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Load Frequency Control (LFC) is essential for ensuring frequency stability in modern power systems subject to load fluctuations, uncertainties, and increasing renewable penetration. This paper introduces a novel hybrid control framework that unifies H∞ stability guarantees, H2 performance, and pole placement for transient shaping. Its originality is threefold. First, it models load variation as a measurable disturbance (D12 = 0, D21 ≠ 0), departing from the standard assumption of an unknown input. This enables a low-order H∞ controller that improves transient response, enhances robustness, and reduces energy consumption. Second, the framework explicitly accounts for a wider spectrum of real-world uncertainties, including governor and turbine dynamics and the transmission-line synchronizing power coefficient. Third, it integrates explicit energy optimization to reduce mechanical stress and extend equipment lifespan. This strategy yields substantial energy savings by minimizing fuel use and operational costs. Simulation results confirm its superiority: the proposed H∞/H2 pole placement controller with measured disturbances achieves a 98% reduction in control energy relative to a standard H∞ controller, along with a 70% reduction in overshoot and a drastic improvement in settling time—from 7 s to 0.2 s—compared to a conventional H∞/H2 controller. These results establish the proposed framework as a new benchmark for robust, efficient, and high-performance LFC design.

Recently, a reference derived some new higher-order output tracking properties for direct model reference adaptive control (MRAC) of linear time-invariant (LTI) systems: lim t →∞ e ( i ) ( t ) = 0, i = 1,…, n * − 1, where n * and e ( i ) ( t ) denote the relative degree of the system and the i -th derivative of the output tracking error, respectively. However, a naturally arising question involves whether indirect adaptive control (including indirect MRAC and indirect adaptive pole placement control) of LTI systems still has higher-order tracking properties. Such properties have not been reported in the literature. Therefore, this paper provides an affirmative answer to this question. Such higher-order tracking properties are new discoveries since they hold without any additional design conditions and, in particular, without the persistent excitation condition. Given the higher-order properties, a new adaptive control system is developed with stronger tracking features. (1) It can track a reference signal with any order derivatives being unknown. (2) It has higher-order exponential or practical output tracking properties. (3) Finally, it is different from the usual MRAC system, whose reference signal’s derivatives up to the n * order are assumed to be known. Finally, two simulation examples are provided to verify the theoretical results obtained in this paper.

This paper investigates the output containment control problem of unknown heterogeneous non-minimum phase linear multi-agent systems over directed communication graphs. The dynamics of each follower are allowed to be unknown. A novel distributed adaptive pole placement control strategy is developed to address the output containment control problem of the concerned multi-agent system. It is shown that the proposed distributed adaptive control strategy guarantees the boundedness of all the signals in the resulting closed-loop system and the convergence of the followers’ outputs to a convex hull spanned by the leaders’ outputs. The efficacy of the proposed control strategy is demonstrated by two simulation examples.

In this paper, the limitations of the standard PID controller for dominant pole placement has been analyzed. Study shows that the modified PID controller, such as PI-D, I-PD, PI-PD and PD-PID controller, is an alternative to solve this problem. For the PI-PD and PD-PID controller, the zeros can be placed on the poles that are close to the specified dominant poles. The conditions for the existence of the dominant poles could be relaxed by pole-zero cancellation. Results show that a good dominant effect with fast response can be realized by the modified PID controllers.

This paper proposes a distributed robust frequency control (DRFC) scheme for industrial applications that can effectively adjust the frequency and regulate the active power-sharing ratio of islanded microgrids (MGs). The proposed method also enhances the H ∞ performance and the transient response of the MGs by imposing pole placement constraints in the linear matrix inequality (LMI) framework. The proposed scheme utilizes the information on active power and frequency deviations of each distributed generator (DG) and its neighboring DGs to generate an auxiliary control signal implemented by the secondary control layer. The auxiliary control signal improves the input of the droop controller block at the primary control layer, ensuring both frequency regulation and proportional active power-sharing among the DGs. To show the robustness of this novel feature, an AC-islanded MG is simulated under various load and fault scenarios. The simulation results demonstrate the effectiveness and efficiency of the proposed scheme in stabilizing the frequency and damping ratio of the MG while maintaining an active power-sharing balance.

A new analytical approach to static output feedback pole placement for linear time-invariant systems is proposed, where the system order equals the product of inputs and outputs, and the controllability and observability indices take the maximum and minimum possible values, respectively. This approach uses the Cayley–Hamilton theorem in relation to the matrix of a closed-loop control system. The applicability of the proposed method of static output feedback pole placement is not limited to fourth-order systems with two inputs and two outputs. In addition, the method’s applicability does not depend on whether the system is reducible to modal control by state with fewer inputs or to modal observation with fewer outputs. On the examples of sixth-order multi-input multi-output systems not reducible to systems with fewer inputs or outputs, the process of obtaining analytical solutions to the problem of modal output control, providing desirable pole placement is demonstrated. For systems from the considering class, the obtained solutions are unique.

A universal analytical method of static output feedback pole placement (for constructing controllers by output) for fourth-order linear time-invariant systems with two control inputs and two observable outputs is proposed, which does not depend on the relations between the controllability and observability indices. The method does not require decomposing or reducing the system and may be applied to any fourth-order systems modally controllable by static output feedback, including systems irreducible to control (observation) with a single input (output). The method is based on linear matrix dependence of the characteristic polynomial of a closed-loop control system on the coefficients and determinant of a matrix of controller by output. The proposed approach gives the necessary and sufficient condition for static output feedback pole placement—it allows defining all possible matrices of controllers by output and the conditions of their existence. A new algebraic criterion of complete modal controllability by output is formulated and proved. Examples of applying the approach to controlling the aviation and space systems based on linearized models both in numerical and symbolic form are given.

Linear quadratic regulator (LQR), a popular technique for designing optimal state feedback controller, is used to derive a mapping between continuous and discrete time inverse optimal equivalence of proportional integral derivative (PID) control problem via dominant pole placement. The aim is to derive transformation of the LQR weighting matrix for fixed weighting factor, using the discrete algebraic Riccati equation (DARE) to design a discrete time optimal PID controller producing similar time response to its continuous time counterpart. Continuous time LQR-based PID controller can be transformed to discrete time by establishing a relation between the respective LQR weighting matrices that will produce similar closed loop response, independent of the chosen sampling time. Simulation examples of first/second order and first-order integrating processes exhibiting stable/unstable and marginally stable open loop dynamics are provided, using the transformation of LQR weights. Time responses for set-point and disturbance inputs are compared for different sampling times as fraction of the desired closed loop time constant.

In this paper, a high dimensional double rotor model is proposed. We establish its dynamic equations, and simply it into a four-dimensional mapping form. The bifurcations of the double rotor mapping under different control parameters are investigated. The chaotic dynamic behavior of the model is controlled by improving the pole assignment method. With the linear control theory, a control parameter is selected and the period-1 is chosen as control target. When the mapping point wanders to the neighborhood of the periodic point, the control parameter is perturbed. The unstable period-1 orbit is controlled to be a stable periodic orbit. Numerical simulations are consistent with the theoretical analysis. The results of this research show that this chaos control method can be applied to the 4-dimensional model and can be realized.The research results indicate when the selected regulator poles are different, the control times are different.

The stability analysis and controller design of stochastic systems have become much more important because the stochastic behaviors usually exist in practical nonlinear systems. In this paper, a robust fuzzy controller design approach is proposed with multiple constraints, including state variance constraints, output variance constraints, and pole placement constraints. At first, nonlinear systems are expressed as the Takagi-Sugeno fuzzy model, and the parallel distributed compensation method is applied to design the robust fuzzy controllers. Next, considering the stability analysis and the performance constraints of perturbed Takagi-Sugeno fuzzy models, Lyapunov conditions are developed based on covariance control theory, pole placement theory and robust control theory. By constructing the stability conditions with multiple constraints, the proposed fuzzy control problem can be effectively transferred into the linear matrix inequality problem. It can be solved by the convex optimal programming algorithm. At last, a nonlinear ship steering system is selected to verify the effectiveness and applicability of the proposed robust fuzzy controller design method.