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An innovative approach combining equivalent-input-disturbance (EID) theory with the internal model principle is applied to achieve periodic disturbance rejection in input-time-delay systems. The EID estimator, which exhibits the synthetic effect of the time-delay and the periodic disturbance as an input-dependent disturbance, is constructed by inserting appropriate time-delay elements to compensate for the total influence of the input-timedelay and the periodic disturbance. A sufficient stability criterion is derived based on the separation theorem and the small-gain theorem. A design algorithm is developed for the system based on the stability criterion. Design and simulation results for the example are also employed to compare our method with the disturbance observer approach, and to demonstrate the validity of our method. [ABSTRACT FROM AUTHOR]

This paper proposes a new integrated design method to simultaneously optimize the coupled structural parameters and controllers of mechanical systems by combining decentralized control techniques and Riccati-based control theories. The proposed integrated design method aims at minimizing the closed-loop H2 norm from the disturbance to the system cost. In this paper, the integrated design problems have been formulated in the cases of full state-feedback controllers and full order output-feedback controllers. We extend the current linear time invariant (LT1) control system to a more general framework suitable for the needs of integrated design, where the structural design is treated as a passive control optimization tackled by decentralized control techniques with static output feedback, while the active controller is optimized by solving modified Riccati equations. By using this dual-loop control system framework, the original integrated design problem is transferred to a constrained structural design problem with some additional Riccati-equation based constraints simultaneously integrating the controller synthesis. This reduces the independent design variables from the structural design parameters and the parameters of the controller to the structural design parameters only. As a result, the optimization efficiency is significantly improved. Then the constrained structural design problem is reformed as an unconstrained optimization problem by introducing Lagrange multipliers and a Lagrange function. The corresponding optimal conditions for the integrated design are also derived, which can be efficiently solved by gradient-based optimization algorithms. Later, two design examples, an active-passive vehicle suspension system and an active-passive tuned mass damper (TMD) system, are presented. The improvement of the overall system performance is also presented in comparison with conventional design methods. [ABSTRACT FROM AUTHOR]

In this work, an error-integral-driven sliding mode controller (EID-SMC) is discussed for multi-input multi-output (MIMO) linear time-invariant (LTI) systems. The boundary layer approach is utilized in order to eliminate the chattering problem. Though the sliding variable remains in the vicinity of the sliding surface without reaching it, it is shown that the steady-state error vanishes exponentially asymptotically within a boundary layer, for systems of relative order one, even if parameter uncertainty and unmatched input disturbances exist. The pole placement is accomplished indirectly with an iterative optimization procedure by considering limits on controls and state. Finally, the output-feedback controller is augmented with a Luenberger full-state and disturbance observer. [ABSTRACT FROM AUTHOR]

While time delays typically lead to poor control performance, and even instability, previous research shows that time delays can, in some cases, be beneficial. This paper presents a new benefit of time-delayed control (TDC) for single-input single-output (SISO) linear time invariant (LTl) systems: it can be used to improve robustness. Time delays can be used to approximate state derivative feedback (SSD), which together with state feedback (SF) can reduce sensitivity and improve stability margins. Additional sensors are not required since the state derivatives are approximated using available measurements and time delays. A systematic design approach, based on solution of delay differential equations (DDEs) using the Lambert W method, is presented using a scalar example. The method is then applied to both single- and two-degree of freedom (DOF) mechanical systems. The simulation results demonstrate excellent performance with improved stability margins. [ABSTRACT FROM AUTHOR]

This paper presents a robust tracking model predictive control (MPC) strategy for offset-free regulation of the output of input-constrained uncertain systems to a non-zero reference signal. To this end, a feedback control law with integral action is proposed, and a feasible and invariant set is explicitly derived on the basis of the feedback law. Finally, a robust one-step-ahead tracking MPC is devised on the basis of the feasible and invariant set in order to improve the control performance. Simulation results show that the proposed tracking MPC successfully achieves robust tracking in terms of both control performance and the size of the feasible set. [ABSTRACT FROM PUBLISHER]

In this article, the static output feedback problem for linear time-invariant systems is considered. For arbitrary assignability of the roots of the characteristic polynomial by static output feedback, a new necessary and sufficient condition is derived. Although, the proof is based on simple analysis, the known sufficient conditions (derived by techniques of algebraic geometry) are directly covered. Furthermore, an algorithm for the calculation of feedback matrices assigning a desired set of eigenvalues is proposed. This algorithm does not require the desired eigenvalues to be distinct and it explicitly exploits the available degrees of freedom for reducing the feedback gain. The presented approach is illustrated on computational examples. [ABSTRACT FROM PUBLISHER]

In order to avoid quality of performance (QoP) degradation resulting from quality of service (QoS), the solution to network congestion from the point of control theory, which marks departure of our results from the existing methods, is proposed in this paper. The congestion and bandwidth are regarded as state and control variables, respectively; then, the linear time-invariant (LTI) model between congestion state and bandwidth of network is established. Consequently, linear quadratic method is used to eliminate the network congestion by allocating bandwidth dynamically. At last, numerical simulation results are given to illustrate the effectiveness of this modeling approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies linear time-invariant systems with an input delay and only real open-loop poles. The systems in discussion have one unstable pole but no zeros. To design P, PD, PI and PID-controllers, the closed-loop system eigenvalue-loci are constructed with respect to the controller gains, like the root-locus for non-delay systems. Via the concept of leading locus, stability criteria are derived for the controllers, and performances of output responses are analyzed. Finally the proposed methods are tested with examples to illustrate the application process and demonstrate the effectiveness. [Copyright &y& Elsevier]

Abstract: This paper aims at assessing the setpoint tracking performance of PID control loops, under certain constraints such as the processes under control are linear-time invariant and the instrumentations of control loops work properly. The lower bounds of integrated absolute errors (IAEs) are established, based on the widely used internal model control (IMC) principle, from closed-loop responses subject to setpoint changes in the form of step, ramp or other general types. Taking the lower bound as a benchmark, an IMC-IAE-based index is proposed to assess the setpoint tracking performance of PID control loops. Numerical and experimental examples, as well as an industrial case study, are provided to verify the lower bound as the performance benchmark and to illustrate the effectiveness of the proposed performance index. [Copyright &y& Elsevier]

We present methods for computing the local null controllability time in the class of linear control systems (not necessarily autonomous) whose families of null controllability sets are monotone with respect to inclusion. [ABSTRACT FROM AUTHOR]

This article studies the problems of stability analysis and controllers design for continuous-time linear systems with the consideration of full state saturation as well as partial state saturation. Owing to the difficulty and complexity in the controller design under state saturation, a new and tractable system is constructed, and it is shown that the constructed system is with the same domain of attraction as the original system. Based on this property, an linear matrix inequality (LMI) based method is presented for estimating the attraction domain of the origin for the new constructed system with state saturation. In addition, an algorithm is developed for designing dynamic output-feedback controllers, which guarantee that the attraction domain of the origin for the closed-loop system is as 'large' as possible. An example is given to illustrate the effectiveness of the design method. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the problem of observer-based fault detection for linear discrete time-varying (LDTV) systems. A problem formulation is first proposed to address the optimization of the fault detection filter (FDF) design, which is expressed in terms of maximizing a finite horizon or performance index. This formulation can be applied to FDF design of LDTV systems subject to -norm bounded unknown inputs or stochastic noise sequences. It is shown that a unified optimal solution to the FDF can be obtained by solving the discrete time Riccati equation and the optimal FDF is not unique. A numerical example is given to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

In controller design, it is essential to achieve stability of the closed-loop system and various performance specifications. Frequency domain criteria such as gain margin, phase margin and H8 norms of the closed-loop transfer functions as well as time domain criteria such as settling time, rise time and overshoot can be counted among important performance specifications. Most of the controllers used in the practical world are low order controllers such as P, PI and PID controllers. It is possible to see that methods for finding stabilizing low order compensators can be considered in three main categories: methods based on Nyquist theorem, methods based on a generalized version of the Hermite- Biehler theorem, and methods based on parameter space and the concept of singular frequencies. Robust stabilization of continuous time single-input single-output (SISO) linear time invariant (LTI) systems with multiplicative uncertainties is considered in this study. In particular, it has been shown that all P and PI controllers that robustly stabilize a given uncertain SISO LTI system can be found by utilizing a generalization of the Nyquist theorem and the parameter space approach, respectively. The generalization of Nyquist stability criterion suggests to determine the number of the unstable poles for gain intervals obtained by calculating the location and direction of the crossing of the Nyquist plot with the real axis. A stable characteristic polynomial, whose roots are in the left half plane, becomes unstable if and only if at least one root crosses the imaginary axis. The parameter values of the root crossing form the stability boundaries in the parameter space, which can be classified into three cases: the real root boundary, where a root crosses the imaginary axis at the origin (substitute s= jw and w = 0 in the characteristic polynomial), the infinite root boundary, where a root leaves the left half plane at infinity (for w → ∞ ) and the complex root boundary, where a pair of conjugate complex roots crosses the imaginary axes (for 0< w<∞). These stability boundaries separate regions in which the number of closed loop system unstable poles do not change in the parameter space. Sometimes, it is not possible to represent uncertainties in a system model with parametric uncertainties. Such uncertainties are usually encapsulated in a norm bounded system block that acts on a nominal system in an additive or multiplicative manner. Although it is possible to find robust controllers that can stabilize systems with such uncertainties by the help of H∞ control theory, the resulting compensators are usually of high order (at least as high as the order of the plant) and therefore impractical in many cases. Several attempts exist to put constraints on the order of H∞ controllers in the literature. However, many of these approaches suffer from computational intractability.… [ABSTRACT FROM AUTHOR]

Abstract: In this paper we derive necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for a finite set of linear positive systems. Both the state dependent and arbitrary switching cases are considered. Our results reveal an interesting characterisation of “linear” stability for the arbitrary switching case; namely, the existence of such a linear Lyapunov function can be related to the requirement that a number of extreme systems are Metzler and Hurwitz stable. Examples are given to illustrate the implications of our results. [Copyright &y& Elsevier]

This study addresses a new digital redesign (DR) problem for a linear time-invariant (LTI) system with a perturbation that is an uncertain non-linear time-varying function but linearly bounded. Given a continuous-time linear controller robustly stabilising the origin of the perturbed system for all admissible perturbations, the concerned DR problem is to design the sampled-data linear controller making trajectories of the continuous-time and the sampled-data non-linear control systems close, or at least robustly stabilising the perturbed system. The proposed approach interprets the DR problem as the stabilisation problem considering the convergence rate for error dynamics between the continuous-time and the sampled-data non-linear control systems. Sufficient conditions for the stabilisation are derived and formulated in the form of linear matrix inequalities (LMIs). A numerical example is used to demonstrate the effectiveness of the proposed design technique. [ABSTRACT FROM AUTHOR]

Abstract: In application of variable spindle speed machining to noncircular turning process, the tracking control of the fast tool servo yields a periodic sampling rate in the real-time domain. However, in the view of the angle domain, the sampling rate is constant. Moreover, the reference acceleration signal is easily available. This implies that it is advantageous to design the control system from the angle domain perspective, but the plant for a linear time-invariant system will become a periodically time-varying system. In this paper, the active disturbance rejection control strategy is applied to actively estimate the time-varying dynamics and other disturbances and compensate for them in the control law. The acceleration feed-forward strategy is employed to achieve better tracking performance. The stability analysis based on the lifting technique is proposed. Experimental machining results demonstrate the tracking performance of the proposed design, as well as the ability to increase machining stability using variable spindle speed machining. [Copyright &y& Elsevier]

In this paper we solve tracking and disturbance rejection problems for stable infinitedimensional systems using a simple low-gain controller suggested by the internal model principle. For stable discrete-time systems, it is shown that the application of a low-gain controller (depending on only one gain parameter) leads to a stable closed-loop system which asymptotically tracks reference signals r of the form r(k) = ∑jN=1 λjk rj, where rj ε Cp and λj ε C with ∣λj∣ ε = 1 for j = 1, … ,N. The closed-loop system also rejects disturbance signals which are asymptotically of this form. The discrete-time result is used to derive results on approximate tracking and disturbance rejection for a large class of infinite-dimensional sampled-data feedback systems, with reference signals which are finite sums of sinusoids, and disturbance signals which are asymptotic to finite sums of sinusoids. The results are given for both input-output systems and state-space systems. [ABSTRACT FROM AUTHOR]

It is a survey of recent extensions and new applications for the classical D-decomposition technique. We investigate the structure of the parameter space decomposition into root invariant regions for single-input single-output systems linear depending on the parameters. The D-decomposition for uncertain polynomials is considered as well as the problem of describing all stabilizing controllers of the certain structure (for instance, PID-controllers) that satisfy given H ∞-criterion. It is shown that the D-decomposition technique can be naturally linked with M-Δ framework (a general scheme for analysis of uncertain systems) and it is applicable for describing feasible sets for linear matrix inequalities. The problem of robust synthesis for linear systems can be also treated via D-decomposition technique. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the problem of determining the set of all stabilizing proportional–integral–derivative (PID) type controllers without parametric models for any given linear time-invariant (LTI) plants. It is shown that the only information for designing is the frequency response data and the number of right-half-plane (RHP) poles of the plant, and all stabilizing domains in the parameter space of PID-type controllers are determined by the boundaries which are analytically described based on the technique of D-decomposition. The method can handle arbitrary order minimum phase, non-minimum phase, stable or unstable plants and particularly, plants that have zeros or poles on the imaginary axis. It is shown that the approach presented does not require any parametric models of plants and can be applied to a wide range of industrial applications, especially where plants parametric models (transfer function and state space) are not available or identification is difficult. Several examples illustrate the proposed method. [Copyright &y& Elsevier]

For certain classes of linear, time-invariant, multi-input multi-output plants, a systematic synthesis method is developed for stabilization using Proportional+Integral+Derivative (PID) controllers, where the closed-loop poles can be assigned to the left of an axis shifted to the left of the origin. For some of these plant classes, the real-parts of the closed-loop poles can be smaller than any arbitrary pre-chosen negative value. Stable and some unstable multi-input multi-input plants with transmission-zeros in the left-half complex-plane are included in these classes that admit PID-controllers with this property of small negative real-part assignability of closed-loop poles. [ABSTRACT FROM AUTHOR]

Model reference adaptive control is a major design method for controlling plants with uncertain parameters. The primary objective of this paper is to develop a new design approach for a differentiator-free model reference adaptive control of a single-input single-output linear time-invariant plant. The proposed method, called the “Identifier-tracking model reference adaptive control”, uses a stacked identifier structure that is new to the field of adaptive control. The goal is to make the output of the plant asymptotically track the output of the first identifier, and then driving the output of the first identifier to track that of the second identifier, and so forth, up to the qth identifier where q is the relative degree of the plant. Lastly, the output of the qth identifier is forced to converge to that of the reference model. Simulation results show the superiority of the proposed method over the traditional model reference adaptive control with augmented error in terms of the transient response. Since the resulting control systems are non-linear and time-varying, the stability analysis of the overall system plays a central role in developing the theory. [ABSTRACT FROM AUTHOR]

The paper addresses both detection and stabilization problems involving communication errors and capacity constraints. Discrete-time partially observed linear systems are studied. Unlike the classic theory, the sensor signals are transmitted to the estimator/controller over a noisy digital communication link modeled as a stochastic stationary discrete memoryless channel. It is shown that for noise-free plants, the Shannon capacity of the channel constitutes the border separating the cases where stabilization and reliable detection (asymptotic state estimation) with arbitrarily large probability are and are not possible, respectively. [ABSTRACT FROM AUTHOR]

A small-gain theorem, which can be applied to a wide class of systems that includes systems satisfying the weak semigroup property, is presented in the present work. The result generalizes all existing results in the literature and exploits notions of weighted, uniform, and nonuniform input-to-output stability properties. Applications to partial state feedback stabilization problems with sampled-data feedback applied with zero order hold and positive sampling rate are also presented. [ABSTRACT FROM AUTHOR]

This paper develops a successive approximation approach (SAA) of optimal sliding mode control (SMC) for linear time-delay systems with sinusoidal disturbances. A sequence of two-point boundary value (TPBV) problems with both time-delay and time-advance terms is derived from the optimal sliding mode design. According to the SAA, the original TPBV problems are transformed into a sequence of linear TPBV problems without delay and advance terms. The obtained SMC ensures that the state trajectories reach the sliding surface in finite time and remain on it thereafter. The stability of the sliding mode is proved. A numerical simulation is employed to verify the effectiveness of the proposed approach. [Copyright &y& Elsevier]

This paper develops a methodology for actuator fault diagnostics and quantitative estimation of fault signals in a class of non-linear systems. The class of non-linear systems considered is one in which the non-linearity is an incremental quadratic type of non-linearity that includes Lipschitz, positive real and sector non-linear functions. The methodology provides for both state estimation and fault vector estimation. An LMI procedure can be utilized for explicit computation of the observer gains. The procedure developed can also be specialized to linear time invariant systems. Compared to previous results for LTI systems, the procedure developed herein does not require the LTI system to be minimum phase. The use of the developed methodology is demonstrated through two illustrative examples of real world physical applications. [ABSTRACT FROM AUTHOR]

An integrated batch-to-batch control and within-batch online control strategy for tracking product quality trajectories in batch processes is proposed. On the basis of a batch-wise linear time-varying perturbation model, iterative learning control (ILC) is implemented for batch-to-batch control and the convergence of tracking errors under ILC is guaranteed. Within a batch, a predictive model is constructed by directly partitioning the linear time-varying model according to time, then batch model predictive control with shrinking horizons is applied online to reduce the effects of model-plant mismatch and/or unknown disturbances. By properly combining these two control methods, the integrated control strategy can complement both methods to obtain good performance. The proposed strategy is demonstrated on a simulated batch polymerisation process, and the results show that the performance can be improved quite significantly under the integrated control strategy than only under ILC, especially when disturbances occur. [ABSTRACT FROM AUTHOR]

The authors present an enhanced composite nonlinear feedback (CNF) control technique for discrete-time systems with input saturation and with external disturbances. The conventional CNF control is proven to be capable of yielding better transient performance in tracking control for systems with input saturation. However, when the given system has external disturbances as in most practical situations, the conventional CNF control yields some steady-state errors in the resulting output response. The enhanced CNF technique presented is an extension of the conventional one. It retains the good transient properties of the conventional CNF control and at the same time has the additional capacity for eliminating steady-state bias because of unknown constant disturbances. A numerical example and practical disk drive servo system design are provided to demonstrate the effectiveness of this control technique. Experimental results show that the new design yields a huge improvement over classical approaches. [ABSTRACT FROM AUTHOR]

We consider robust adaptive control designs for relative degree one, minimum phase linear systems of known high frequency gain. The designs are based on the dead-zone and projection modifications, and we compare their performance w.r.t. a worst case transient cost functional with a penalty on the $$\mathcal{L}$$ ∞ norm of the output, control and control derivative. We establish two qualitative results. If a bound on the $$\mathcal{L}$$ ∞ norm of the disturbance is known and the known a priori bound on the uncertainty level is sufficiently conservative, then it is shown that a dead-zone controller outperforms a projection controller. The complementary result shows that the projection controller is superior to the dead-zone controller when the a priori information on the disturbance level is sufficiently conservative. [ABSTRACT FROM AUTHOR]

Robust non-fragile feedback stabilization is studied for causal linear time-invariant (LTI) input–output systems defined in an L 2 () signal space setup, or equivalently in an L 2 (j) setup in the frequency domain. Two-operator descriptions for the plant and the controller are used with bounded operators defined on the full space L 2 (). Basic properties of causal LTI operators on weighted L 2 spaces, L 2 (,&ThickSpace; w ), which are relevant to stabilization theory, are also established for different choices of the weighting function w . Weighted L 2 spaces allow the inclusion of persistent signals such as steps and thus provide the potential of important generalizations of the robust stabilization theory on L 2 (). In particular, it is shown that there is a large class of weights w for which the L 2 (,&ThickSpace; w ) setup leads to H ∞ optimization. This implies that robust H ∞ design can be applied to a large class of weighted L 2 spaces on . Problems of closability of unstable causal LTI convolution operators are discussed. This strengthens the importance of the two-operator model Ay &ThickSpace;=&ThickSpace; Bu as the basic plant input–output model on the full time axis. It is discussed how to obtain such models with A and B bounded causal coprime operators defined on the full signal space. [ABSTRACT FROM AUTHOR]

Recent designs for brake-by-wire systems use ‘resolvers’ to provide accurate and continuous measurements for the absolute position and speed of the rotor of the electric actuators in brake callipers (permanent magnet DC motors). Resolvers are absolute-angle transducers that are integrated with estimator modules called ‘angle tracking observer’ and together they provide position and speed measurements. Current designs for angle-tracking observers are unstable in applications with high acceleration and/or speed. In this paper, we introduce a new angle-tracking observer in which a closed-loop linear time-invariant (LTI) observer is integrated with a quadrature encoder. Finite-gain stability of the proposed design and its robustness to three different kinds of parameter variations are proven based on theorems of input-output stability in nonlinear control theory. In our experiments, we examined the performance of our observer and two other methods (a well-known LTI observer and an extended Kalman filter) to estimate the position and speed of a brake-by-wire actuator. The results show that because of the very high speed and acceleration of the actuator in this application, the LTI observer and Kalman filter cannot track the rotor position and diverge. In contrast, with a properly designed open-loop transfer function and selecting a suitable switching threshold, our proposed angle-tracking observer is stable and highly accurate in a brake-by-wire application. [ABSTRACT FROM AUTHOR]

This paper proposes a nonlinear multi-input control law using sliding mode concepts for continuous-time, uncertain, linear systems. The control law introduces a state-dependent layer around the sliding mode plane to remove chattering. This layer combines two types of boundary layers: a constant layer and a sector-shaped layer. The states will always enter the state-dependent boundary layer and the choice of the sliding mode will be seen to determine the ultimate system performance. A proof of stability shows ultimate boundedness. The controller is applied to a nonlinear simulation model of a cart-pendulum and exhibits a high degree of robustness. The new boundary layer in connection with a novel dynamically changing, state-dependent gain can be used to obtain a narrow boundary-layer shape in the operating region of interest. This permits rejection of disturbances without chattering of the control and improves on the performance expected of a sliding-mode control with constant boundary layer. [ABSTRACT FROM AUTHOR]

Relations are derived that allow standard MATLAB routines to be used to solve the static output-feedback control problem for a periodic discrete-time system. The efficiency of the approach proposed to design optimal static output-feedback controllers is demonstrated by examples [ABSTRACT FROM AUTHOR]

Singular $$\mathcal{H}$$ 2-optimization problems are considered for the standard discrete-time control system. Two types of singularity (type I and type II) are distinguished. A detailed treatment of problems with singularity of type II, which leads to nonuniqueness of solution, is presented. New algorithms for design of optimal controllers are presented both in frequency domain and state space, which generalize standard procedures onto the case of singular $$\mathcal{H}$$ 2-problems. A parameterization of the set of optimal controllers is given. [ABSTRACT FROM AUTHOR]

Studies underactuation and undersensing in dynamical systems with the objective of reducing cost, weight and system complexity. Role of switching in enhancing controllability and observability in underactuated and undersensed linear time-invariant systems; Switching requirements for observer-based control designs; Vibration suppression in a flexible beam instrumented with piezoelectric transducers.

In this paper, we address some robustness issues for a class of switched linear systems with non-linear perturbations. We illustrate through an example that the well-known state-space-partition-based switching law may lead to chattering in the event that the systems undergo perturbations. To overcome this, we propose a state-feedback switching law with a non-zero level set. We prove that this switching law can prevent the system from chattering. In addition, this switching law makes the perturbed systems bounded with bounded perturbations, and practically convergent with convergent perturbations. We also propose an observer-based switching law to steer the switched system stable with nice robustness performances. [ABSTRACT FROM AUTHOR]

Proposes an alternative delay-dependent H∞ controller design for linear, continuous, time-invariant systems with unknown state delay. Effectiveness of the H∞ controller in reducing the effect of the disturbance input on the controlled output to within a prescribed level.

Considers the performance of pulse width control (PWC) systems. Introduction of a quantitative measure of the performance of a PWC system; Demonstration of piecewise-linear-gain PWC laws; Demonstration of the performance measure and piecewise-linear-gain PWC design method in applications of PWC to control the y position of the end-effector of an industrial robot.

Analyzes the use of constant-gain pulse width control laws for precise positioning of structurally flexible plants subject to stiction and Coulomb friction. Application of Pulse Width Control (PWC) law to the Standard Rigid Body plant; Development of a sufficient conditions for asymptotic stability of a PWC system.

The paper presents a design method for optimizing the loop-gain of unstable-non-minimum phase feedback systems. Because obvious gain-bandwidth limitations exist in such systems, the proposed best loop gain optimization goal is maximization of the stability gain and phase margins, which are inherently low in such feedback systems. The design procedure is based on coprime factorization of the plant and controller, and the Bezout identity. An optimization process varies iteratively the observer-based controller parameters until maximization of the gain and phase margins is achieved. The same design technique also allows one to solve the mixed sensitivity H ∞ standard control problem for linear time invariant feedback systems. [ABSTRACT FROM AUTHOR]

Three new qualitative control concepts are introduced and developed in the framework of general MIMO linear, time-invariant, continuous time systems to be controlled: natural trackability, elementwise and stablewise tracking, and natural tracking control. The study of these concepts opens new problems in control science, which are solved in the form of their necessary and sufficient conditions. Different physical natures and/or purposes of the system output variables, as well as their mutual independence, may require that each output be assigned a specific settling time and/or a reachability time. Such times compose corresponding vector times. The natural tracking control ensures elementwise output tracking which obeys a prespecified vector settling time and/or vector reachability time. A controller should use information only about the system output error and the realized control itself in order for the control to be natural tracking control. But the controller does not use any information about the system internal dynamics description, system state and external disturbances. The necessary and sufficient conditions are proved for the stability of systems that exhibit tracking. They permit possible independent and separate synthesis of a stabilizing control and of a tracking control. A natural tracking control synthesis and natural tracking controller design for a fourth-order MIMO system and simulation results illustrate and verify the new control theory avenues. [ABSTRACT FROM AUTHOR]