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Model-free control and intelligent PID controllers: towards a possible trivialization of nonlinear control?
TL;DR: In this paper, a model-free control and a control with a restricted model for finite-dimensional complex systems are presented, which can be viewed as a contribution to intelligent PID controllers.
Abstract: We are introducing a model-free control and a control with a restricted model for finite-dimensional complex systems. This control design may be viewed as a contribution to "intelligent" PID controllers, the tuning of which becomes quite straightforward, even with highly nonlinear and/or time-varying systems. Our main tool is a newly developed numerical differentiation. Differential algebra provides the theoretical framework. Our approach is validated by several numerical experiments.
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TL;DR: Model-free control and the corresponding ‘intelligent’ PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account.
Abstract: ''Model-free control'' and the corresponding ''intelligent'' PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account. The basics of model-free control is now employing some old functional analysis and some elementary differential algebra. The estimation techniques become quite straightforward via a recent online parameter identification approach. The importance of iPIs and especially of iPs is deduced from the presence of friction. The strange industrial ubiquity of classic PID's and the great difficulty for tuning them in complex situations is deduced, via an elementary sampling, from their connections with iPIDs. Several numerical simulations are presented which include some infinite-dimensional systems. They demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them.
645 citations
TL;DR: An improved MFPCC based on the extended state observer of PMSM drives that does not require motor parameters and needs less tuning work and lower computational time while achieving the better performance in terms of current harmonics, tracking error, and dynamic overshoot is proposed.
Abstract: Conventional model predictive current control (MPCC) is a powerful control strategy for three-phase inverters that has the advantages of simple concept, quick response, easy implementation, and good performance. However, MPCC is sensitive to machine parameter variation, and the performance degrades substantially if a mismatch exists between the model parameters and real machine parameters. Model-free predictive current control (MFPCC) based on an ultralocal model, which uses only the input and output of the system without considering any motor parameters, has been proposed to solve this problem in this article. Since parameters are not required, the robustness of the control system is improved. However, conventional MFPCC based on an ultralocal model uses many control parameters, which increases the tuning work. Furthermore, the control performance is not ideal at low sampling frequency. This article proposes an improved MFPCC based on the extended state observer of PMSM drives that does not require motor parameters and needs less tuning work and lower computational time while achieving the better performance in terms of current harmonics, tracking error, and dynamic overshoot. The proposed method is compared to conventional MPCC and MFPCC, and the effectiveness is confirmed by the simulation and experimental results.
220 citations
TL;DR: The experimental validation on a twin rotor aerodynamic system is included and the new structures are compared with a model-free intelligent proportional-integral (iPI) control system structure.
129 citations
TL;DR: In this article, an inclusive and enhanced formulation of TDC for robust control of robot manipulators is presented, which consists of three intuitive terms: 1) time delay estimation (TDE), inherited from the original TDC, for cancellation of mostly continuous nonlinearities; 2) nonlinear desired error dynamics (DED) (i.e., a "mass" or "nonlinear damper" injection term; and 3) a TDE error correction term based on a nonlinear sliding surface).
Abstract: Thanks to its simplicity and robustness, time delay control (TDC) has been recognized as a simple and yet effective alternative to robot model-based controls and/or intelligent controls. An inclusive and enhanced formulation of TDC for robust control of robot manipulators is presented in this paper. The proposed formulation consists of three intuitive terms: 1) time delay estimation (TDE), inherited from the original TDC, for cancellation of mostly continuous nonlinearities; 2) nonlinear desired error dynamics (DED) (i.e., a “mass”–“nonlinear damper”– “nonlinear spring” system) injection term; and 3) a TDE error correction term based on a nonlinear sliding surface. The proposed TDC formulation has an inclusive structure. Depending on the gain/parameter set chosen, the proposed formulation can become Hsia's formulation, Jin's formulations including a type of terminal sliding mode control (SMC), an SMC with a switching signum function, or a novel enhanced formulation. Experimental comparisons were made using a programmable universal manipulator for assembly-type robot manipulator with various parameter sets for the proposed control. Among them, the highest position tracking accuracy was obtained by using a terminal sliding DED with a terminal sliding correction term.
115 citations
TL;DR: In this paper, a model-free control of an SMA-spring-based actuator is proposed for industrial applications, which relies on new results for fast derivative estimation of noisy signals.
104 citations
References
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TL;DR: In this paper, the three principal control effects found in present controllers are examined and practical names and units of measurement are proposed for each effect and corresponding units for a classification of industrial processes in terms of two principal characteristics affecting their controllability.
Abstract: In this paper, the three principal control effects found in present controllers are examined and practical names and units of measurement are proposed for each effect. Corresponding units are proposed for a classification of industrial processes in terms of the two principal characteristics affecting their controllability. Formulas are given which enable the controller settings to be determined from the experimental or calculated values of the lag and unit reaction rate of the process to be controlled
5,412 citations
TL;DR: In this paper, the authors introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous feedback, which subsumes the physical properties of a linearizing output and provides another nonlinear extension of Kalman's controllability.
Abstract: We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra where flatness- and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of plane curves. The three non-flat examples, the simple, double and variable length pendulums, are borrowed from non-linear physics. A high frequency control strategy is proposed such that the averaged systems become flat.
3,025 citations
Book•
13 Jul 2005
TL;DR: This paper presents SVD-Krylov Methods and Case Studies, a monograph on model reduction using Krylov methods for linear dynamical systems, and some examples of such reduction schemes.
Abstract: Preface Part I. Introduction: 1. Introduction 2. Motivating examples Part II. Preliminaries: 3. Tools from matrix theory 4. Linear dynamical systems, Part 1 5. Linear dynamical systems, Part 2 6. Sylvester and Lyapunov equations Part III. SVD-based Approximation Methods: 7. Balancing and balanced approximations 8. Hankel-norm approximation 9. Special topics in SVD-based approximation methods Part IV. Krylov-based Approximation Methods: 10. Eigenvalue computations 11. Model reduction using Krylov methods Part V. SVD-Krylov Methods and Case Studies: 12. SVD-Krylov methods 13. Case studies 14. Epilogue 15. Problems Bibliography Index.
2,893 citations
TL;DR: What are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system-identification application of these techniques are described, from a user's perspective.
2,031 citations
Book•
22 Jun 1999
TL;DR: In this article, the authors compare Linear vs. Nonlinear Control of Differential Geometry with Linearization by State Feedback (LSF) by using Linearization and Geometric Non-linear Control (GNC).
Abstract: 1 Linear vs. Nonlinear.- 2 Planar Dynamical Systems.- 3 Mathematical Background.- 4 Input-Output Analysis.- 5 Lyapunov Stability Theory.- 6 Applications of Lyapunov Theory.- 7 Dynamical Systems and Bifurcations.- 8 Basics of Differential Geometry.- 9 Linearization by State Feedback.- 10 Design Examples Using Linearization.- 11 Geometric Nonlinear Control.- 12 Exterior Differential Systems in Control.- 13 New Vistas: Multi-Agent Hybrid Systems.- References.
1,925 citations