State Feedback Loop Research Articles

Stability constraints of active magnetic bearing control systems

Direct Lyapunov stability method is employed to analyse the closed-loop stability of an electromagnetically suspended rotor system in which non-linearity and singular perturbation nature are embedded. Five explicit sets of stability constraints are proposed so that the state feedback loop is not over-designed. Under impact of modeling inaccuracy, due to neglected higher-order terms, stability conditions for equilibrium point, slow-mode manifold and boundary layer are studied. In addition, the singular perturbation order-reduction technique is used to simplify the feedback loop and reduce the order of a state feedback controller. The stability margin can be numerically evaluated as long as the upper bound of the singular perturbation parameter is available. The proposed state feedback controller is verified by intensive computer simulations such that superior performance in terms of stiffness, rise time and overshoot is illustrated, in comparison to output feedback law and deadbeat control. The reported state feedback loop not only stabilizes the inherently unstable open-loop system, but also preserves the robustness with respect to the parasitic parameter variation and modeling error due to neglected higher-order terms of magnetic control force.

Discrete time linear optimal multi-periodic repetitive control: a benchmark tracking solution

The use of optimal control tracking methodologies for the development of feedback control schemes for arbitrary discrete-time linear systems is considered for the special case when the demand signal is multi-periodic, i.e. can be expressed as a finite sum of periodic signals of different but known frequencies. By embedding the reference signal into plant dynamics, the problem is reduced to a classical linear quadratic control problem which yields an explicit formula for a globally stabilizing tracking controller. Asymptotic perfect tracking is guaranteed by the presence of the familiar internal model of the demand signal dynamics within the control structure. Transfer function analysis of the controller indicates that it consists of an inner state feedback loop plus an error actuated forward path control element containing the internal model.

Fuzzy Modeling and Control of Wheeled Mobile Robot

In this paper, a new model, which is a Takagi-Sugeno fuzzy model, for mobile robot is presented. A controller, consisting of two loops the one of which is the inner state feedback loop designed for stability and the outer loop is a PI controller designed for tracking the reference input, is suggested. Because the robot dynamics is nonlinear, it requires the controller to be insensitive to the nonlinear term. To achieve this objective, the model is developed by well known T-S fuzzy model. The design algorithm of inner state-feedback loop is regional pole-placement. In this paper, regions, for which poles of the inner state feedback loop are lie in, are formulated by LMI's. By solving these LMI's, we can obtain the state feedback gains for T-S fuzzy system. And this paper shows that the PI controller is equivalent to the state feedback and the cost function for reference tracking is equivalent to the LQ(linear quadratic) cost. By using these properties, it is also shown in this paper that the PI controller can be obtained by solving the LQ problem.

Improved temperature control of a PWR nuclear reactor using an LQG/LTR based controller

State feedback assisted classical (SFAC) control has been developed to improve the temperature response performance of nuclear reactors via modifying the embedded classical controller reference signal. This is done by means of an outermost state feedback controller. A linear quadratic Gaussian with loop transfer recovery (LQG/LTR) at the plant output seems a good candidate for the state feedback loop of SFAC structure, but it ends up in a closed loop system with tightly controlled power. To pay more attention to temperature responses, this paper presents the results of using LQG/LTR at the plant input in SFAC structure. We impose a minor change for considering, to some extent, the variation of system poles (and hence its speed) due to linearization of the nonlinear plant in equilibrium conditions other than the design power. The results are compared to an existing LQG controller with LTR at the plant output. Sensitivity of dominant closed loop poles and nonlinear simulations are used for demonstration and comparison.

An integrated probabilistic risk analysis decision support methodology for systems with multiple state variables

Abstract Probabilistic risk analysis (PRA) methods have been proven to be valuable in risk and reliability analysis. However, a weak link seems to exist between methods for analysing risks and those for making rational decisions. The integrated decision support system (IDSS) methodology presented in this paper attempts to address this issue in a practical manner. In consists of three phases: a PRA phase, a risk sensitivity analysis (SA) phase and an optimisation phase, which are implemented through an integrated computer software system. In the risk analysis phase the problem is analysed by the Boolean representation method (BRM), a PRA method that can deal with systems with multiple state variables and feedback loops. In the second phase the results obtained from the BRM are utilised directly to perform importance and risk SA. In the third phase, the problem is formulated as a multiple objective decision making problem in the form of multiple objective reliability optimisation. An industrial example is included. The resultant solutions of a five objective reliability optimisation are presented, on the basis of which rational decision making can be explored.

A Tracking Controller for Linear Time-Varying Systems

This paper proposes a new tracking control design for linear time-varying systems. The proposed control input, which is in the span of finitely many preselected input data, minimizes the L2-norm of the output tracking error. The more input data is used, the less L2-norm of the tracking error is achieved. The design of the new controller, which consists of a feedforward controller and a discretized state feedback loop, requires a finite-time preview of the system parameters and the reference trajectory. It is shown that as long as the preview time is longer than a critical value, the closed-loop stability is maintained irrespective of the stability property of the system’s zero dynamics. When the system parameters are periodically time-varying, the proposed design can be solely based on a set of experimental input and output data instead of on the exact information of system parameters.

Design for safety of engineering systems with multiple failure state variables

Since possible failure events of large engineering systems with a higher level of innovation may not be identified by experience or from previous accidents and incident reports of similar systems, and since ‘design for safety’ of such systems requires no omission of failure causes associated with possible system failure events, a top-down approach is not always satisfactorily applied in the risk identification and risk estimation phases and a more objective and flexible bottom-up approach may be more effective. This paper proposes an inductive bottom-up risk identification and estimation methodology combining Failure Mode, Effects and Criticality Analysis (FMECA) and the Boolean Representation Method (BRM). This methodology can be used to identify all possible system failure events and associated causes, and to assess the probabilities of occurrence of them particularly in those cases where multiple state variables and feedback loops are involved. The Boolean representation method is presented together with its use in modelling cause and effect relationships. The overall model and the algorithms are described and tested in association with the associated computer software. The applications of this methodology in association with other formal safety modelling methods are discussed. An illustrative example is presented to demonstrate the methodology.

Stochastic hybrid control of hysteretic structures

A method of stochastic control for seismic-excited hysteretic structures is presented. Emphasis is placed on hybrid control of base-isolated buildings. The earthquake excitation is modeled as a filter shot noise and the equations of motion of the structure are augmented by the earthquake model. Based on the stochastic optimal control algorithm, the resulting control vector consists of a feedforward compensation and a state feedback loop. The nonstationary response statistics, such as the mean square function, are obtained using the methods of random vibration and equivalent linearization. Simulation results indicate that for a range of earthquake model parameters of practical interest, the performance of the control method using both the feedforward compensation and the state feedback loop does not offer a significant improvement over that of the control method using only the state feedback.

Loop transfer recovery for nonminimum phase plants

A study of what happens when the loop transfer recovery (LTS) procedure is applied to nonminimum-phase (NMP) plants, how design limitations due to right-half-plane zeros manifest themselves in the LTR procedure, and how this knowledge can be incorporated into design is presented. Explicit expressions are given for the asymptotic behavior of the loop transfer and sensitivity functions resulting from application of the LTR procedure to nonminimum-phase plants. It is shown that there exists a tradeoff between the feedback properties of the state feedback loop and the ability to recover those properties using the LTR procedure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Parameterization of reduced-order compensator in the frequency domain

Abstract After a brief survey of the relations between time and frequency domain representations of the observer-based linear state feedback loop, the parameterization of the reduced-order compensator is discussed. It is shown that the free design parameters are the coefficients in the polynomial matrices and , characterizing the closed-loop dynamics in the frequency domain. Starting from these polynomial matrices, the doubly coprime fractional representations of the system and of the compensator transfer matrices can directly be computed without recurrence to the time domain results. From these representations the right and left coprime compensator matrix fraction descriptions can easily be evaluated using standard algorithms.

Parameterization of reduced-order compensator in the frequency domain

Abstract After a brief survey of the relations between time and frequency domain representations of the observer-based linear state feedback loop, the parameterization of the reduced-order compensator is discussed. It is shown that the free design parameters are the coefficients in the polynomial matrices and , characterizing the closed-loop dynamics in the frequency domain. Starting from these polynomial matrices, the doubly coprime fractional representations of the system and of the compensator transfer matrices can directly be computed without recurrence to the time domain results. From these representations the right and left coprime compensator matrix fraction descriptions can easily be evaluated using standard algorithms.

Parameterization of the full-order compensator in the frequency domain

After a brief survey of the relations between time-and frequency-domain representations of the observer-based linear state feedback loop, the parameterization of the compensator is discussed. It is shown that the free parameters specified by the state feedback matrix K and the output error feedback matrix L in the time domain appear as coefficients in the polynomial matrices [Dtilde](s) and (s), characterizing the closed-loop dynamics in the frequency domain. These polynomial matrices can either be chosen arbitrarily (pole-placement problem) or they may be derived as solutions from the corresponding optimal control or the optimal estimation problems, respectively. Starting from the polynomial matrices [Dtilde](s) and (s), the doubly coprime fractional representations of the system and of the compensator transfer matrices can be computed directly without recurrence to the time domain results. From these representations, the right and left coprime compensator matrix fraction descriptions can easily be evalu...

Loop shaping design related to LQG/LTR for SISO minimum phase plants

One method of model-based compensator design for linear systems consists of two stages: state feedback design and observer design. A key issue in recent work in multivariable synthesis involves selecting the observer (state feedback) gain so that the final loop transfer function is the same as the state feedback (observer) loop transfer function. This is called loop transfer recovery (LTR)(Athans and Stein 1987, Kazerooni and Houpt 1986, Kazerooni et al. 1985, Doyle and Stein 1981). This paper shows how identification of the internal mechanism of the LTR provides simple design rules with little algebra for single-input single-output (SISO) systems. In the SISO case, the LQG/LTR reduces to computation of a compensator that shapes the loop transfer function by (i) cancelling the zeros of the plant with the compensator poles, and (ii) locating a new set of zeros for the compensator to shape the loop transfer function.

On the loop transfer recovery

One method of model-based compensator design for linear multivariate systems consists of state-feedback design and observer design (Athans 1971). A key step in recent work in multivariate synthesis involves selecting an observer gain so the final loop-transfer function is the same as the state-feedback loop transfer function (Doyle and Stein 1979, Goodman 1984). This is called loop transfer recovery (LTR). This paper shows how identification of the eigenstructure of the compensators that achieve LTR makes possible a design procedure for observer gain (Luenberger 1971). This procedure is based on the eigenstructure assignment of the observers. The sufficient condition for LTR and the stability of the closed-loop system is that the plant be minimum-phase. The limitation of this method might arise when the plant has multiple transmission zeros.