 18, 2005

EXPERIMENTAL MEASUREMENT OF STEADY STATE FLOW CONDUCTANCE COEFFICIENT Kv. Forward Kv as a function of Pressure differential and input current Reverse Kv as a function of Pressure differential and input current Forward: Side to nose Reverse: Nose to side May 18, 2005

FORWARD Kv AND isol MAP LEARNING Kv map Kv map learning isol map isol map learning May 18, 2005

REVERSE Kv AND isol MAP LEARNING Kv map Kv map learning isol map isol map learning May 18, 2005

FEEDBACK CONTROL If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, e-mail, or the Internet. Develop each point adequately to communicate with your audience. May 18, 2005

TRACKING CONTROL Let the behavior of the EHPV be expressed by: Then linearizing about, yields, Assumptions: 1. The system is strongly controllable: there is a unique input so that 2. The controllability matrix Q has full rank for all inputs and states. May 18, 2005

Upon substitution into the error equation, Proposed control law: where, (NLPN learning) Upon substitution into the error equation, It can be shown that: for a functional approximation bound and estimation bounds: May 18, 2005

GRADIENT BASED METHOD: MODIFIED BROYDEN ESTIMATION TASK Control law requires knowledge of Jacobian Jk and controllability Qk: Estimation Schemes: Gradient based methods Least squares methods GRADIENT BASED METHOD: MODIFIED BROYDEN Error dynamics: Approximated Error dynamics: General form: Update law: May 18, 2005

LEAST SQUARES METHOD: RECURSIVE LS (Cov. Reset/Forgetting Factor) ESTIMATION TASK Control law requires knowledge of Jacobian Jk and controllability Qk: Estimation Schemes: Gradient based methods Least squares methods LEAST SQUARES METHOD: RECURSIVE LS (Cov. Reset/Forgetting Factor) Error dynamics: Approximated Error dynamics: General form: Update law: May 18, 2005

EXPERIMENTAL RESULTS May 18, 2005

EHPV HYDRAULIC TESTBED Hydraulic circuit employed Hydraulic robot employed May 18, 2005

Close view of the EHPV mounted on stationary arm EHPV HYDRAULIC TESTBED ELECTRONICS: Signal Amplifier Power Supply Breakout box CONTROLLER: Host and Target PC SIMULINK xpctarget AMPLIFIER BREAKOUT BOX EHPV FLOWMETER PC - HOST PC - TARGET May 18, 2005 Close view of the EHPV mounted on stationary arm

EHPV HYDRAULIC TESTBED (Experimental Data) INITIAL RESPONSE: Kv measured and desired Input voltage to amplifier INITIAL RESPONSE: Temperature Port to port pressure differential May 18, 2005

EHPV HYDRAULIC TESTBED (Experimental Data) INITIAL RESPONSE: Kv measured Kv desired Kv approximated from estimation INITIAL RESPONSE: Estimated J Estimated Q May 18, 2005

EHPV HYDRAULIC TESTBED (Experimental Data) STEADY RESPONSE: Kv measured and desired Input voltage to amplifier STEADY RESPONSE: Temperature Port to port pressure differential May 18, 2005

EHPV HYDRAULIC TESTBED (Experimental Data) STEADY RESPONSE: Kv measured Kv desired Kv approximated from estimation STEADY RESPONSE: Estimated J Estimated Q May 18, 2005

FUTURE WORK If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, e-mail, or the Internet. Develop each point adequately to communicate with your audience. May 18, 2005

TASKS TO BE ACCOMPLISHED: Investigation of other possible algorithms to extend parameter estimation Investigate robustness Development of Kv observer Explore control performance for the different metering modes If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, e-mail, or the Internet. Develop each point adequately to communicate with your audience. May 18, 2005

CONCLUSIONS If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, e-mail, or the Internet. Develop each point adequately to communicate with your audience. May 18, 2005

Development of nonlinear mapping tool. RESEARCH OBJECTIVE Investigation and development of an advanced control methodology to control systems employing EHPV NLPN Development of nonlinear mapping tool. Design with flexibility in basis functions Approximation of f: Rn Rm CURRENT TO Kv MAPPING Experimental application for forward and reverse flow conditions on both direct and inverse mappings If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, e-mail, or the Internet. Develop each point adequately to communicate with your audience. CONTROL APPROACH Development of NLPN controller Estimation methods Experimental tracking results May 18, 2005