Goele Pipeleers

Extended LMI characterizations for stability and performance of linear systems

Over the past ten years, extensive research has been devoted to extended LMI characterizations for stability and performance of linear systems. These characterizations constitute a valuable tool for reducing conservatism in hard problems like multi-objective control, and robust stability and performance analysis. The present paper proposes a general, projection lemma based methodology for deriving such extended LMIs and hereby provides a straightforward and unified proof for all known literature results as well as some currently missing extended LMIs.

Brief paper: Robust high-order repetitive control: Optimal performance trade-offs

High-order repetitive control has previously been introduced to either improve the robustness for period-time uncertainty or reduce the sensitivity for non-periodic inputs of standard repetitive control schemes. This paper presents a systematic, semidefinite programming based approach to compute high-order repetitive controllers that yield an optimal trade-off between these two performance criteria. The methodology is numerically illustrated through trade-off curves for various controller orders and levels of period-time uncertainty. Moreover, existing high-order repetitive control approaches are shown to correspond to specific points on these curves.

A Data-Driven Constrained Norm-Optimal Iterative Learning Control Framework for LTI Systems

This brief presents a data-driven constrained norm-optimal iterative learning control framework for linear time-invariant systems that applies to both tracking and point-to-point motion problems. The key contribution of this brief is the estimation of the systems impulse response using input/output measurements from previous iterations, hereby eliminating time-consuming identification experiments. The estimated impulse response is used in a norm-optimal iterative learning controller, where actuator limitations can be formulated as linear inequality constraints. Experimental validation on a linear motor positioning system shows the ability of the proposed data-driven framework to: 1) achieve tracking accuracy up to the repeatability of the test setup; 2) minimize the rms value of the tracking error while respecting the actuator input constraints; 3) learn energy-optimal system inputs for point-to-point motions.

Gain-Scheduled Controller Design: Illustration on an Overhead Crane

This paper extends a recently developed interpolation-based approach to design gain-scheduled controllers for linear parameter-varying systems with a thorough evaluation, comprising both simulations and experiments, on an overhead crane system. In the first step of the approach, linear time-invariant controllers are designed for local working conditions of the system using a multiobjective H∞ method. With the help of this method, the fundamental tradeoff between reference tracking and disturbance rejection in the overhead crane control problem is analyzed. In the second step, a state-space interpolation method is used to calculate a gain-scheduled controller. Although this approach does not guarantee stability and performance under parameter variations, experiments on the crane setup show that these variations do not compromise the performance of the obtained controller.

Time-Optimal Path Following for Robots With Convex–Concave Constraints Using Sequential Convex Programming

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time. In the case of a robotic manipulator with simplified constraints, a convex reformulation of this optimal control problem has been derived previously. However, many applications in robotics feature constraints such as velocity-dependent torque constraints or torque rate constraints that destroy the convexity. The present paper proposes an efficient sequential convex programming (SCP) approach to solve the corresponding nonconvex optimal control problems by writing the nonconvex constraints as a difference of convex (DC) functions, resulting in convex-concave constraints. We consider seven practical applications that fit into the proposed framework even when mutually combined, illustrating the flexibility and practicality of the proposed framework. Furthermore, numerical simulations for some typical applications illustrate the fast convergence of the proposed method in only a few SCP iterations, confirming the efficiency of the proposed framework.

A physiology based inverse dynamic analysis of human gait: potential and perspectives

One approach to compute the musculotendon forces that underlie human motion is to combine an inverse dynamic analysis with a static optimisation procedure. Although computationally efficient, this classical inverse approach fails to incorporate constraints imposed by muscle physiology. The present paper reports on a physiological inverse approach (PIA) that combines an inverse dynamic analysis with a dynamic optimisation procedure. This allows the incorporation of a full description of muscle activation and contraction dynamics, without loss of computational efficiency. A comparison of muscle excitations and MT-forces predicted by the classical and the PIA is presented for normal and pathological gait. Inclusion of muscle physiology primarily affects the rate of active muscle force build-up and decay and allows the estimation of passive muscle force. Consequently, it influences the onset and cessation of the predicted muscle excitations as well as the level of co-contraction.

Generalized KYP Lemma With Real Data

A recent generalization of the Kalman-Yakubovich-Popov (KYP) lemma establishes the equivalence between a semi-infinite inequality on a segment of a line or circle in the complex plane and a linear matrix inequality (LMI). In this technical note we show that when the data are real, the matrix variables in the LMI can be restricted to be real, even when the frequency range is asymmetric with respect to the real axis.

Optimal Performance Tradeoffs in Repetitive Control: Experimental Validation on an Active Air Bearing Setup

In repetitive control, the bode sensitivity integral dictates a tradeoff between improved suppression of periodic disturbances and degraded performance for non-periodic inputs. This paper experimentally demonstrates the implications of this tradeoff by applying a recently developed repetitive controller design approach to reduce the error motion of the spindles axis of rotation on an active air bearing setup. This design methodology translates the performance tradeoff into tradeoff curves between a non-periodic and periodic performance index, of which the practical relevance is illustrated by the obtained experimental results. Second, the relation is investigated between these two performance indices and the adaptive performance of the repetitive controller during large variations of the spindles rotational speed setpoint. The experiments suggest that, although defined for steady state, the two performance indices also relate to the adaptive performance of the repetitive controller.

Initialization of ILC based on a previously learned trajectory

Iterative learning control (ILC) is an open-loop control strategy that learns the system input to track a desired trajectory from previous executions. A major limitation of ILC is that for every new trajectory, the ILC is reinitiated and thus takes a number of iterations to learn the new optimal system input. This paper presents a novel methodology for linear time-invariant systems to calculate a better initialization of an ILC based on a previously learned similar trajectory and a disturbance model. To illustrate the potential of the developed method, it is applied to a permanent magnet linear motor and compared to a model-based feedforward control scheme. The experimental results show that the proposed method outperforms the model-based feedforward control scheme in the case of similar motion trajectories, yielding a better initialization of an ILC.

Unified Analysis of Iterative Learning and Repetitive Controllers in Trial Domain

While iterative learning control (ILC) and repetitive control (RC) have much ground in common, they fundamentally differ in the initial conditions at each repetition. This difference has lead to distinct analysis techniques, hereby clouding the interrelations between both control strategies. To facilitate the transfer of results, this paper presents a unified approach to ILC and RC. Both control problems are formulated in the trial domain using so-called system lifting. For a given system, the corresponding ILC and RC trial-domain models differ, and a thorough system theoretic analysis and comparison of these models is performed. To illustrate the value of a unified formulation of ILC and RC, the analysis of the most commonly used ILC and RC structures is harmonized. This analysis reveals central differences and similarities between various stability, monotonic convergence and steady-state performance conditions.