Development of a low-cost PID setup for engineering technology students

Csurcsia, Péter Zoltán; Bhandari, Pujan; De Troyer, Tim

Abstract

PID controllers are the most frequently used controllers. Theoretical understanding of the system to be controlled and the working principle of PID controllers are crucial for closed-loop control. This fundamental knowledge is - in principle - learned by all engineering students at the undergraduate level. However, understanding the practical aspects of the application of a PID controller and their connections to theoretical concepts must be combined in a clever way. This paper explores the process of the development of a low-cost, easy to manufacture demonstration setup which can act as the bridge between the theoretical and practical world of the control system knowledge.
As a reaction to the COVID epidemy, this project is made with the philosophy that the students should be able to take these setups home or even replicate them themselves. The proposed setup comes with an interactive block diagram-based graphical user interface which allows the user to observe the physical changes of the process in -nearly- real-time.
The aim of the provided exercises is to comprehend the similarities and the difference between the theoretical and practical aspects of closed-loop control. This paper explains the components of the setup, the development process, the recommended exercises, and feedback from our students.

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Frequency Response Function Estimation for Systems with Multiple Inputs using Short Measurement: A Benchmark Study

Csurcsia, Péter Zoltán; Peeters, Bart; De Troyer, Tim

Abstract

This paper illustrates a combined nonparametric and parametric system identification framework for modeling nonlinear vibrating structures. First step is the analysis: multiple-input multiple-output measurements are (semi-automatically) preprocessed, and a nonparametric Best Linear Approximation (BLA) method is performed. The outcome of the BLA analysis results in nonparametric frequency response function, noise and nonlinear distortion estimates. Based on this information, a linear parametric (state-space) model is built. This model is used to initialize a high complexity Polynomial Nonlinear State-Space PNLSS model. The nonlinear part of a PNLSS model is manifested as a combination of high-dimensional multivariate polynomials. The last step in the proposed approach is the decoupling: transforming multivariate polynomials into a simplified, alternative basis, thereby dramatically reducing the number of parameters. In this work a novel filtered canonical polyadic decomposition (CPD) is used. The proposed methodology is illustrated on, but of course not limited to, a ground vibration testing measurement of an air fighter.

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Nonlinear Modelling of an F16 Benchmark Measurement

Csurcsia, Péter Zoltán; Decuyper, Jan; Renczes, Balázs; De Troyer, Tim

Abstract

Engineers and scientists want mathematical models of the observed system for understanding, design and control. Many mechanical and civil structures are nonlinear. This paper illustrates a combined nonparametric and parametric system identification framework for modeling a nonlinear vibrating structure. First step of the process is the analysis: measurements are (semi-automatically) preprocessed, and a nonparametric Best Linear Approximation (BLA) method is applied. The outcome of the BLA analysis results in nonparametric frequency response function, noise and nonlinear distortion estimates. Second, based on the information obtained from the BLA process, a linear parametric (state-space) model is built. Third, the parametric model is used to initialize a complex Polynomial Nonlinear State-Space (PNLSS) model. The nonlinear part of a PNLSS model is manifested as a combination of high-dimensional multivariate polynomials. The last step in the proposed approach is the decoupling: transforming multivariate polynomials into a simplified, alternative basis, thereby significantly reducing the number of parameters. In this work a novel filtered canonical polyadic decomposition (CPD) is used. The proposed methodology is illustrated on, but of course not limited to, a ground vibration testing measurement of an F16 aircraft.

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An empirical study on decoupling PNLSS models illustrated on an airplane

Csurcsia, Péter Zoltán; De Troyer, Tim

Abstract

This paper illustrates a combined nonparametric and parametric system identification framework for modeling nonlinear vibrating structures. First step is the analysis: multiple-input multiple-output measurements are (semi-automatically) preprocessed, and a nonparametric Best Linear Approximation (BLA) method is performed. The outcome of the BLA analysis results in nonparametric frequency response function, noise and nonlinear distortion estimates. Based on this information, a linear parametric (state-space) model is built. This model is used to initialize a high complexity Polynomial Nonlinear State-Space PNLSS model. The nonlinear part of a PNLSS model is manifested as a combination of high-dimensional multivariate polynomials. The last step in the proposed approach is the decoupling: transforming multivariate polynomials into a simplified, alternative basis, thereby dramatically reducing the number of parameters. In this work a novel filtered canonical polyadic decomposition (CPD) is used. The proposed methodology is illustrated on, but of course not limited to, a ground vibration testing measurement of an air fighter.

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A simplified frequency domain approach for local module identification in dynamic networks

Csurcsia, Péter Zoltán; Ramaswamy, Karthik; Schoukens, Johan; Van den Hof, Paul

Abstract

In classical approaches of dynamic network identification, in order to identify a (sub)system (module) embedded in a dynamic network, one has to formulate a MISO identification problem that requires identification of a parametric model for all the modules constituting the MISO setup - including the noise model - and determine their model orders. This requirement leads to model order selection steps for modules that are of no interest to the experimenter which increases the computational complexity for large-sized networks. In this work, we provide a two-step identification approach to avoid these problems. The first step involves performing a nonparametric indirect approach for a MISO identification problem to get the non-parametric frequency response function estimates and its variance as a function of frequency. In the second step, the estimated FRF of the target module is smoothed using a parametric frequency domain estimator with the estimated variance from the previous step as the non-parametric noise model.
The developed approach is practical with weak assumptions on noise, uses already available toolboxes, requires a parametric model only for the target module of interest, and uses a non-parametric noise model to reduce the variance of the estimates.

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