Fixed-Order Controller Design for Systems with Polytopic Uncertainty Using LMIs

Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as an LMI using KYP Lemma. This parameterization is a convex inner-approximation of the whole non- convex set of stabilizing controllers and depends on the choice of a central polynomial. It is shown that with an appropriate choice of the central polynomial, the set of all fixed-order controllers that place the closed-loop poles of a polytopic system in a disk centered on the real axis, can be outbounded with an LMI. This way, robust regional pole placement can be achieved by convex optimization for systems with polytopic uncertainty

State dependent regional pole assignment controller design for a 3-DOF helicopter model

For linear systems, a state feedback control law can be easily designed to keep all closed-loop poles inside a specified disk since the locations of the poles are unique. However, its application to nonlinear systems is not so simple. Therefore, this paper introduces a new pole placement method, named as State Dependent Regional Pole Assignment, for nonlinear systems. This proposed method produces a state dependent feedback control law, enabling the eigenvalues of the closed-loop matrix to be placed in a specified disk to achieve the desired control performance characteristics. The effectiveness of the method is tested on the 3 DOF Helicopter experimental setup. To verify its effectiveness, the experimental results of the nonlinear method are compared with those of the linear method

Sliding surface optimization via regional pole placement for a class of nonlinear systems

In this paper, a new approach is introduced which combines Eigenvalue Assignment, State Dependent Riccati Equation (SDRE) and Sliding Mode Control (SMC) methods for nonlinear systems. In the classical SDRE based SMC (SDRESMC) approach, a nonlinear system is frozen at each time instant to obtain a linear-like structure model that is used to design a sliding surface (SS) at each time instant. This mechanism produces a state-dependent SS to hold the states on the SS. The approach proposed here is built on this mechanism and offers a new way to design a state-dependent SS for nonlinear systems so that the pointwise eigenvalues of the closed-loop system matrix of the control-free dynamics in the regular form can be kept in a specified disk. This gives a great advantage to shape the transient response characteristics. The performance of the nonlinear controller approach proposed here is investigated in simulations

Observer based active fault tolerant control of descriptor systems

The active fault tolerant control (AFTC) uses the information provided by fault detection and fault diagnosis (FDD) or fault estimation (FE) systems offering an opportunity to improve the safety, reliability and survivability for complex modern systems. However, in the majority of the literature the roles of FDD/FE and reconfigurable control are described as separate design issues often using a standard state space (i.e. non-descriptor) system model approach. These separate FDD/FE and reconfigurable control designs may not achieve desired stability and robustness performance when combined within a closed-loop system.This work describes a new approach to the integration of FE and fault compensation as a form of AFTC within the context of a descriptor system rather than standard state space system. The proposed descriptor system approach has an integrated controller and observer design strategy offering better design flexibility compared with the equivalent approach using a standard state space system. An extended state observer (ESO) is developed to achieve state and fault estimation based on a joint linear matrix inequality (LMI) approach to pole-placement and H∞ optimization to minimize the effects of bounded exogenous disturbance and modelling uncertainty. A novel proportional derivative (PD)-ESO is introduced to achieve enhanced estimation performance, making use of the additional derivative gain. The proposed approaches are evaluated using a common numerical example adapted from the recent literature and the simulation results demonstrate clearly the feasibility and power of the integrated estimation and control AFTC strategy. The proposed AFTC design strategy is extended to an LPV descriptor system framework as a way of dealing with the robustness and stability of the system with bounded parameter variations arising from the non-linear system, where a numerical example demonstrates the feasibility of the use of the PD-ESO for FE and compensation integrated within the AFTC system.A non-linear offshore wind turbine benchmark system is studied as an application of the proposed design strategy. The proposed AFTC scheme uses the existing industry standard wind turbine generator angular speed reference control system as a “baseline” control within the AFTC scheme. The simulation results demonstrate the added value of the new AFTC system in terms of good fault tolerance properties, compared with the existing baseline system

Fixed-Order H-infinity Controller Design via Convex Optimization Using an Alternative to Youla Prameterization

All H-infinity controllers of a SISO LTI system are parameterized thanks to the relation between Bounded Real Lemma and Positive Real Lemma and a new concept of strict positive realness of two transfer functions with the same Lyapunov matrix in the matrix inequality of the Kalman-Yakubovic-Popov lemma. This new parameterization shares the same features with Youla parameterization, namely on the convexity of H-infinity norm constraints for the closed-loop transfer functions. However, in contrary to Youla parameterization, it can deal with any controller order and any controller structure such as e.g. PID. The main feature of the proposed method is that it can be extended easily for the systems with polytopic uncertainty. This way, a convex inner approximation of all H-infinity controllers for polytopic systems is given, which can be enlarged by increasing the controller order. In order to design a low-order robust H-infinity controller with less conservatism, rank of the k-th Sylvester resultant matrix of the controller is made to be deficient via a convex approximation of the rank minimization problem. The effectiveness of the proposed method is shown via simulation results

Design of wide-area damping control systems for power system low-frequency inter-area oscillations

The recently developed robust control theories and wide-area measurementtechnologies make the wide-area real-time feedback control potentially promising. Theobjective of this research is to develop a systematic procedure of designing a centralizeddamping control system for power grid inter-area oscillations by applying wide-areameasurement and robust control techniques while putting emphasis on several practicalconsiderations.The first consideration is the selection of stabilizing signals. Geometric measuresof controllability/observability are used to select the most effective stabilizing signals andcontrol sites. Line power flows and currents are found to be the most effective inputsignals. The second consideration is the effects of time-delay in the communication ofinput/output signals. Time-delays reduce the efficiency of the damping control system. Insome cases, large delays can destabilize the system. Time-delays should be modeled inthe controller design procedure so that the resulting controller can handle a range of timedelays.In this work, time-delays are modeled by Padé Approximations and the delayuncertainty is described by Linear Fractional Transformations (LFT). The thirdconsideration is the controller robustness. The synthesis of the controller is defined as aproblem of mixed H2/H∞ output-feedback control with regional pole placement and isresolved by the Linear Matrix Inequality (LMI) approach. The controller designed byrobust control techniques has satisfactory performance in a wide range of operatingpoints. The fourth consideration is the efficiency of the controller designed by lineartechniques in realistic nonlinear discrete environments. A tuning process and nonlinearsimulations are used to modify the controller parameters to ensure the performance androbustness of the controller designed with linear techniques. The last consideration is theselection of PMU data reporting rates. The performance of controllers designed in the sdomainis tested in digital environments and proper PMU data reporting rates are selectedwith consideration of the effects of time-delay.The design procedure of wide-area damping systems is illustrated by three studysystems. The first study system is a two-area four-machine system. The second one is theNew England 39-bus 10-machine system. The last one is a 29-generator 179-bus studysystem, which is a reduced order model of the Western Electricity Coordinating Council(WECC) system