Internal Model Controller Design for a Robot arm

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Senior Project
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
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Senior Project

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

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Functional Description

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

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Functional Description
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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
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Functional Description
Acquisition Board Port Interface
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Functional Description
Power Module
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High Level System Block Diagram
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Project Abstract

• The goal of this Electrical Engineering Senior
  Capstone Project is to design a Internal Model
  Controller for controlling the non-linear 6th
  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.

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Project Description

• 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
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Project Description

• Internal Model Control Closed-Loop

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Project Description

• Internal Model Control Advantages
• Provides time-delay compensation
• 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 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.

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Project Description

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

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Prespective

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

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Applications

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

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Functional Requirements

• Single Loop Proportional , ProportionalDerivati
  ve Controller
• FD Design for P, PD, PI controllers
• Internal Model Control
• Internal Model Control with Adaptive Model

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Performance Specifications

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

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Fall 07 Work

• System Identification without arm

Experimental Simulation
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Fall 07 Work

• Proportional Controller Design without arm
• Gc(s) K 0.3

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Fall 07 Work

• Proportional Derivative Controller Design
  without arm
• Gc(s) 0.61(s 61.5)/(s120)?

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Spring 08 Work

• System Identification with Arm
• 45.73 e ( -0.110s)?
• Gp(s) --------------------------
• s(s/30.0 1.0)?
• Gain and Delay found by experimental data
• Pole found by multiple simulation best fit method
• This is the best fit 2nd order model for the
  plant.

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Spring 08 Work

• System Identification with Arm
• Experimental vs. Model results are close but
  not perfect

Experimental Simulation
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Spring 08 Work

• F.D.Design P controller
• F.D. Design PD controller
• F.D. Design PI controller
• F.D. Design Optimum Phase Margin PI controller
• Standard Classical Control Techniques
• Design, Simulate, Implement, Evaluate

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Spring 08 Work
Uncompensated Partially Compensated
PI Proportional Controller Compensated PI Optimum
PI
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Spring 08 Work
IMC Controller Design

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Spring 08 Work

• Final Design by Tuning

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Spring 08 Work
IMC step Response
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Spring 08 Work

• Specification Value Spec. Met?
• Percent Overshoot 5 max Yes
• Time to Peak(max) 50ms max No
• Time to settle 200ms max No
• Closed Loop Bandwidth 2Hz min Yes
• Peak CL Frequency Resp. 3dB max Yes
• Gain Margin 5.0 min Yes
• Phase Margin 60 degrees min Yes
• Steady State Error 1 degree max Yes
• Controller Execution Time 1ms max Yes

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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.
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Questions? Comments?