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Data-based optimal control

This paper deals with data-based optimal control. The control algorithm consists of two complementary subsystems, namely a data-based observer and an optimal feedback controller based on the systems Markov parameters. These parameters can be identified on-line using only input/output data. The effectiveness of the resulting controller is evaluated with a regulation and a tracking control experiment, performed on a direct-drive robot of spatial kinematics.

H 2 performance analysis of reset control systems

To overcome fundamental limitations of linear controllers, reset controllers were proposed in literature. Since the closed loop system including such a reset controller is of a hybrid nature, it is difficult to determine its performance. The focus in this paper is to determine the performance of a SISO reset control system in H2 sense. The method is generally applicable in the sense that it is valid for any proper LTI plant and linear-based reset controller. We derive convex optimization problems in terms of LMIs to compute an upperbound on the H2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. Finally, by means of a simple multiobjective tracking example, we show that reset control can outperform a linear controller obtained via a standard multiobjective control design method.

LPV control of an active vibration isolation system

Non-stationary disturbances in motion systems generally limit the closed-loop performance. If these disturbance can be measured, this measurement can be used to enable a linear parameter varying (LPV) controller to adapt itself to the current operating condition, resulting in a closed-loop system with an overall increased performance. In this paper, this idea is applied to an active vibration isolation system.

An LMI-based L 2 gain performance analysis for reset control systems

In this paper we present a general LMI-based analysis method to determine an upperbound on the L2 gain performance of a reset control system. These computable sufficient conditions for L2 stability, based on piecewise quadratic Lyapunov functions, are suitable for all LTI plants and linear-based reset controllers, thereby generalizing the results available in literature. Our results furthermore extend the existing literature by including tracking and measurement noise problems by using strictly proper input filters. We illustrate the approach by a numerical example.

Linear control of time-domain constrained systems

This paper presents a general framework for the design of linear controllers for linear systems subject to time-domain constraints. The design framework exploits sums-of-squares techniques to incorporate the time-domain constraints on closed-loop signals and leads to conditions in terms of linear matrix inequalities (LMIs). This control design framework offers, in addition to constraint satisfaction, also the possibility of including an optimization objective that can be used to minimize steady state (tracking) errors, to decrease the settling time, to reduce overshoot and so on. The effectiveness of the framework is shown via a numerical example.

Feedforward for multi-rate motion control: Enhanced performance and cost-effectiveness

In traditional feedback control, a single sampling rate is used for all control loops. Consequently, achieving higher performance by increasing the sampling rate is generally costly. The aim of this paper is to develop a multi-rate control framework to create a breakthrough in the performance/cost trade-off in digital controller implementation. In the proposed approach one of the control loops is implemented at a lower rate of which the feedforward controller is designed through norm-based minimalization of the tracking error in this multi-rate framework. By designing and implementing one of the control loops at a lower rate, the cost is reduced and the multi-rate problem is addressed. Through simulation the adequate performance of the proposed multi-rate approach is demonstrated.

Data-based control of motion systems

This paper presents recent research results for feedback control design of motion systems. Two model-free approaches are investigated, that exploit the ease of experimentation which is typical for motion systems. One approach is data-based design of a linear feedback controller which realizes desired closed-loop sensitivity and complementary sensitivity transfer functions. These transfer functions are specified via a data-based performance cost. The designer can prescribe both the controller structure and the complexity. Experimental results obtained in a direct-drive robot motion control problem confirm the effectiveness of the design. A second line of research is unfalsified control where a set of controllers is iteratively tested against measured data. Experimental results for the well-known fourth order benchmark motion system show feasibility of the approach. Finally, we implemented a nonlinear SPAN filter on the same system, which outperforms a linear feedback design

Time-domain performance based non-linear state feedback control of constrained linear systems

This article describes a method to design a non-linear state feedback controller that meets a set of time-domain specifications not attainable by linear state feedback. Using a constrained polynomial interpolation technique, an input signal is computed that satisfies the desired time-domain constraints on the input and state-trajectories. The computed input is constructed by non-linear combinations of the states, such that a non-linear state feedback law is obtained. Stability of the resulting closed-loop polynomial system is analysed using sum-of-squares techniques. An illustrative example is presented, showing that the proposed non-linear controller outperforms the best linear static state feedback. To validate the proposed method, experiments on a fourth-order motion system have been carried out.

Time domain performance based nonlinear state feedback control of constrained linear systems

This paper describes a method to design a nonlinear state feedback controller that meets a set of time-domain specifications not attainable by linear state feedback. Using a constrained polynomial interpolation technique, an input signal is computed that satisfies the desired time-domain constraints on the input and state-trajectories. The computed input is constructed by nonlinear combinations of the states, such that a nonlinear state feedback law is obtained. Stability of the resulting closed-loop polynomial system is analyzed using sum-of-squares techniques. An illustrative example is presented, showing that the proposed nonlinear controller outperforms its linear counterpart. To validate the proposed method, experiments on a fourth-order motion system have been carried out.