Internal Model Controller Design for a Robot arm By Vishal Kumar Advisor: Gary L. Dempsey 5/6/08 Bradley University Department of Computer and Electrical Engineering Senior Project

1. Functional Description 2. Project Focus 3. Functional Requirements and Specifications 4. Lab work and comparison of results

Functional Description Individual Components 1.46 GHz Windows Based PC with plenty of RAM 1.46 GHz Windows Based PC with plenty of RAM Quanser Plant SRV-02 with embedded position sensors, gripper and motor Quanser Plant SRV-02 with embedded position sensors, gripper and motor Q8 High-Performance H.I.L Control Board and I/O port interface Q8 High-Performance H.I.L Control Board and I/O port interface Power Module PAO103 Power Module PAO103

Functional Description

Q8 High-Performance H.I.L Control Board 8 A/D / 8 D/A Simultaneous Sampling of all A/D and Simultaneous Update to all D/A Supported by Real-Time Targets – RTX, xPC

Functional Description Acquisition Board Port Interface

Functional Description Power Module

High Level System Block Diagram

Project Abstract The goal of this Electrical Engineering Senior Capstone Project is to design a Internal Model Controller for controlling the non- linear 6 th order Quanser Plant in the level configuration. The disturbance rejection capability of Internal Model Control architecture is capable of controlling high-order plants despite their non-linearities and external disturbances.

Project Description Internal Model Control Open-Loop Internal Model Control Open-Loop Let Gp(s) = approx(Gp(s)) And Gc(s) = approx(Gp(s)) ^ -1 Then Gp(s)*Gc(s) = approx(Gp(s)) * approx(Gp(s)) ^ -1 = 1

Project Description Internal Model Control Closed-Loop Internal Model Control Closed-Loop

Project Description Internal Model Control Advantages Internal Model Control Advantages Provides time-delay compensation Provides time-delay compensation At steady-state, the controller will give offset free responses(perfect control at S.S) At steady-state, the controller will give offset free responses(perfect control at S.S) The controller can be used to shape both the input tracking and disturbance rejection responses The controller can be used to shape both the input tracking and disturbance rejection responses The controller is the inverse of the plant without non-invertible components(time-delay) The controller is the inverse of the plant without non-invertible components(time-delay) Perfect Tracking is achieved despite model-mismatch, as long as the controller is the perfect inverse of the model. Perfect Tracking is achieved despite model-mismatch, as long as the controller is the perfect inverse of the model.

Project Description Model Implementation Techniques Model Implementation Techniques 2 nd order model(Linear)  used for Proj. 2 nd order model(Linear)  used for Proj. Look-up Tables(Linear and Non-Linear) Look-up Tables(Linear and Non-Linear) State-Space Model(Linear) State-Space Model(Linear) Adaline model(Linear) Adaline model(Linear) Non-Linear Perceptron model(Non Linear) Non-Linear Perceptron model(Non Linear)

Prespective What makes this project different? What makes this project different? New Tools Simulink/Real Time Execution(RTX) Workshop Simulink/Real Time Execution(RTX) Workshop WinCon Client and WinCon Server environment WinCon Client and WinCon Server environment Implementing an advanced controller architecture – IMC – basis for adaptive control Implementing an advanced controller architecture – IMC – basis for adaptive control

Applications Adaptive Signal Processing Adaptive Signal Processing Flight Control – Adaptive models are of importance Flight Control – Adaptive models are of importance Hydraulics – disturbance rejection is of importance Hydraulics – disturbance rejection is of importance

Functional Requirements 1. Single Loop – Proportional, Proportional–Derivative Controller 2. FD Design for P, PD, PI controllers 3. Internal Model Control 4. Internal Model Control with Adaptive Model

Performance Specifications Percent Overshoot 5% max Percent Overshoot 5% max Time to Peak 50ms max Time to Peak 50ms max Time to settle 200ms max Time to settle 200ms max Closed Loop Bandwidth 2Hz min Closed Loop Bandwidth 2Hz min Closed Loop Frequency Resp. 3dB max Closed Loop Frequency Resp. 3dB max Gain Margin 5.0 min Gain Margin 5.0 min Phase Margin 60 degrees min Phase Margin 60 degrees min Steady State Error 1 degree max Steady State Error 1 degree max Controller Execution Time 1ms max Controller Execution Time 1ms max

Fall ’07 Work System Identification without arm System Identification without arm Experimental Simulation

Fall ’07 Work Proportional Controller Design without arm Proportional Controller Design without arm Gc(s) = K = 0.3 Gc(s) = K = 0.3

Fall ’07 Work Proportional – Derivative Controller Design without arm Proportional – Derivative Controller Design without arm Gc(s) = 0.61(s )/(s+120)‏ Gc(s) = 0.61(s )/(s+120)‏

Spring ‘08 Work System Identification with Arm System Identification with Arm e^ ( s)‏ e^ ( s)‏ Gp(s) = Gp(s) = s(s/ )‏ s(s/ )‏ Gain and Delay found by experimental data Pole found by multiple simulation best fit method This is the best fit 2 nd order model for the plant.

System Identification with Arm System Identification with Arm Experimental vs. Model – results are close but not perfect Spring ’08 Work Experimental Simulation

Spring ‘08 Work F.D.Design – P controller F.D.Design – P controller F.D. Design – PD controller F.D. Design – PD controller F.D. Design – PI controller F.D. Design – PI controller F.D. Design – Optimum Phase Margin PI controller F.D. Design – Optimum Phase Margin PI controller Standard Classical Control Techniques Design, Simulate, Implement, Evaluate

Spring ‘08 Work Uncompensated Partially Compensated PI Proportional Controller Compensated PI Optimum PI

Spring ‘08 Work IMC Controller Design

Spring ‘08 Work Final Design by Tuning

Spring ‘08 Work IMC step Response

Spring ‘08 Work Specification ValueSpec. Met? Percent Overshoot 5% maxYes Percent Overshoot 5% maxYes Time to Peak(max) 50ms maxNo Time to Peak(max) 50ms maxNo Time to settle 200ms maxNo Time to settle 200ms maxNo Closed Loop Bandwidth 2Hz minYes Closed Loop Bandwidth 2Hz minYes Peak CL Frequency Resp.3dB maxYes Peak CL Frequency Resp.3dB maxYes Gain Margin5.0 minYes Gain Margin5.0 minYes Phase Margin60 degrees minYes Phase Margin60 degrees minYes Steady State Error1 degree maxYes Steady State Error1 degree maxYes Controller Execution Time1ms maxYes Controller Execution Time1ms maxYes

Conclusion Internal Model Control(IMC) provides excellent performance for stable plants. Due to a integration in the plant model, meaning that the plant is marginally stable/unstable, the controller architecture reaches limitations and has to be modified. As shown above, in the Simulink Block Diagram, the new architecture provides velocity and position feedback with Internal Model for the velocity of the plant. Literature analyzing controller design provides no insight for controlling unstable plants. The aforementioned technique has powerful implications for controlling unstable plants using the IMC architecture.

Questions? Comments?