Conditions For Internal Stability Research Articles

Design of active disturbance rejection controller for the system with unknown model using Laguerre functions

This paper concentrates on the design problem of linear active disturbance rejection control (LADRC) for uncertain systems, whose order and parameters are unknown. In general, LADRC has diversified structural forms due to different order and parameters selection. To clarify the prerequisites for constructing the LADRC strategy, a Laguerre-based LADRC (LLADRC) method is proposed, which provides controller design guidance for systems with unknown models by capturing the impulse response. Then, intensive attention is focused on establishing internal stability conditions of the feedback system and parameter tuning rules of the prescribed controller. To gain a better understanding, the internal correlation between LLADRC and standard LADRC of the same order is analyzed. It is shown that observer and controller gains of the standard LADRC can be tuned via a workable LLADRC to achieve better control performance. Finally, a numerical example and an application design of DC motor speed control are studied, both of which demonstrate the feasibility and validity of the proposed method.

Robust H-infinity control for connected vehicles in lattice hydrodynamic model at highway tunnel

In this paper, a macro hydrodynamic model suitable for tunnel traffic in the network environment is proposed. Firstly, according to the characteristics of tunnel traffic, we establish the corresponding lattice hydrodynamics model, and design the corresponding control strategy according to the information obtained by connected vehicles. Through the theoretical analysis, the internal stability conditions of the traffic system are obtained. After the external disturbance caused by the tunnel is considered, a robust H-infinity (H∞) control strategy is proposed, and the corresponding robust stability conditions are obtained. The string stability is also studied to ensure that the instantaneous disturbance is not amplified. Numerical simulation compares the evolution of the traffic system with and without control. The results reflect that the control strategy proposed in this paper can effectively maintain the stability of tunnel traffic system.

Event-Triggered Vehicle Platoon Control Under Random Communication Noises

As an effective way of improving traffic efficiency, vehicle platoon control has attracted extensive interest recently. Communication between vehicles tends to be affected by communication noises. Aimed at improving communication efficiency, an event-triggered vehicle platoon control under random communication noises is studied in this paper. First, for vehicle platoons with linear third-order dynamics, a time-varying consensus gain $c(t)$ is introduced to reduce the effects of the communication noises. Second, with the introduction of the algebraic graph theory and matrix analysis theory, conditions for internal stability and $l_{p}$ -string stability under random additive communication noises are derived. Third, by utilizing the Lyapunov approach and $It\hat {o}$ stochastic differential equations, the consensus of vehicle platoon under random additive communication noises is proved. Last, to reduce the frequent communication between vehicles, an event-triggered mechanism is introduced, and the design for the triggering parameter is derived. The effectiveness of the proposed method is verified with some numerical simulations.

Necessary and Sufficient Conditions for Internal Stability of Linear Formations

Necessary and sufficient conditions for the internal stability of formations whose dynamics are defined by linear differential equations have been obtained. The classes of admissible controls are specified as programmed controls for leaders and affine feedback controls depending on the object and leader states for followers. The conditions obtained are easy to verify and consist of (i) the stabilizability of a pair of matrices for the follower equations, (ii) the Hurwitz property and (iii) the coincidence of matrices for leaders in the multi-leader case, and (iv) the solvability of some linear equations and equality constraints on the vectors defining the desired relative leader–follower positions. Furthermore, the entire class of controls ensuring linear internal stability is described. By using the conditions obtained, it is shown that, in fact, only single-leader formations can possess internal stability. In the class of single-leader formations, a subclass of formations (whose graph is an input tree) is identified that are free of equality constraints, which are the main obstacle to the internal stability of multi-leader formations.

Event-triggered internally stabilizing sporadic control for MIMO plants with non measurable state

AbstractThis paper proposes a new approach to the sporadic networked control problem: the output of a remotely controlled sampled plant is required to track an external reference with a reduced communication cost. The main novelty is that internal stability conditions are derived without assuming a measurable state of the plant. The new event driven Communication Logic (CL) is composed of a Sensor CL (SCL) and of a Controller CL (CCL). The SCL is based on the explicit computation of a Lyapunov-like functional of the tracking error and of a corresponding time-varying threshold: a network message from the sensor to the controller is triggered only if the functional exceeds the current value of the threshold. The CCL is directly driven by the SCL: the dynamic output controller sends a feedforward message to the plant only if it has received a message from the sensor at the previous time instant.

A Lyapunov Approach to Cascade Interconnection of Integral Input-to-State Stable Systems

This technical note deals with the stability of cascade interconnection of integral input-to-state (iISS) time-varying systems. A new technique to construct smooth Lyapunov functions of cascaded systems is proposed. From the construction, sufficient conditions for internal stability and stability with respect to external signals are derived. One of the derived conditions is a trade-off between slower convergence of the driving system and steeper input growth of the driven system. The trade-off is no more necessary if the speed of convergence of the driven system is not radially vanishing. The results are related to trajectory-based approaches and small-gain techniques for feedback interconnection. The difference between the feedback case and the cascade case is viewed from the requirement on convergence speed of autonomous parts.

Rejection of Persistent Bounded Disturbance for a Class of Time-Delay Systems

This paper considers the problem of persistent bounded disturbance rejection for a class of time-delay systems by Lyapunov function and positively invariant set analysis method. Sufficient conditions for internal stability and L1–performance analysis are given in terms of linear matrix inequalities (LMIs). Based on which, a dynamic output-feedback controller is then designed. All the obtained results are delay-dependent, and therefore, are less conservative. A numerical example is included to illustrate the proposed method.

A stability and contractiveness analysis of discrete-time Markovian jump linear systems

We propose performance criteria for discrete-time linear systems with Markov jumping parameters. Exact convex conditions for internal stability and contractiveness of such systems are expressed in terms of linear matrix inequalities. These conditions are of the same form as that in the Kalman–Yacubovich–Popov lemma.

Robust stability of impulsive switched systems with disturbance

AbstractThis paper studies a class of impulsive switched systems with persistent bounded disturbance using robust attractor analysis and multiple Lyapunov functions. Some sufficient conditions for internal stability of the systems are obtained in terms of linear matrix inequalities (LMI). Based on the results, a simple approach for the design of a feedback controller is presented to achieve a desired level of disturbance attenuation. Numerical examples are also worked out to illustrate the obtained results.

Optimal Design of the Refined Ziegler−Nichols Proportional-Integral-Derivative Controller for Stable and Unstable Processes with Time Delays

In this paper, the well-known refined Ziegler−Nichols (RZN) method is analyzed and extended to the control of unstable processes with time delays. It is shown that both the RZN control structure and the inner stabilizing control structure can be equivalent to the unity feedback loop with a set-point filter or, equivalently, a two-degree-of-freedom control structure. This implies that those analysis and design techniques developed for the classical control structure can be applied to the two special control structures. The original formulas for the RZN proportional-integral-derivative (PID) controller are empirical and can only be used in restricted scope. A new procedure is developed for designing the RZN PID controller. Suboptimal formulas without the restriction are analytically derived. In the procedure, the load response can be independently optimized. Nominal performance of the closed-loop system is discussed, and sufficient and necessary conditions for internal stability and robust stability are given. Numerical examples are provided to illustrate the proposed method and compare it with the original RZN method.

On Coalition Formation with Heterogeneous Agents

We propose a framework to analyze coalition formation with heterogeneous agents. Existing literature defines stability conditions that do not ensure that, once an agent decides to sign an agreement, the enlarged coalition is feasible. Defining the concepts of refraction and exchanging, we set up conditions of existence and enlargement of a coalition with heterogeneous agents. We use the concept of exchanging agents to give necessary conditions for internal stability and show that refraction is a sufficient condition for the failure of an enlargement of the coalition. With heterogeneous agents, we can get a situation where a group of members of an unstable coalition does not deviate, neither within the coalition nor within the extended coalition. Hence, the possibilities of agreement are richer than in the standard analysis with homogeneous agents. Examples of industrial economics are used for illustration, and an application to climate change negotiations is discussed in more detail.

Design of Robust High-Speed Motion Controller for a Plant With Actuator Saturation

A robust high-speed motion controller is proposed. The proposed controller consists of the proximate time optimal servomechanisms (PTOS) for high-speed motion, disturbance observer (DOB) for robustness, friction compensator, and saturation handling element. In the proposed controller, DOB basically provides the chance to apply PTOS to nondouble integrator systems by drastically reducing disturbances as well as unwanted signals due to difference between real system and the double integrator model. But, in DOB-based systems, if control input is saturated due to control input of PTOS and/or DOB, overall system stability cannot be guaranteed, which is first found and analyzed in this paper. To solve this problem, robust stability and internal stability conditions of DOB-based system are derived. It is also shown that DOB could violate the internal stability, when the control input is saturated. Eventually, a simple saturation handling element is inserted to maintain internal stability of overall system. Also, we explain that our two saturation handling methods, i.e., Additional Saturation Element (ASE) and Self Adjusting Saturation (SAS) are the equivalent solutions of saturation problem to maintain internal stability. The stability and performances of the proposed controller are verified through numerical simulations and experiments using a precision linear motor system. [S0022-0434(00)01103-5]

Power system stabilizer based on inverse dynamics using an artificial neural network

A stable power system stabilizer (PSS) based on the inverse dynamics of the controlled system using an artificial neural network (ANA) is suggested to enhance the dynamic performances of a power system. First, an output feedback control law is driven with some conditions satisfied, which guarantees the internal stability and robustness against the asymptotically stable external disturbances. Then the control law is implemented using the inverse dynamics of the controlled plant. The inverse dynamics of the controlled plant is identified by an ANN, inverse dynamics neural network (IDNN), off-line. The pole-shifting technique and a scaling factor are introduced for the control system to meet the conditions for internal stability and robustness. The proposed controller is applied to a typical single-machine infinite-bus power system. Simulation results under various operation conditions are given which show that the proposed controller damps the low frequency oscillation in an efficient manner.

Feedback representation of precompensators: the general case

Using the transfer approach, we give, under internal stability conditions, a necessary and sufficient condition of equivalence between open-loop precom-pensation and a closed-loop configuration that consists of dynamic output feedback and inside-loop precompensation. Our result is the generalization of Hammer's result (Hammer 1983) to the general case. This result emphases the use of skew-prime relationships. The parametrization of this problem's solutions will throw new light on multipurpose controllers.

Algebraic necessary and sufficient conditions for the stability of 2-D discrete systems

Algebraic necessary and sufficient conditions for the stability analysis of 2-D discrete systems are presented. These conditions are based on the frequency-dependent formulation of the Lyapunov equation using Kronecker products. It is shown that these conditions for internal stability of 2-D discrete systems are equivalent to testing the eigenvalues of constant matrices only. >

Dynamic output feedback control of nimimum-phase nonlinear processes

Abstract This paper concerns the synthesis of dynamic output feedback controllers for minimum-phase nonlinear processes. The problem is addressed first for open-loop stable and then for general minimum-phase nonlinear processes, leading to one- and two-degree-of-freedom controllers, respectively. The synthesis of the controllers essentially involves combination of state feedback and state observers. An input/output interpretation of the resulting control structures illustrates the importance of alternative state—space realizations of the process inverse for the controller implementation. Internal stability conditions are derived for the closed-loop system. Simulation studies in a chemical reactor example illustrate the application of the control methodology developed.

Stability of control systems and graphs of linear systems

New conditions for internal stability of a closed-loop control system are given in terms of the graphs of the multiplication operators induced by the transfer functions of the plant and the controller. These conditions can be given a geometrical interpretation. This relates closed-loop stability to the minimal angle between the graph space associated with the system and the graph space associated with the controller. The maximally stabilizing controller is defined as the controller that maximizes the minimum angle between the graph space associated with the system and the graph space associated with the controller. It is shown that this controller can be calculated as a Nehari extension of the coprime factors of the system.

Inversion and zero dynamics in nonlinear multivariable control

AbstractThis work concerns general multiple‐input/multiple‐output (MIMO) nonlinear systems with nonsingular characteristic matrix. For these systems, the problem of inversion is revisited and explicit formulas are derived for the full‐order and the reduced inverse system. The reduced inverse naturally leads to an explicit calculation of the unforced zero dynamics of the system and the definition of a concept of forced zero dynamics. These concepts generalize the notion of transmission zeros for MIMO linear systems in a nonlinear setting. Chemical engineering examples are given to illustrate the calculation of zero dynamics. Input/output linearization is then interpreted as canceling the forced zero dynamics of the system, and precise internal stability conditions are derived for the closed‐loop system.

Relationships between internal and external stability for infinite-dimensional systems with applications to a servo problem

A study is made of the relationships among various stability motions for a class of infinite-dimensional systems, which contains a class of systems not covered by existing methods, e.g. those having infinitely many unstable poles. It is proved that: internal L/sup 2/-stability and exponential stability are equivalent; and internal stability implies H/sup infinity /-stability. Several necessary and sufficient conditions for internal stability are derived. In particular, under certain conditions, a canonical realization is internally stable if it is externally stable. These results are applied to the servo problem involving this class of systems. It is shown that: (i) an internal model is necessary for tracking; (ii) an internal model along with closed-loop stability implies tracking. A typical example, called a repetitive control system, is discussed to illustrate the results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Input/output linearization: A nonlinear analog of placing poles at process zeros

AbstractThis paper deals with SISO nonlinear processes and their control with state feedback. The Byrnes‐Isidori concept of non‐linear zeros is first reviewed and illustrated with two chemical engineering exemples. This concept is then used to interpret input/output linearizing state feedback as a nonlinear analog of placing poles at the process zeros. This interpretation leads to closed‐loop internal stability conditions for nonlinear processes under input/output linearizing state feedback.