Interval analysis and design of robust pole assignment controllers

In this study, anti-sway control of an experimental overhead crane system is proposed with acceleration control approach. In this approach, acceleration of the cart is considered as control input. In order to satisfy transient performance objectives in the presence of parameter variations, a robust pole placement controller is designed. The parameter variations are modelled with a linear polytopic model. Hence, controller design is formualted as a convex optimization problem under linear matrix inequalities (LMIs) constraints. LMI regions are employed to restrict closed-loop pole locations in prescribed convex domains in complex plane. Performance of the proposed control has been verified in both simulation and experimental studies.

Bellman’s discrete dynamic programming is one of the most general approaches to solve optimal control problems. For discrete-time dynamical systems, it is, at least theoretically, capable to determine globally optimal control laws. In most practical cases, both state and control variables are subject to constraints. Due to the necessity for gridding of the range of both state and control variables in numerical implementations of dynamic programming, the computational effort grows exponentially with increasing system dimensions. This fact is well known as the curse of dimensionality. Furthermore, gridding of intervals representing uncertain system parameters is inevitable, if dynamic programming is used for the design of optimal controllers for systems with uncertainties. In this contribution, an interval arithmetic procedure for the design of optimal and robust controllers is presented. This procedure relies on the basic concepts of dynamic programming. Sophisticated techniques for the exclusion of non-optimal control strategies significantly reduce the computational burden. Since interval techniques can be applied to both continuous-time and discrete-time dynamical systems, the interval arithmetic optimization approach presented in this chapter is applicable to both cases. In addition, the inclusion of effects of uncertain parameters in the underlying optimality criteria is demonstrated. For that purpose, interval arithmetic routines for analysis and design of optimal and robust controllers have been developed. Details about computationally efficient implementations of interval arithmetic optimization procedures and numerical results for a mechanical positioning system with statedependent switchings between different dynamical models for viscous and Coulomb friction are summarized.

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.

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.

Robust STATCOM voltage controller design using loop-shaping technique

Background: The conventional method using one-degree-of-freedom (1DOF) controller for Permanent Magnet Synchronous Motor (PMSM) servo system has the trade-off problem between the dynamic performance and the robustness. Methods: In this paper, by using H∞ control theory, a novel robust two-degree-of-freedom (2DOF) controller has been proposed to improve the position control performance of PMSM servo system. Using robust control theory and 2DOF control theory, a H∞ robust position controller has been designed and discussed in detail. Results: The trade-off problem between the dynamic performance and robustness which exists in one-degree-of-freedom (1DOF) control can be dealt with by the application of 2DOF control theory. Then, through H∞ control theory, the design of robust position controller can be translated to H∞ robust standard design problem. Moreover, the control system with robust controller has been proved to be stable. Conclusion: Further simulation results demonstrate that compared with the conventional PID control, the designed control system has better robustness and attenuation to the disturbance of load impact.

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.

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.

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.

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.

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 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.

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.

Robust SVC controller design and analysis for uncertain power systems

This paper presents an approach to the design of an output voltage regulator for a boost converter operating in continuous conduction mode. This approach relies on 'robust control' design techniques, but uses some heuristic rules for defining the controller design procedure instead of being based on a precise definition of model uncertainties. Design algorithms of H∞ robust controllers are cast in a 'black-box' framework, leaving some free design parameters to be tuned by the user. The resulting controller attenuates input?output transmission (low audio-susceptibility), has decentralised structure and uses only local information, guaranteeing stability and the desired closed-loop dynamic response. The main contribution of the tuning rules is that the controller parameters can be obtained using one design parameter which reflects the trade-off between stability robustness and time domain performance. Various aspects of the design, including the associated practical problems and the proposed solutions, are detailed. Simulation results on a boost converter, using a poorly regulated voltage source, are presented to assess the performance of our approach.