This paper provides a survey of results in linear parameter-varying (LPV) control that have been validated by experiments and/or high-fidelity simulations. The LPV controller synthesis techniques employed in the references of this survey are briefly reviewed and compared. The methods are classified into polytopic, linear fractional transformation, and gridding-based techniques and it is reviewed how in each of these approaches, synthesis can be carried out as a convex optimization problem via a finite number of linear matrix inequalities (LMIs) for both parameter-independent and parameter-dependent Lyapunov functions. The literature is categorized with regard to the application, the complexity induced by the controlled system’s dynamic and scheduling orders, as well as the synthesis method. Exemplary cases dealing with specific control design problems are presented in more detail to point control engineers to possible approaches that have been successfully applied. Furthermore, key publications in LPV control are related to application achievements on a timeline.

A Survey of Linear Parameter-Varying Control Applications Validated by Experiments or High-Fidelity Simulations

This paper deals with the important topic of industrial robot identification. The usual identification method is based on the inverse dynamic identification model and the least squares technique. This method has been successfully applied on several industrial robots. Good results can be obtained, provided a well tuned derivative band-pass filtering of joint positions is used to calculate the joint velocities and accelerations. However, one cannot be sure whether or not the band-pass filtering is well tuned. An alternative is the instrumental variable (IV) method, which is robust to data filtering and is statistically optimal. In this paper, a generic IV approach suitable for robot identification is proposed. The instrument set is the inverse dynamic model built from simulated data calculated from simulation of the direct dynamic model. The simulation is based on previous estimates and assumes the same reference trajectories and the same control structure for both actual and simulated robots. Finally, gains of the simulated controller are updated according to IV estimates to obtain a valid instrument set at each step of the algorithm. The proposed approach validates the inverse and direct dynamic models simultaneously, is not sensitive to initial conditions, and converges rapidly. Experimental results obtained on a six-degrees-of-freedom industrial robot show the effectiveness of this approach: 60 dynamic parameters are identified in three iterations.

A Generic Instrumental Variable Approach for Industrial Robot Identification

https://escholarship.org/content/qt69n1p5vd/qt69n1p5vd.pdf

A review on data-driven linear parameter-varying modeling approaches: A high-purity distillation column case study

https://hal.archives-ouvertes.fr/hal-02611783/document

Model predictive control design for linear parameter varying systems: A survey

In this studies, adaptive boundary control for a flexible two-link manipulator with a changeable payload at the free-end. Taking into account the infinite-dimensionality of the flexural dynamics, this study proposes a partial differential equation (PDE) model, so that the problem of possible spillover instability caused by the neglect of flexible modes can be avoided. Based on the PDE model, an adaptive boundary control scheme is designed to regulate joint position and suppress elastic vibration while compensating for parametric uncertainties. The asymptotic stability of the closed-loop system is validated theoretically. The effectiveness of the control scheme is also verified by the numerical simulations.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2011.0593

Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model

Low-complexity linear parameter-varying modeling and control of a robotic manipulator

LPV state-feedback control of a control moment gyroscope

This paper presents the construction of a realistic linear parameter-varying (LPV) model of a robotic manipulator using parameter set mapping, for the purpose of synthesizing an LPV gain-scheduled controller. A nonlinear dynamic model of the manipulator is obtained and a quasi-LPV model is derived. Since the quasi-LPV model has a large number of affine scheduling parameters and a large overbounding, parameter set mapping is used to reduce conservatism and complexity in controller design by finding tighter parameter regions with fewer scheduling parameters. Then, a polytopic LPV gain-scheduled controller is synthesized and implemented experimentally on an industrial robot for a trajectory tracking task. Comparison of results with a decentralized PD controller illustrates that the designed LPV controller improves the tracking error significantly. Moreover, it achieves a slightly better accuracy than a model-based inverse dynamics controller while being of lower complexity.

LPV modelling and control of a 2-DOF robotic manipulator using PCA-based parameter set mapping

This document proposes the nonlinear control of an industrial three-degrees-of-freedom (3-DOF) robotic manipulator as a benchmark problem for controller synthesis methods, that are applicable to complex plants, but can provide implementation with low complexity. Full details on the nonlinear model of the industrial robotic manipulator Thermo CRS A465 are provided. Furthermore, a solution is presented by considering linear parameter-varying (LPV) controller synthesis based on a reduced parameter set. Stability and performance guarantees are rendered void as the plant's parameter dependency is first approximated by means of principle component analysis. The guarantees are recovered by tools which have previously been reported.

Benchmark problem — nonlinear control of a 3-DOF robotic manipulator

A major difficulty encountered in the application of linear parameter-varying (LPV) control is the complexity of synthesis and implementation when the number of scheduling parameters is large. Often heuristic solutions involve neglecting individual scheduling parameters, such that standard LPV controller synthesis methods become applicable. However, stability and performance guarantees are rendered void, if controller designs based on an approximate model are implemented on the original plant. In this brief, a synthesis method for LPV controllers that achieves reduced implementation complexity is proposed. The method is comprised of first synthesizing an initial controller based on a reduced parameter set. Then closed-loop stability and performance guarantees are recovered with respect to the original plant, which is considered to be accurately modeled. Iteratively solving a nonconvex bilinear matrix inequality may further improve performance. A two-degrees-of-freedom (2-DOF) and three-degrees-of-freedom robotic manipulator is considered as an illustrative example, for which experimental results indicate a good performance for controllers of reduced scheduling order. Furthermore, in the 2-DOF case, controller performance has been significantly improved.

Seyed Mahdi Hashemi

Papers

Low-complexity linear parameter-varying modeling and control of a robotic manipulator

LPV state-feedback control of a control moment gyroscope

LPV modelling and control of a 2-DOF robotic manipulator using PCA-based parameter set mapping

Benchmark problem — nonlinear control of a 3-DOF robotic manipulator

Synthesis of LPV Controllers With Low Implementation Complexity Based on a Reduced Parameter Set