Proportional-derivative State Feedback Control Research Articles

Robust fault estimation and proportional derivative fault tolerant control for a class of singular systems with interval time‐varying delay and disturbance

SummaryThis paper deals with observer‐based fault estimation (FE) and proportional derivative state feedback fault tolerant control (FTC) schemes for singular systems affected by actuator fault, interval time‐varying delay and external disturbance. Firstly, the system transformation method of constructing the derivative matrix into a full‐rank matrix is adopted to transform the singular system into a normal system, which effectively eliminates the impulse characteristic of the singular system. Secondly, in the design of the dynamic observer, fault estimation utilizes the real‐time output error and its derivative simultaneously, which can achieve better estimation performance when the fault change frequently. Most importantly, the observer‐based FTC adopts a proportional derivative state feedback control, considers disturbance and interval time‐varying delay, and the introduction of state estimation derivative term can eliminate the impulse property of the closed‐loop system, which optimizes the design scheme of the fault‐tolerant controller. The obtained sufficient conditions for stability can be solved by the strict linear matrix inequality (LMI), and the superiority of the conclusions will be further verified by the simulations.

Optimal Design of a Proportional-Derivative State Feedback Controller Based on Meta-Heuristic Optimization for a Quarter Car Suspension System

This paper presents a Proportional-Derivative State Feedback (PDSF) controller approach to design an active suspension system for quarter car. The objective of the PDSF controller is to eliminate the effects of road disturbances to achieve ride comfort of the driver and passengers. Finding the optimal feedback gain matrix of the PDSF controller is formulated as an optimization problem. Then, two meta-heuristic optimizations named Bees Algorithm (BA) and Grey Wolf Optimization (GWO) are employed to optimize the feedback gain matrix of the PDSF controller based on the Integral Time of Absolute Error (ITAE) index. The results show the superiority of the BA-based PDSF controller in terms of reducing the ITAE index in comparison with the results obtained from GWO based PDSF.

Robust normalization and H∞ stabilization for uncertain Takagi-Sugeno fuzzy singular systems with time-delays

This work deals with the simultaneous robust normalization and H∞ stabilization problems for uncertain Takagi-Sugeno fuzzy singular systems (TSFSSs) with time-delays via a novel fuzzy proportional-derivative state feedback controller (PDSFC). It is worth pointing out that the uncertainties involved in this paper exist in all different system matrices including Ei. Without using any model transformations, some new criteria that ensure the closed-loop system to be robustly normal and stable for all admissible uncertainties are exactly deduced by means of the free-weighting matrix method, and clearly expressed as strict linear matrix inequalities. Meanwhile, the prescribed H∞ performance is also achieved. Then, based on the obtained criteria, the specific expression of desired fuzzy PDSFC is given. Finally, the correctness and feasibility of our theoretical results are verified via two academic examples.

Proportional-Derivative State-Feedback Control for Singular Systems With Input Quantization

This paper deals with an admissibilization problem of singular systems with uniform input quantization. The aim is to design a controller to guarantee the admissibility of the closed-loop system. To achieve this, this paper proposes a proportional-derivative state-feedback controller which includes non-linear control part to reject the effect of uniform input quantization. Based on the proposed controller, sufficient conditions are obtained in terms of linear matrix inequalities. Two examples show the feasibility of the proposed controller.

Normalisation design for delayed singular Markovian jump systems based on system transformation technique

ABSTRACTThis paper deals with the problem of normalisation and stabilisation for time-varying delayed singular Markovian jump systems by virtue of proportional-derivative state feedback control. Based on the system transformation technique, the normalisation problem of singular systems is changed into the stabilisation problem of the augmented singular systems. Sufficient conditions are provided in terms of linear matrix inequalities by constructing mode-dependent and delay-dependent Lyapunov–Krasovskii functional. Simulation examples including an oil catalytic cracking process are utilised to verify the effectiveness and usefulness of the proposed method.

New insight into reachable set estimation for uncertain singular time-delay systems

This paper investigates the problem of reachable set estimation for a class of uncertain singular systems with time-varying delays from a new point of view. Our consideration is centered on the design of a proportional-derivative state feedback controller (PDSFC) such that the considered singular system is robustly normalizable and all the states of the closed-loop system can be contained by a bounded set under zero initial conditions. First, a nominal singular time-delay system is considered and sufficient conditions are obtained in terms of matrix inequalities for the existence of a PDSFC and an ellipsoid. In this case, the considered system is guaranteed to be normalizable and the reachable set of the closed-loop systems is contained by the ellipsoid. Then, the result is extended to the case of singular time-delay systems with polytopic uncertainties and relaxed conditions are derived by introducing some weighting matrix variables. Furthermore, based on the obtained results, the reachable set of the considered closed-loop singular system can be contained in a prescribed ellipsoid. Finally, the effectiveness of our results are demonstrated by two numerical examples.

Robust non-fragile guaranteed cost control for singular Markovian jump time-delay systems

This paper deals with the problem of robust non-fragile guaranteed cost control for a class of uncertain singular Markovian jump systems with time-varying delays. The time-varying and norm-bounded parameter uncertainties exist in both the state matrix and the derivative matrix. A non-fragile proportional-derivative state feedback controller is designed to guarantee the closed-loop singular Markovian jump system is normal and robustly stochastically stable. By proposing an optimization strategy in the framework of linear matrix inequalities, the upper bound of the cost function can be minimized. Finally, a numerical example is given to demonstrate the effectiveness of the results.

H∞-control of linear state-delay descriptor systems: an LMI approach

For continuous-time, linear descriptor system with state-delay a H ∞-control problem is solved. Sufficient conditions for delay-dependent/delay-independent stability and L 2-gain analysis are obtained in terms of linear matrix inequalities (LMIs). A bounded real lemma and state-feedback solutions are derived for systems which may contain polytopic parameter uncertainties. The filtering problem is also solved and an output-feedback controller is then found by solving two LMIs. The first LMI is associated with a proportional-derivative state-feedback control. The second LMI is derived in two different forms, the first one corresponds to the adjoint of the system that describes the estimation error and the other stems from the original system. These two forms lead to different results. Numerical examples are given which illustrate the effectiveness of the new theory.