A control and fault detection is designed for a shake table with mounted structure. The focus is on the modeling and analysis, controller design and its technical implementation.
Table of Contents
Introduction
Introduction
Motivation
Goals
1 System Description
1.1 Hardware
1.2 Software
2 Modeling
2.1 Modeling of the Shake Table
2.1.1 Continuous Transfer Function
2.1.2 Continuous State Space Representaion
2.1.3 Discrete Transfer Function
2.1.4 Discrete State Space Representaion
2.2 Modeling of a Frame
2.2.1 Time Continuous Transfer Function
2.2.2 Time Continuous State Space Representation
2.2.3 Time Discrete Transfer Function
2.2.4 Time Discrete State Space Representation
3 Control
3.1 Control of the Shake Table
3.1.1 State Controller
3.1.2 State Controller with preset Integrator
3.2 Shake Table Observer
3.2.1 Complete Observer
3.2.2 Reduced Observer
3.3 Control of the Shake Table with a Frame
3.3.1 State Controller
3.3.2 State Controller with preset Integrator
4 Fault Detection
4.1 Tolerance Band Method
4.1.1 Constant Band Method
4.1.2 Proportional Band Method
4.2 Residual Method
4.3 Anti Jitter Automatism
4.4 Application in the real System
4.5 Further Ideas of Fault Detection Methods
4.5.1 Finite State Machine analyzing Reference Velocity
4.5.2 Integration of the Table Acceleration
Conclusion
Objectives & Core Topics
The primary goal of this research project is to design, model, and implement control and fault detection systems for an electromechanical shake table, both with and without a mounted structure. The study focuses on deriving mathematical models, implementing state controllers and observers in Matlab/Simulink, and investigating fault detection automatisms to identify position sensor errors.
- Modeling of the shake table and a mounted frame structure.
- Design of digital state controllers for precise positioning.
- Development of observers for state estimation (velocity).
- Implementation of fault detection methods and anti-jitter logic.
Excerpt from the Book
3.2 Shake Table Observer
The control described in 3.1 feeds the derivative of the measured platform position back. It is used as an approximation of the real platform velocity. However, it is not guaranteed that this approximation represents exactly the real velocity. In order to get a unity that represents exactly the real platform velocity, the observer is used for a state estimation. The design of an observer for the shake table states is described in this section.
3.2.1 Complete Observer
The complete observer is used to estimate all states of a system with a known model. The system equation of the complete observer is ([Is1], [Og1], [Val])
xˆ(k + 1) = A · xˆ(k) + b · u(k) + H [y(k) − c^T · xˆ(k)] (92)
The structure can be seen in figure (22) showing an observer for the shake table.
An observer can be designed, if the determinant of the observability matrix
MB = [c^T / c^T · A] (93)
is unequal to zero [Is1]. For the shake table this results with
MB = [1 0 / 1 0, 0092] (94)
Chapter Summaries
Introduction: Provides the overview of the project, defining goals such as modeling, controller design, and the implementation of fault detection for the shake table.
System Description: Describes the hardware components, including the 12V DC motor, encoders, accelerometers, and the software environment based on Matlab/Simulink and WinCon.
Modeling: Details the experimental identification of the shake table and frame structure, deriving both continuous and discrete transfer functions and state-space representations.
Control: Focuses on the design of state controllers, including those with preset integrators to eliminate steady-state error, and the implementation of complete and reduced observers.
Fault Detection: Introduces constant and proportional tolerance band methods, the residual method, and an anti-jitter automatism to handle sensor faults and rapid reference changes.
Keywords
Shake Table, Electromechanical Systems, State Control, Matlab/Simulink, Fault Detection, Observer Design, State Space Representation, Transfer Function, Position Sensor, Anti-Jitter, Integration, Modeling, Control Engineering, Feedback Control, Digital Controller
Frequently Asked Questions
What is the primary focus of this research project?
The project focuses on the modeling, controller design, and technical implementation of control systems and fault detection automatisms for an electromechanical shake table equipped with a mounted structure.
What are the main thematic areas covered?
The work covers system modeling, digital state control, observer design for state estimation, and various fault detection strategies for position sensors.
What is the core objective or research question?
The objective is to enable the shake table to follow specific reference positions while minimizing the oscillations of mounted structures and reliably detecting sensor faults.
Which scientific methodology is employed?
The project employs experimental modeling to identify system coefficients, state-space control theory, Z-transformation for discrete-time analysis, and finite state machine theory for fault detection.
What does the main part of the work address?
The main part addresses the derivation of state-space models, the design of state-feedback controllers with integrators, the estimation of unmeasurable states via observers, and the evaluation of fault detection methods through simulation and real-world testing.
Which keywords characterize this work?
Key terms include Shake Table, State Control, Fault Detection, Observer Design, and Matlab/Simulink modeling.
Why are observers necessary for the shake table?
Observers are required because the platform velocity is not directly measurable by any sensor, and an accurate state estimation is crucial for high-performance control.
How does the anti-jitter automatism function?
The anti-jitter automatism uses a finite state machine to differentiate between actual sensor faults and short-term deviations caused by fast reference signal changes.
- Quote paper
- Dipl-Ing. Thomas Heidenreich (Author), 2004, Modeling, Control and Fault Analysis in Electromechanical Systems applicated on a Shake Table, Munich, GRIN Verlag, https://www.grin.com/document/113105
