Educational Model of Control System SYS 5100 - Modern Control Engineering - Winter 2007 Educational Model of Control System for Robot Arm Team Members : Irena Karasik Sylvain Ganter Olivier Paultre Jeong Ja Kong TA : Wei Yang Professor : Riadh Habash - April 4th, 2007 -

References [1] Kok Kiong Tan and Han Leong Goh, “Development of a Mobile Spreadsheet-Based PID Control Simulation System”, IEEE Transaction on Education, PP. 199-207, may 2006 [2] Guoguang Zhang and Junji Furusho, “Control of Robot Arms using Joint Torque Sensors”, IEEE Control Systems, pp.48-55, 1998 [3] Gloria Suh, Dae Sung Hyun, Jung Il Park, Ki Dong Lee, Suk Gyu Lee, “Design of a Pole Placement Controller for Reducing Oscillation and Settling Time in a Two-Inertia Motor System”, IECON’01:The 27th Annual Conference of the IEEE Industrial Electronics Society, pp.615-620, 2001 [4] Estico Rijanto, Antonio Moran and Minoru Hayase, “Experimental Positioning Control of Flexible Arm Using Two-Degrees-of-Freedom Controller”, p127 [5] Miomir K. Vukobratovic, Aleksandar D. Rodic, “Control of Manipulation Robots Interacting with Dynamic Environment: Implementation and Experiments”, IEEE Transactions on Industrial Electronics, Vol.42, No.4, August 1995 [6] Textbook : “Modern Control Theory”

References [1] Development of a Mobile Spreadsheet-Based PID Control Simulation System - To control the Temperature of Thermal Chamber - Mobile PID Tuning Preparatory Exercise - Mobile Spreadsheet Simulator

References [2] Control of Robot Arms using Joint Torque Sensors - Two-Inertia System Modeling - With Joint Torque Feedback - Dealt with Pole Assignment & Effect of Disturbance - ½ Bandwidth of resonance frequency (PD Controller) - Identical Damping Coefficients ( 1 = 2 ) - A wider bandwidth and better disturbance rejection over conventional PD control

References [3] Design of a Pole Placement Controller for Reducing Oscillation and Settling Time in a Two-Inertia Motor System - Identical Real Part  settling time - Comparison among 3 controller I-P, I-PD, State Feedback control - Conventional ITAE & Weighted ITAE - Full state feedback control is the best  in terms of oscillation & settling time

References [4] Experimental Positioning Control of Flexible Arm Using Two-Degrees-of-Freedom Controller Two Methods: * 2) is better 1) Feedback Control (frequency domain)  Based on Model matching method using the inverse dynamics of the arm system 2) Feed-forward Control (time domain) Using the inverse dynamics of the non-minimum phase system of the arm

References [5] Control of Manipulation Robots Interacting with Dynamic Environment: Implementation and Experiments

Our Goals To design a control system for Robot Arm, To practice the control theories acquired in class, To provide an educational model of control theories with Robot Arm model, To help the students understand the control system theory and increase their interest in the subject matter.

Team & Roles Start Topic Selection Role Assignment References Search Irena Karasik (Model Analysis) Sylvain Ganter (Controller Design) Olivier Paultre (SIMULINK) Jeong Ja Kong (Controller Design, Leader) Weekly Meeting Plant Modeling Controllers Design MATLAB Simulation Educational Model End

Steps Step3 Step1 Actuator + Process (Robot Arm) Step2 Controller GUI Input (Reference) Output (Arm Dynamics) Controller GUI (Controller Gain Adjust) Step3  Step1 : Analysis of system characteristic (From the Dynamics of Robot Arm)  Step2 : Controller Design (P, PI, PD, PID, Phase-Lead or -Lag Compensator)  Step3 : Simulation (MATLAB) & User Interface Design (SIMULINK)  Step4 : Evaluation of the performance of the Controlled system

Dynamic Model of Robot Arm 250 . s(s+2)(s+40)(s+45) G (s) =

Characteristics of Plant Model State-space Model | -87 -1970 -3600 0 | | 1 | | | | | A = | 1 0 0 0 | B = | 0 | | 0 1 0 0 | | 0 | | 0 0 1 0 | | 0 | C = | 0 0 0 250 | D = | 0 |

Characteristics of Plant Model Location of Poles & Zeros

Characteristics of Plant Model Steady state error (Type ) Step Input : ess= 0 Ramp Input : With unit ramp input, Kv = lim sG(s) = .0694 ess = A/Kv =14.4 Parabolic Input : ess = 

Characteristics of Plant Model Controllability & Observability det [Pc] = 3.9  10 9  Process is controllable det [Po] = 1  Process is observable

Characteristics of Plant Model Time Response & Frequency Response Ts =  P.O =  Phase Margin = 87.8º

Design Criteria Settling Time, Ts  1.2 sec Maximum Overshoot, P.O  20% Phase Margin, PM  45°

Controller Design Unity Feedback Control Ts = 80 sec P.O = 0 % PM = -180°

Controller Design P Control Settling time is several times greater than the desired value Ts = 4.26 sec P.O = 20 % PM = 79.7 °

Controller Design PI Control Settling time is still too large Ts = 4.25 sec P.O = 20 % PM = 77.3 °

Controller Design PD Control Settling time is better, but still does not meet our criteria Ts = 1.43 sec P.O = 20 % PM = 96.7 °

Controller Design PID Control Settling time is better, but still does not meet our criteria Ts = 1.75 sec P.O = 20 % PM = 69.1 °

Controller Design Phase Lead Compensator Ts = .84 sec P.O = 20 % PM = 45 ° meets our design criteria

(Loop Transfer function) Controller Design Phase Lead Compensator (Continued) Open loop (Loop Transfer function) Closed-loop

Educational GUI Design

Open-Loop Response

Closed-Loop Response Input Selection Controller Selection Output Scope Root-Locus Drawing Scope Selection Controllability & Observability Check Comparison Between Controllers Pole-zero & Others Bode Plot

Closed-Loop Response

System Analysis (Pole-zero Map, Root-locus, Bode Plot )

Controller Selection & Parameter Change

Comparison Between 2 Controllers

System Output Analysis

Conclusion It is not possible to meet the design criteria with P, PI, PD, & PID Controller of this Arm Model Controller Gain Change  Effects on Both (Time, Overshoot)! The Best Controller for this model is Phase-Lead Compensator. Student can learn the Control theory easily: Parameter Change  See the effect ! 2 Different Controllers  Compare the effect !

Challenge To Model the Robot-Arm System To find out more interacting educational Model To provide more Visual Learning To add more controllers