Abstract: In this work, a control law for an unstable, non-minimum phase model of a hypersonic vehicle is developed. The control problem is difficult due to the locations of the plant poles and zeros. For an unstable system, feedback is required to stabilize the plant. However, one cannot make the loop gains arbitrarily large without driving one or more of the closed-loop poles into the right-half of the s-plane, since the system is nonminimum phase. Thus, there is a limited range of feedback gain that results in a stable system. The nonminimum phase behavior also places restrictions on the closed-loop bandwidth. For the hypersonic vehicle control problem, low frequency control is desired and a rule of thumb is that the closed-loop bandwidth must be less than one-half the right-half plane zero location. A right-half plane zero located in the region of the desired gain-crossover frequency makes it impossible to achieve the desired level of tracking performance. The achievable closed-loop bandwidth might be so small that adequate control of the system is not achieved. Direct cancellation of the right-half plane zero with an unstable pole in the controller is not an option. In this work, a modified dynamic inversion controller is developed for a linear, time-invariant model of a hypersonic vehicle. This modified dynamic inversion controller differs from the standard dynamic inversion approach in that it does not attempt to cancel the right-half plane zero with a pole, instead, it retains right-half plane zeros in the closed-loop transfer functions and uses an additional feedback loop to stabilize the zero dynamics.

Abstract: This paper investigates both analysis and synthesis techniques for robust pole placement in linear matrix inequality (LMI) regions involving observer-based fuzzy control. The class of systems considered here is the continuous Takagi-Sugeno (T-S) fuzzy model with parametric structured uncertainties and unavailable state variables. Sufficient global stability conditions are established which make it possible to robustly assign the closed-loop poles of the augmented system containing both the fuzzy controller and observer in the left half complex plane and also to guarantee control performances by imposing a pole placement. Because of uncertainties, the separation property is not applicable to design the fuzzy controller and observer separately. The idea of the proposed approach is to assign both state and estimation error poles to a desired LMI region and to use the H/sub /spl infin// technique in order to guarantee that the estimation error converges faster to the equilibrium point zero. An example is given to illustrate the effectiveness of the proposed approach.

Abstract: The Lambert W function is defined as the multivalued inverse of the function w→wew=z. It has been applied to stability analysis of a class of fractional delay systems whose transcendental characteristic equation (TCE) can be remodelled in the form (as+b)ecs+d=0. The approach of using the Lambert W function to time-domain analysis of a class of feedback fractional-order time-delay systems is extended. It should be noted that, owing to the multivaluedness of a transfer function of fractional order, the approach has two pitfalls that must be circumvented with care. Because remodelling the TCE of a feedback fractional delay system to allow for the Lambert W function representation of roots introduces superfluous poles to the original TCE, a clarification of the relationship between the roots of the remodelled TCEs and the poles of the system is provided. As a result, the time response function of the system can be approximated by a finite series of eigenmodes written in terms of Lambert W functions. As the singularities of a fractional-order system include both the poles and the branch cut(s) of the transfer function, the neglect of the response portion contributed by the branch cut(s) incurs a significant transient response error. In order to compensate for such a transient response error, three schemes of optimal approximation with specified poles are developed. Simulation results show that the proposed approaches to time-domain analysis of feedback fractional delay systems can indeed enlarge the application scope of the emerging Lambert W function.

Abstract: In this paper, performance limitations in the linear control of general linear discrete-time scalar systems are considered. The performance is measured with the 2-norm of an error function which, at the same time, ensures that the closed loop poles lie in a prescribed region. The deleterious effect of this constraint on a classical performance measurement is also quantified, in such a way, that the interplay between the size of the desired region and structural features of the plant is revealed.

Abstract: AC-coupled equivalent series resistance (ESR) is introduced into a control circuit to provide additional stability in the feedback control loop. A sub-circuit emulates the effect of a higher value ESR in the output capacitor. The additional ESR in the feedback control loop inserts a zero into the transfer function that describes the circuit response at a desired frequency. The added zero compensates for the effects of unwanted or unavoidable poles in the transfer function, allowing for a greater range of input signal frequencies.

Abstract: This paper describes a linear matrix inequality (LMI) approach to the design of low-order power system stabilizers (PSSs), which are used to damp out local-mode oscillations of synchronous generators The performance of a PSS is expressed as the location of the closed-loop poles, and a single fixed-gain pole-placement controller is synthesized for a wide range of operating conditions The synthesis results in simultaneous regional pole-placement stabilization through static output feedback, and it is formulated as an LMI feasibility problem with a rank condition The rank-constrained LMI problem is solved by the recently developed iterative penalty function method Numerical experiments with a single machine connected to an infinite bus system were performed to demonstrate the proposed LMI method

Abstract: In the present work, it is observed that, to maintain stability, different sets of feedback control gains should be applied for free and forced vibration attenuation. For forced vibrations, feedback controllers with certain optimum positions of closed loop poles give maximum vibration reduction. By combining the feedback and feed forward controllers (i.e. by using a hybrid controller), better transient performance can be obtained in the case of forced vibrations. By using the concept of a dead zone and making the hybrid controller adaptive, ideal performance and guaranteed stability of the closed loop system can be achieved for both free and forced vibrations. The proposed controller remains effective for large variation in system parameters.

Abstract: Robust output-feedback controller against various perturbations is proposed for satellite formation keeping. The mixed H2/Hinfin controller with regional pole placement constraints is designed based on linear Hill's equations. The mixed H2/Hinfin controller takes into account both the disturbance rejection aspects and the LQG aspects. In addition, the closed-loop poles can be forced into some sector of the stable half-plane to obtain well-damped transient responses. The problem is reduced to a convex optimization involving linear matrix inequalities (LMIs), so it can be solved efficiently. Extensive simulation studies were conducted for the validation of the proposed robust controller using Matlabtrade. The simulation results demonstrate that the developed multi-objective control system is robust stable and optimal in the sense of H2 norm, and has good steady-state and dynamic performances against various disturbances for the satellite formation system

Abstract: Uncertainties in control systems models often have to be taken into account in their analysis and/or design. Negligence of such uncertainties is often unjustifiable and is done only due to lack of methods to treat the uncertainties. The presented work is concerned with analysis and design of interval uncertainty control systems, with regard to clustering of poles inside a simple symmetric bounded contour ?. We extend the well known Nyquist and Mikhailov stability theorems to ? - stability tests of uncertain systems, defined by their generalized Bode envelopes. Also, using generalized definitions and theorems we solve the design problem of a controller which ensures clustering of closed loop poles of an interval uncertain family of transfer functions inside such prescribed ? -region.

Abstract: This paper presents a continuous time solution to the problem of the design of a relatively optimal control, precisely, a dynamic control which is optimal with respect to a given initial condition and it is stabilizing for any other initial state. This technique provides a drastic reduction of the complexity of the controller and successfully applies to systems in which (constrained) optimality is necessary for some "nominal operation" only. The technique is combined with a pole assignment procedure. It is shown that once the closed-loop poles have been fixed and an optimal trajectory originating from the nominal initial state compatible with these poles is computed, a stabilizing compensator which drives the system along this trajectory can be derived in closed form. There is no restriction about the optimality criterion and the constraints. The optimization is carried out over a finite-dimensional parameterization of the trajectories. However, although the complexity of the compensator is not affected by the choice of cost and constraints, (the compensator dimension is fixed as a design data) it is not in general easy to optimize in the proposed space since, in general, the constraints are infinite dimensional so approximations are necessary. In the case of quadratic optimization with simultaneous pole assignment, an efficient solution based on convex quadratic programming is proposed.

Abstract: This paper develops linear fractional representations for uncertain flexible structures with non-collocated piezoelectric actuators and sensors in the modal space, taking into account uncertainties due to modal parameters variation and un-modeled residual high-frequency modes. Using linear matrix inequality, a dynamic output feedback controller is designed to suppress the vibration due to external disturbances by setting an upper bound on H-infinity norm from the disturbances to given performance outputs. In order to achieve a specified decay rate and damping ratio in all controlled modes, and achieve the desired dynamic response, closed-loop poles of the uncertain system are placed in the desired region. Finally, robust H-infinity method with uncertain poles assignment is compared with robust H-infinity method by a simple example. The simulation results show that, without obviously scarifying state-steady characteristics of the system, excellent dynamic response can be obtained by considering uncertain poles assignment in robust H-infinity vibration control.

Abstract: In this brief, a simple approach is proposed for decentralized control of linear large-scale systems. Sufficient conditions for diagonal dominance of closed-loop large-scale systems are derived. Based on these conditions, the interactions between the subsystems can be considered as external disturbances for each isolated subsystem. Then, a previously proposed approach is used to attenuate disturbances via dynamic output compensators based on complete parametric eigenstructure assignment. Through attenuation of the disturbances, the closed-loop poles of the overall system are assigned in the desirable region, by assigning the eigenstructure of each isolated subsystem appropriately. An example is given to show the effectiveness of the proposed method

Abstract: The paper presents a procedure for designing state feedback controllers to achieve a standard form closed loop system step response. Apart from addressing directly the step response in the design it also allows consideration of time scaling and control signal magnitude, important aspects not often considered in other approaches. The method can be used for a forward loop transfer function with one or no zero. Thus if a PI controller is used the plant transfer function must have no zero.

Abstract: In this paper algebraic approach is employed for controller design. The objective is to find a robust controller which guarantees the robust stability and decoupled result control of the longitudinal model of a scaled remotely controlled vehicle version of the advanced fighter HIMAT. The control design is performed by decoupling the MIMO system into two identical SISO plants which are approximated by a 4th order transfer function. The algebraic approach is then used for the pole placement design and the nominal closed loop poles are tuned so that the peak of the μ-function is minimal. As an optimization tool an evolutionary algorithm Differential Migration is used in order to overcome the problem of multimodality of the cost function. Final controllers are compared with D-K iteration through simulation of standard longitudinal manoeuvres.

Abstract: This paper addresses the design of fuzzy state feedback controller that has not only the ability to stabilize the fuzzy model/system but also to control the transient behavior and closed loop pole location for wind energy conversion system which present interesting control demands and exhibits intrinsic nonlinear characteristics. The proposed fuzzy controller is employed to regulate indirectly the power flow in the DC link by regulating the DC current. First, a Takagi-Sugeno fuzzy model is employed to represent a nonlinear system. Then a model-based fuzzy controller design utilizing the concept of parallel distributed compensation is developed. Additional constraints on the closed loop pole location are satisfied. Satisfactory time response and closed loop damping are achieved by forcing the closed loop poles into a suitable sub-region of the left half plane. These conditions are expressed in terms of linear matrix inequalities (LMI's) which can be solved very efficiently using convex optimization techniques. The design techniques are applied to a dynamic model of wind energy conversion system to illustrate the feasibility of the proposed solution

Abstract: In this paper, the H2 control for a class of discrete time-delay systems with the closed-loop pole constraints is considered. By employing LMI approach, the problem can be transformed to a convex optimal problem with constraints that is easy to be calculated. The obtained controller not only guarantees all the closed-loop poles to be placed inside a specified region, but also provides an H2 performance upper bound. In particular, the obtained results are delay-dependent, and therefore, have less conservativeness. Numerical examples are given to illustrate the validity of the proposed method.

Abstract: The constrained control of triple integrator based on the modes decomposition is introduced in this paper. The design combines the well known time optimal control with the linear pole assignment control, i.e. the control consist of n phases similar to the time optimal control, however the transients between these phases are ?smooth? and the dynamics of the transients is given by the closed loop poles.

Abstract: In order to solve the problem of pole disposition in controller designing with closed loop system, based on polynomial homotopic mapping and the corresponding zero loci, this article gave the definition of the homotopic fixed point, deducted and proved a pole disposition method based on the homotopic fixed point, which was equivalent to the pole disposition theorem original in the means of closed loop poles. The conclusion of the study can be applied in control system compensating design by root locus method effectively.

Abstract: For a class of discrete-time switched linear systems with norm-bounded time-varying uncertainty, the problem of designing dynamic output feedback controller to guarantee that all closed-loop poles be assigned in the prespecified disk was investigated. With multiple Lyapunov functions approach, it is shown that this existence condition of the desired output feedback controller is equivalent to the solvability problem of a set of certain linear matrix inequalities (LMIs), which can be solved by the existing efficient convex optimization techniques. A construction of the desired controllers is provided in terms of feasible solutions to the LMIs. Finally, An example is given to illustrate the effectiveness of the proposed method.

Abstract: This paper addresses the design of fuzzy state feedback controller that has not only the ability to stabilize the fuzzy model/system but also to control the transient behaviour and closed loop pole location for wind energy conversion system which present interesting control demands and exhibits intrinsic non-linear characteristics The proposed fuzzy controller is employed to regulate indirectly the power flow in the DC link by regulating the DC current First, a Takagi-Sugeno fuzzy model is employed to represent a non-linear system Then a model-based fuzzy controller design utilizing the concept of parallel-distributed compensation is developed Additional constraints on the closed loop pole location are satisfied Satisfactory time response and closed loop damping are achieved by forcing the closed loop poles into a suitable sub-region of the left half plane These conditions are expressed in terms of linear matrix inequalities (LMI's), which can be solved very efficiently using convex optimization techniques The design techniques are applied to a dynamic model of wind energy conversion system to illustrate the feasibility of the proposed solution

Abstract: Based on satisfactory control strategy, a design method of robust satisfactory fault-tolerant controller is investigated for a class of uncertain linear discrete-time systems under sensor faults condition. The state-feedback gain matrix is calculated by linear matrix inequality approach. The designed controller guarantees that the closed-loop system meets the pre-specified consistent constraints on regional pole index and steady state-variance index simultaneously for normal case and admissible sensor faults case. The consistency of the indices is also discussed. Furthermore, with constraints on the mentioned indices, a solution is obtained to the robust satisfactory fault-tolerant controller with minimum control-cost by convex optimal technique.