J. De Caigny

AN APPLICATION OF INTERPOLATING GAIN-SCHEDULING CONTROL

Abstract This work investigates an application of interpolating gain-scheduling control for a structural acoustic problem. The dynamics of the system under consideration are highly sensitive to variation in the temperature. Therefore, linear time invariant ℋ 2 output feedback controllers are designed for different temperature conditions. Afterwards, these controllers are interpolated to provide a global discrete-time linear parameter-varying controller. The closed-loop stability is a posteriori guaranteed using recent less conservative analyses that consider bounds on the rate of variation of the temperature.

Optimal Splines for Rigid Motion Systems: A Convex Programming Framework

This paper develops a general framework to synthesize optimal polynomial splines for rigid motion systems driven by cams or servomotors. This framework is based on numerical optimization, and has three main characteristics: (i) Spline knot locations are optimized through an indirect approach, based on providing a large number of fixed, uniformly distributed candidate knots; (ii) in order to efficiently solve the corresponding large-scale optimization problem to global optimality, only design objectives and constraints are allowed that result in convex programs; and (iii) one-norm regularization is used as an effective tool for selecting the better (that is, having fewer active knots) solution if many equally optimal solutions exist. The framework is developed and validated based on a double-dwell benchmark problem for which an analytical solution exists.

Gain-scheduled H ∞ -control of discrete-time polytopic time-varying systems

This paper presents synthesis procedures for the design of both robust and gain-scheduled H∞ static output feedback controllers for discrete-time linear systems with time-varying parameters. The parameters are assumed to vary inside a polytope and have known bounds on their rate of variation. The geometric properties of the polytopic domain are exploited to derive a finite set of linear matrix inequalities that consider the bounds on the rate of variation of the parameters. A numerical example illustrates the proposed approach.

A linear programming approach to design robust input shaping

Input shaping is an established technique to generate prefilters that move flexible mechanical systems with little or no residual vibration. While traditional input shaping design strategies are often analytical, the present paper introduces a design method based on numerical optimization. It is shown that, through a careful selection of the optimization variables, objective function and constraints, it is possible to obtain a linear optimization problem. As a result, it is guaranteed that the globally optimal input shaper be found in a few seconds of computational time. The presented optimization framework is able to handle higher-order, linear time-invariant dynamic systems, as opposed to traditional input shapers, which are mainly based on second- order systems. Moreover, constraints on input, output and state variables are easily accounted for, as well as robustness against parametric uncertainty. Numerical results illustrate the capability of the proposed design approach to reproduce existing input shaping design approaches, while experimental results illustrate its potential for higher-order systems.

Optimal Design of Spline-Based Feedforward for Trajectory Tracking

This paper presents a new feedforward design method for linear time invariant systems. The feedforward design is formulated as a linear program that optimizes a polynomial spline of order M + 2, which is continuous up to the M-th derivative. The desired tracking accuracy is specified in advance and is traded off with the smoothness of the feedforward signal. Avoidance of actuator saturation is handled through imposing input constraints. Simulation results are presented to validate the developed feedforward design method. The considered test case is a flexible one-link robot, which is a nonminimum phase system. The obtained numerical results improve those of an earlier benchmark method, the extended bandwidth zero phase tracking control method. Furthermore, the results show that in practice, the proposed linear programming framework behaves as an algorithm that is capable of automatically selecting the number and location of the knots of a polynomial spline of order M + 2.

Dynamically Compensated and Robust Motion System Inputs Based on Splines: A Linear Programming Approach

For motion systems such as cam-follower mechanisms and loads driven by servo motors, this paper considers the design of system inputs that are continuous up to their M-th derivative and minimize some design criterion subject to user- defined constraints. This problem is tackled by optimizing a piecewise-linear continuous parametrization (based on a large number of second-order B-splines) of the M-th derivative of the system input. Furthermore, the design criterion and constraints are chosen such that the resulting optimization problem is a linear program. As an application, the system input of a linear dynamic system is optimized to reduce the residual vibration in a robust manner. The obtained numerical results improve those of an earlier benchmark, based on Bernstein-Bezier harmonics. Furthermore, they suggest that the proposed linear programming approach behaves in practice as an algorithm that is capable of automatically selecting the optimal number and location of the knots of a polynomial spline of order M + 2.

Polynomial spline input design for LPV motion systems

This paper considers the concurrent design of point- to-point trajectories and corresponding feedforward inputs for mechatronic motion systems. This design approach is an extension of a recently developed linear optimization framework for polynomial splines of a chosen degree. This optimization framework minimizes the higher derivatives of the spline, thereby ensuring smoothness of the systems input, and is capable of automatically selecting the optimal number and location of the knots of the polynomial spline inputs. By including a discrete- time linear system model in the optimization framework, the input of the motion system is obtained as a dynamically optimal polynomial spline, taking into account boundary and bound constraints on both system input and output, as well a their derivatives. Numerical results illustrate the potential of the presented design approach for linear parameter varying systems.

Design of dynamically optimal spline motion inputs: Experimental results

This work considers the design of point-to-point input trajectories for flexible motion systems. The objective is to excite the systems dynamics as little as possible so as to reduce residual vibration and settling time. Simulation and experimental results of a recently developed optimization framework for polynomial splines are presented. This framework is capable of automatically selecting the optimal number and location of the knots of the polynomial spline and allows input constraints and robustness against parametric uncertainty and unmodeled dynamics to be included during the design. The obtained results are compared to two literature benchmark methods.

Dynamically optimal polynomial splines for flexible servo-systems: Experimental results

This work considers the design of point-to-point input trajectories that result in minimal residual vibration of flexible motion systems. The design is based on a recently developed optimization framework for polynomial spline design. This framework is based on linear programming and automatically selects the optimal number and location of the spline knots, while also allowing the designer to consider input constraints and robustness against parametric uncertainty and unmodeled dynamics. Simulation and experimental results are presented for a two-degree-of-freedom (2-DOF) test setup and compared to two literature benchmark methods.