Estimation of Frequency Domain Model Uncertainties with Application to Robust Controller Design

Robust velocity and height control problem is dealt with for hypersonic vehicles subject to highly nonlinearity and uncertainties. The linear robust controller design for nonlinear systems suffers from the conservation problem, because the nonlinear dynamics are considered as uncertainties. In this paper, a feedback linearization controller is firstly applied to achieve the dynamic decoupling of the velocity and height channels. Then, robust controllers are designed for each channel to restrain the effects of the parametric uncertainties, external disturbances, and nonlinear dynamics, which cannot be counteracted accurately by the feedback linearization technique. This method can guarantee the robust stability and robust tracking properties of the closed-loop control system, while the conservation of the robust controller design can be reduced because the nonlinear information of dynamic system is used. Simulation comparisons are given to show the advantages of the proposed robust nonlinear control method.

This paper studies the robust discrete-time pole-placement state feedback controller design in the LMI framework. The inner ellipse is used to approximate originally non-convex discrete-time closed loop pole region respective to the prescribed damping factor. The resulting LMI conditions use parameter dependent Lyapunov function to reduce conservatism in robust controller design. Contribution of this paper is in the application of this procedure on the case study - unstable Magnetic Levitation System, analysis of the results and comparison with standard robust stabilizing controller design.

This paper is concerned with a design of a collision avoidance robust controller. Based on a genetic algorithm, this paper deals with the problem of designing a robust safety controller with additional integral type which forces the plant output of a linear multivariable time system to converge to that of a reference model without any collision even if there are variations of the plant parameters.

The problem of robust velocity and height control is dealt with for hypersonic vehicles subject to high nonlinearity and uncertainties. Robust linear controller design for nonlinear systems suffers from the problem of conservation because the nonlinear dynamics are considered as uncertainties. In this paper, a feedback linearization controller is firstly applied to achieve dynamic decoupling of the velocity and height channels. Robust controllers are then designed for each channel to achieve the desired tracking and restrain the effects of parametric uncertainties, external disturbances, and nonlinear dynamics, which cannot be accurately counteracted by the feedback linearization technique. This method can guarantee the robust stability and robust tracking properties of the closed-loop control system. Moreover, the conservation of the robust controller design can be reduced because the nonlinear information of the dynamic system is used. Simulation results are given to show the advantages of the proposed robust nonlinear control method compared with its linear counterpart.

This paper presents an innovative many-objective metaheuristic (MnMH) algorithm designed to tackle the challenges of robust and optimal controller design for fixed-structure heading autopilots. The proposed approach leverages the radial basis function (RBF)-learning operator during the reproduction phase of the MnMH to generate high-quality solutions. A key feature of the method is its generation of a target Pareto front, in which a z-surrogate model makes predictions to guide design solutions toward achieving optimal performance. The effectiveness of the new algorithm is validated through both fixed-structure heading autopilot controller design problems and standard benchmark optimization problems. Results consistently show that the proposed algorithm outperforms several existing MnMHs across all tested scenarios. This study offers valuable insights into many-objective optimization and demonstrates the algorithm’s potential for enhancing robust controller design in heading autopilot systems.

Robust STATCOM voltage controller design using loop-shaping technique

The cross-coupled control (CCC) has been recognized as an efficient motion controller that reduces contouring errors, but theoretical analysis of it is lacking, and there is no systematic design approach for obtaining a CCC system with guaranteed control performance. Consequently, the compensators C in CCC are commonly implemented in a PID structure and their contouring accuracy is usually degraded in real applications under different operating conditions. In an attempt to overcome the CCC design limitations described above, this paper introduces a robust CCC design based on a novel formulation: the contouring error transfer function (CETF), leading to an equivalent formulation as in the feedback control design problem. Then, methods in robust control design can be readily employed to achieve robust CCC with specified stability margins and guaranteed contouring performance. Furthermore, the proposed design has been verified as being internally stable. All provided experimental results indicate that the proposed robust CCC design consistently renders satisfactory contouring accuracy under different operating conditions.

Detailed in this paper is a SISO non-linear modelling and robust controller design methodology experimentally verified on an internal combustion engine. The methodology begins with the identification of a NARMAX model that captures the non-linear dynamics relating the input to the output of a system. This model is converted to a describing function representation for the purpose of robust feedback controller design. The ideology for the describing function recovery is developed in the form of an algorithm which can be extended to other NARMAX model structures not considered here. The controller design is executed in the frequency domain where the output performance specification is |y(t)|≤β∀t>0 and the actuator saturation constraint is |u(t)|≤K∀t>0. For the engine idle speed control application of this study, a SISO NARMAX model of the engine is developed between the by-pass idle air valve (BPAV) and engine speed. The performance objective for the controller design is the time domain tolerance of |Δ rpm| ≤ 100 rpm on idle speed perturbations despite a non-measurable 20 N m external torque disturbance. The controller is validated through numerical simulations as well as experimental verification.

The problem of synthesizing robust pole placement controllers for interval linear time-invariant plants is addressed in the context of the concepts and methods of interval analysis. The robust pole placement design problem is associated with the solution of an interval Diophantine equation, whose basic properties axe analyzed. Robust pole placement controllers axe viewed as inner solutions of the interval Diophantine equation. Simple and computationally efficient characterizations of the set of all robust pole placement controllers are then obtained and some of its geometric properties, discussed. Several aspects of the design of robust controllers by interval analysis are integrated into a linear goal programming formulation, which can also incorporate additional constraints on the controller parameters. Robust pole placement design problems are easily modeled and solved through the approach proposed. Numerical examples illustrate its main characteristics.

A nonlinear robust controller design method is proposed for the lateral control of heavy vehicles for automated highway systems. In the controller design, the actuator dynamics is explicitly taken into account. A first order pre-filter is introduced to reduce chattering which is inherent in the nonlinear robust controller and to prevent the saturation in the front wheel steering angle and steering system slew rate. A constructive backstepping design technique is utilized in the design of a robust controller for the augmented system. Simulation results are shown.

This paper reviews robust feedback control applications in power system. Robust control concept in power system control area evolves by the way of uncertainty modeling. Uncertainties can be caused by variation of loading, load parameters, network topology and machine parameters. One direct way to take into consideration of uncertainties is to enumerate various system operating conditions and use a set of linear time invariant systems to model the power systems. Enumeration method is used in robust control signal selection and robust controller design. Another way is to model uncertainties as structured or unstructured uncertainties. Controllers are designed based on nominal system condition to tolerate uncertainty as much as possible. The controller synthesis problem is solved by either Algebraic Ricatti Equation (ARE) or Linear Matrix Inequality (LMI). LMI is shown to be more flexible in controller design since it provides a way to specify system dynamic performance. Most recently, linear parameter varying (LPV) concept expands the use of enumeration method to express a set of linear time invariant (LTI) systems with state space dependent on linear parameters. LPV based control methods extend gain scheduling to design linear control for each operating conditions and overall a nonlinear controller for the varying parameter system.

Inverse-NARMA: a robust control method applied to SI engine idle-speed regulation

The three-tank (3-tank) liquid-level control system commonly exists in industries under the proportional-integral-derivative (PID) control loop. However, the proportional-integral-derivative-accelerated (PIDA) can yield better responses than the PID for higher order plant. In this paper, the robust PIDA controller design by the cuckoo search (CS) for the 3-tank liquid-level control system is proposed. Results obtained will be compared with the PID controller designed by the CS. As results, the responses of the 3-tank liquid-level controlled system with the robust PIDA controller optimally designed by the CS are better than the PID controller designed by the CS. Due to model uncertainty within ±10% of each parameter of the nominal plant model, the robust PIDA controller optimized by the CS can provide the very satisfactory responses in both time and frequency domains with robust performance and robust stability.

In this paper, a novel robust controller for a Static Synchronous Compensator (STATCOM) is presented to enhance the fault ride-through (FRT) capability of fixed speed induction generators (FSIGs), the most common type of generators that can be found in wind farms. The effects of STATCOM rating and wind farm integration on FRT capability of FSIGs are studied analytically using the power-voltage and torque-slip relationships as well as through simulations. The wind generator is a highly nonlinear system, which is modelled in this work as a linear part plus a nonlinear part, the nonlinear term being the Cauchy remainder term in the Taylor series expansion and of the equations used to model the wind farm. Bounds derived for this Cauchy remainder term are used to define an uncertain linear model for which a robust control design is performed. The controller resulting from this robust design provides an acceptable performance over a wide range of conditions needed to operate the wind farm during severe faults. The performance of the designed controller is demonstrated by large disturbance simulations on a test system.

This article investigates the robust observer-based controller design problem for nonlinear parameter-varying systems subject to uncertainty and external disturbances. First, a novel augment vector is constructed, and an corresponding model of the resulting closed-loop system is obtained. Second, by applying the Lyapunov stability theory, a class of state-and-parameter-dependent robust asymptotic stability criteria is established, and the state-and-parameter-dependent sufficient conditions for the design of the robust observer-based controller are then acquired to guarantee the stability of the resulting closed-loop system, which can be effectively solved by sum-of-squares techniques. Different from the previous researches, the proposed control algorithm enables the state-and-parameter-dependent observer and the state-and-parameter-dependent controller design of the nonlinear parameter-varying systems to enjoy the advantage of separate design. The advantage can effectively reduce the computational complexity. Finally, simulation results demonstrate that the proposed robust observer-based controller shows improved performance in presence of uncertainty and external disturbances.