Yashar Kouhi

Non-Smooth Control Design for Stabilizing the Switching Linear Systems by Left Eigenstructure Assignment

Abstract Novel design algorithms for exponential stability of switched linear systems using the left eigenstructure assignment approach by state feedback control are proposed in this article. For given switching constraints in the state space R n , a state feedback controller for single-input switched systems is designed, based on the fact that closed loop system solutions are enforced to converge towards the invariant hyperplane attractor in R n , as defined by the imposed common left eigenvector. The latter is appropriately constructed to guarantee the simultaneous stabilization of all constituent linear sub-systems, and to avoid the intersection of the switching manifolds with its invariant attractor set. For arbitrary switching, a set of n linearly independent common left eigenvectors in R n is selected, introducing n hyperplane attractors, and n ( n – 1) switching control hyperplane manifolds. The attrators are sequentially “turned on”, in accordance with the switching event generated by the Filippov solutions upon hitting the underlying control manifolds. Thereby, an additional state feedback control action for a second input is designed, using the nonsmooth Lyapunov stability criteria to avoid sliding modes and guarantee exponential stability for the Filippov solutions.

On the quadratic stability of switched linear systems associated with symmetric transfer function matrices

In this paper we give necessary and sufficient conditions for weak and strong quadratic stability of a class of switched linear systems consisting of two subsystems, associated with symmetric transfer function matrices. These conditions can simply be tested by checking the eigenvalues of the product of two subsystem matrices. This result is an extension of the result by Shorten and Narendra for strong quadratic stability, and the result by Shorten et?al. on weak quadratic stability for switched linear systems. Examples are given to illustrate the usefulness of our results.

On the left eigenstructure assignment and state feedback design

A general method for assigning the left eigenvectors and their corresponding eigenvalues for the single-and multi -input LTI systems using linear state feedback is proposed. Moreover, the concept of the common left eigenstructure assignment is shown to be useful for the exponential stabilization of switching linear systems under arbitrary switching conditions.

On a geometrical approach to quadratic Lyapunov stability and robustness

A geometrical approach to quadratic Lyapunov stability for the class of switched linear systems which share a common invariant subspace is contributed in this article. The robustness with respect to canonical gap perturbations of common invariant subspaces associated with constituent system matrices is additionally addressed. Some well-known results on common quadratic stability are naturally recovered in this framework.

Robust control of switched linear systems

We consider robust control of switched linear systems under arbitrary time-dependent switching signals. First, we introduce a common quadratic Lyapunov function for the class of switched linear systems with Hurwitz constituent matrices in ℝn×n sharing n − 1 linearly independent common left eigenvectors. The common quadratic Lyapunov function is then used for robust stability analysis of the convexified differential inclusion associated with the underlying switched linear system. Finally, using the common left eigenstructure assignment approach for multi-input systems, robust design by means of state-feedback control is proposed.

Multivariable Control Design for MIMO Flow-Level Control Plant

In this paper, two methods of designing controller for a practical MIMO Flow-Level pilot plant are achieved. Since the open loop plant is unstable, it is stabilized by using inner controller. Then the stabilized plant is identified at different operating points. A nominal model which is non-minimum phase is selected. This system has two outputs which have completely different time constants. Therefore, the identification problem is difficult. The other problem associated with the system is the time delay that is one of the characteristics of the process plants. The transfer function of system is close to triangular and the RGA matrix of plant is close to the identity matrix. Hence, decentralized control can be a good selection for this system which is used in our work. The robustness of the system with decentralized controller is also checked. Two Hinfin, robust controllers based on the knowledge of the disturbance are derived and the results are compared to the results of the decentralized one. To have a good robust performance the mu-synthesis and DK-iteration approach is used.

Flow Control Using a Combination of Robust and NeuroFuzzy Controllers in Feedback Error Learning Framework

In this paper a novel hybrid strategy is employed in order to improve the controller performance. The main idea is combination of classical and intelligent controllers. Feedback error learning (FEL) as a two degrees of freedom (2DOF) control scheme, has been introduced based on this idea. This paper takes a step ahead of traditional FEL schemes which combine a PID controller with an intelligent inverse based controller. We introduce a robust FEL scheme and the robust controller replaces the conventional PID controller. The Robust controller is designed based on the Hinfin approach and the intelligent controller has ANFIS structure. This novel algorithm is implemented in a Flow plant to track the desired value of flow and reject unwanted disturbances in the practical system. The results are brought to prove the practical power of the novel method and are compared with other control schemes.

Real-time allocation of tire adhesion forces for electric vehicles

A fully distributed computational algorithm for optimal allocation of tire friction forces as an integral part of a feedforward vehicle dynamics control scheme is presented. To this end, the projected subgradient method extended by an average consensus layer is utilized, leading to a simple and real-time capable algorithm. The proposed concept is of interest for the powertrain systems featuring redundant single-wheel actuation and electric cars equipped with wheel-hub drives.

Decentralized set-valued state estimation based on non-deterministic chains

A general decentralized computational framework for set-valued state estimation and prediction for systems that assume a hybrid state machine representation is introduced in this article. The decentralized scheme consists of a conjunction of a finite set of distributed state machines that are specified by a decomposition of the external signal space. While, in general, the latter is shown to be an outer approximation of the corresponding outcome of the original state machine, here, specific rules for the signal space decomposition are devised by utilizing structural properties of the underyling transition relation, leading to a recovery of the exact state set results. Finally, we illustrate the reduction of the overall computational complexity in a decentralized setting by appyling ℓ-complete approximation representation of the distributed state machines.

H∞ and QFT robust control designs for level control plant

In this paper two robust controllers are designed for a practical process trainer level plant. The system nonlinearity, time delay and change of parameters are the main problems in design of a desired controller for this plant. To design a controller, the linear models of the system and the disturbance models at different operating points are derived. Then, a parametric uncertainty profile is obtained by system identification strategies which is used in QFT control design. Indeed, for Hinfin control design a multiplicative unstructured model is extracted from the parametric uncertainty. All constraints in control design, disturbance rejection and control signal are derived. Based on these constraints, appropriate controllers are determined. To improve robust performance mu-synthesis with DK iteration is used. Finally all results are compared by applying the different controllers to the plant.