Hybrid modeling and control of mechatronic systems using a piecewise affine dynamics approach

This thesis investigates the topic of modeling and control of PWA systems based on two experimental cases of an electrical and hydraulic nature with varying complexity that were also built, instrumented and evaluated. A full-order model has been created for both systems, including all dominant system dynamics and non-linearities. The unknown parameters and characteristics have been identi ed via an extensive parameter identi cation. In the following, the non-linear characteristics are linearized at several points, resulting in PWA models for each respective setup. Regarding the closed loop control of the generated models and corresponding experimental setups, a linear control structure comprised of integral error, feed-forward and state-feedback control has been used. Additionally, the hydraulic setup has been controlled in an autonomous hybrid position/force control mode, resulting in a switched system with each mode's dynamics being de ned by the previously derived PWA-based model in combination with the control structure and respective mode-dependent controller gains. The autonomous switch between control modes has been de ned by a switching event capable of consistently switching between modes in a deterministic manner despite the noise-a icted measurements. Several methods were used to obtain suitable controller gains, including optimization routines and pole placement. Validation of the system's fast and accurate response was obtained through simulations and experimental evaluation. The controlled system's local stability was proven for regions in state-space associated with operational points by using pole-zero analysis. The stability of the hybrid control approach was proven by using multiple Lyapunov functions for the investigated test scenarios.publishedVersio

FeedNetBack-D04.03 - Design of Robust Variable Rate Controllers

A consequence of the execution of control algorithms on digital distributed platforms is inducing delays, jitter and various limitations in sampling rate from different sources in the control loops. These disturbances should be taken into account in the control algorithms design and tuning. Control systems are often cited as examples of "hard real-time systems" where jitter and deadline violations are strictly forbidden. In fact experiments show that this assumption may be false for closed-loop control. Any practical feedback system is designed to obtain some stability margin and robustness w.r.t. the plant parameters uncertainty. This also provides robustness w.r.t. timing uncertainties: closed-loop systems are able to tolerate some amount of sampling period and computing delays deviations, jitter and occasional data loss without loss of stability or integrity. Hence the design of dependable distributed control systems may rely on robust controllers, i.e. controllers which are slightly sensitive to both process model and execution resource uncertainties, or on controllers which are made adaptive w.r.t. the variations of the control intervals and other implementation induced disturbances. Section 2 provides new results concerning the control of systems with delays. A novel analysis of linear systems under asynchronous sampling is provided. This approach is based on the discrete-time Lyapunov Theorem applied to the continuous-time model of the sampled-data systems. Tractable conditions are derived to ensure asymptotic stability and also to obtain an estimate of the exponential rate of the solutions. Examples show the efficiency of the method and the reduction of the conservatism compared to other results from the literature. Moreover the methodology addresses the stability analysis of systems under several sampling periods. We show that a sampled-data system can be stable even if one of the sampling period leads to instability. This has been treated by a continuous-time approach and allows considering uncertain or time-varying systems. An extension of the method includes transmission delays in the control loop. As the variations of the control intervals can be both a consequence of network induced delays and a control variable to manage the CPU and/or network load, robust variable sampling control design is investigated in section 3. Here it is assumed that the control interval is itself a control parameter, e.g. which can be adapted at run-time by a feedback scheduler to cope with operating conditions in a varying environment. The control design is stated using the formulation of Linear Parameters Varying (LPV) systems, where the sampling interval is considered as a varying and measurable parameters of the system. Previous results using a polytopic model of a discretized plant are recalled. A new design using a Linear Fractional Transform (LFT) is developed, where the control interval is considered as a system's uncertainty. This new approach is expected to be more tractable that the polytopic one when the system has several varying parameters. Both designs are assessed and compared using as testbed the control of Autonomous Underwater Vehicles using scheduled ultrasonic sensors for control and navigation.

Wide-area monitoring and control of future smart grids

Application of wide-area monitoring and control for future smart grids with substantial wind penetration and advanced network control options through FACTS and HVDC (both point-to-point and multi-terminal) is the subject matter of this thesis. For wide-area monitoring, a novel technique is proposed to characterize the system dynamic response in near real-time in terms of not only damping and frequency but also mode-shape, the latter being critical for corrective control action. Real-time simulation in Opal-RT is carried out to illustrate the effectiveness and practical feasibility of the proposed approach. Potential problem with wide-area closed-loop continuous control using FACTS devices due to continuously time-varying latency is addressed through the proposed modification of the traditional phasor POD concept introduced by ABB. Adverse impact of limited bandwidth availability due to networked communication is established and a solution using an observer at the PMU location has been demonstrated. Impact of wind penetration on the system dynamic performance has been analyzed along with effectiveness of damping control through proper coordination of wind farms and HVDC links. For multi-terminal HVDC (MTDC) grids the critical issue of autonomous power sharing among the converter stations following a contingency (e.g. converter outage) is addressed. Use of a power-voltage droop in the DC link voltage control loops using remote voltage feedback is shown to yield proper distribution of power mismatch according to the converter ratings while use of local voltages turns out to be unsatisfactory. A novel scheme for adapting the droop coefficients to share the burden according to the available headroom of each converter station is also studied. The effectiveness of the proposed approaches is illustrated through detailed frequency domain analysis and extensive time-domain simulation results on different test systems

Variable structure techniques in control system design

During the last twenty years, control theorists belonging almost exclusively to the USSR, have laid down the foundations of variable-structure systems (commonly abbreviated to vsS). As the name implies, such systems are allowed to change their structure through time in accordance with some preassigned algorithm. The theory has demonstrated that some significant advantages could be gained by adopting that approach in the, design of automatic control systems, amongst which are good transient responses and insensitivity to parametric variations and to external disturbances. The VS controller is slightly more complex than a fixed structure design based on standard methods such as state feedback or frequency response techniques, but is a great deal less complex than some adaptive designs. It also lends itself to a straightforward microcomputer implementation. While the theoretical aspect of VSS has been well explored, its general applicability to engineering problems is yet to be established. There are still unanswered questions as to the suitability of the method for practical systems, which invariably contain a certain amount of noise, uncertainties and nonlinearities. The work described in this thesis concentrates on that particular aspect and is, in brief, an investigation of VSS as an engineering design procedure. The theory of VSS is reviewed and the principles are then applied to a number of engineering examples. The performance of the systems are assessed from digital simulation runs, hybrid computation and the microcomputer control of a DC motor