Seyed Mahdi Hashemi

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

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.

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

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.

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

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 plants parameter dependency is first approximated by means of principle component analysis. The guarantees are recovered by tools which have previously been reported.

LPV Modelling and Control of Burgers’ Equation

Abstract Linear parameter-varying (LPV) modelling and control of a nonlinear PDE is presented in this paper. The one-dimensional viscous Burgers’ equation is discretized using a finite difference scheme and the boundary conditions are taken as control inputs. A nonlinear high-order state space model is generated and proper orthogonal decomposition is used for model order reduction and the accuracy of the reduced model is verified. A discrete-time quasi-LPV model that is affine in scheduling parameters is derived based on the reduced model and a polytopic LPV controller is synthesized. A low-order functional observer is designed to estimate the scheduling parameters required for LPV controller. Simulation results demonstrate the high tracking performance and disturbance and measurement noise rejection capabilities of the designed LPV controller comparing with an LQG controller based on a linearized model.

LPV gain-scheduled control of a control moment gyroscope

This paper presents the design and successful experimental validation of a linear parameter-varying (LPV) control strategy for a four-degrees-of-freedom control moment gyroscope (CMG). First, a linearized model with moving operating point is used to construct an LPV model. Then, a gridding-based LPV state-feedback control is designed that clearly outperforms linear time-invariant (LTI) controllers. Moreover, a way is proposed to select pre-filter gains for reference inputs that can be generalized to a large class of mechanical systems. Overall, the strategy allows a simple implementation in real-time. Experimental results illustrate that the proposed LPV controller achieves indeed a better performance in a much wider range of operation than linear controllers reported in the literature.

Synthesis of LPV controllers with reduced implementation complexity

The application of linear parameter-varying (LPV) control techniques proves difficult when the number of scheduling parameters is large. This paper reviews and extends practical methods for linear fractional transformation (LFT) based LPV controller design, in order to achieve reduced implementation complexity via affine parameter dependence. Methods to approximate a given affine LPV model are reinterpreted in terms of a nonlinear mapping from rational to reduced affine parameter dependence and a procedure is proposed, that does not rely on experimental data and is therefore also applicable to unstable systems. It is further proposed, to evaluate multiplier conditions by taking into account rational dependence of affine parameters on LFT parameters via a secondary application of the full-block S-procedure. Numerical examples illustrate that the proposed methods can result in reduced conservatism, implementation and synthesis complexity.

Black-box versus grey-box LPV identification to control a mechanical system

This paper presents a comparison of black-box and grey-box linear parameter varying (LPV) identification techniques to control a mechanical systems. It is illustrated by a practical example that if a physical model of a system is not available or too complicated for controller synthesis, black-box identification techniques may lead to a model and controller which achieves a reasonable performance. As an application, a black-box LPV model of a three-degrees-of-freedom robotic manipulator is identified experimentally from a sufficiently reach input-output data set. After model validation, a polytopic gain-scheduled LPV controller is designed for both models. Another LPV controller is designed based on a grey-box model. To compare the performance of the designed controllers, they are implemented on the manipulator to do a trajectory tracking task. In addition, an inverse dynamics and a PD controller are also implemented for comparison. It is shown that back-box LPV identification can potentially give reasonable performance, but not as high as grey-box modelling.

Closed-loop stability and performance optimization in LPV control based on a reduced parameter set

A difficulty encountered in applying linear parameter-varying (LPV) control is the complexity of synthesis and implementation for large numbers of scheduling parameters. Often, heuristic solutions involve neglecting individual scheduling parameters, such that LPV controller synthesis methods become applicable. However, stability and performance guarantees are rendered void, if a controller design based on an approximate model is implemented on the original plant. In this paper, a posteriori conditions are proposed to assess closed-loop stability and performance and possibly recover guarantees. The controller - synthesized based on a reduced parameter set - is first transformed back to depend on the original parameters. Then analysis is performed with respect to the original plant model, which is considered to be accurate. Moreover, an iterative approach for optimizing controllers with few scheduling parameters is sketched. A two-degrees-of-freedom (2-DOF) robotic manipulator is considered as an illustrative example. Experimental results indicate a significant increase in performance.

Decentralized LPV Gain-Scheduled PD Control of a Robotic Manipulator

In this paper, low-complexity linear parameter-varying (LPV) modeling and control of a two-degrees-of-freedom robotic manipulator is considered. A quasi-LPV model is derived and simplified in order to facilitate LPV controller synthesis. An LPV gain-scheduled, decentralized PD controller in linear fractional transformation form is designed, using mixed sensitivity loop shaping to take — in addition to high tracking performance — noise and disturbance rejection into account, which are not considered in model-based inverse dynamics or computed torque control schemes. The controller design is based on the existence of a parameter-dependent Lyapunov function — employing the concept of quadratic separators — thus reducing the conservatism of design. The resulting bilinear matrix inequality (BMI) problem is solved using a hybrid gradient-LMI technique. Experimental results illustrate that the LPV controller clearly outperforms a decentralized LTI-PD controller and achieves almost the same accuracy as a model-based inverse dynamics and a full-order LPV controllers in terms of tracking performance while being of significantly lower complexity.Copyright