Robust Controller Design Method Research Articles

Robust Control Contraction Metrics: A Convex Approach to Nonlinear State-Feedback <inline-formula> <tex-math notation="LaTeX">${H}^\infty$ </tex-math> </inline-formula> Control

This letter proposes a new method for robust state-feedback control design for nonlinear systems. We introduce robust control contraction metrics (RCCM), extending the method of control contraction metrics from stabilization to disturbance attenuation and robust control. An RCCM is a Riemannian metric that verifies differential $L^{2}$ -gain bounds in closed-loop, and guarantees robust stability of arbitrary trajectories via small gain arguments. Numerical search for such a metric can be transformed to a convex optimization problem. We also show that the associated Riemannian energy can be used as a robust control Lyapaunov function. A simple computational example based on jet-engine surge illustrates the approach.

Robust Control System Design for Small UAV Using H2-Optimization

Abstract Unmanned aerial vehicles are famous for their wide range of applications. In D3 (Dirty-Dull-Dangerous) UAV applications flight conditions may vary on large scale. External disturbances like atmospheric turbulences and gusts may be subjected to UAV, and as a result, UAV flight mission might be conducted with high level of the degradation of the accuracy. Sensor noises are also present, and theirs negligence might lead to improper dynamic performances of the closed loop control systems. Uncertainties of the control systems being structured or unstructured may tend the closed loop control system to stability bounds. In worst case, uncertainties may destabilize closed loop control systems. The purpose of the author is to present a robust controller design method called H2-optimal design ensuring stability of the closed loop control systems with simultaneous dynamic performances predefined for the closed loop control system.

A Novel Robust Flight Controller Design for an Air-Breathing Hypersonic Vehicle

A novel robust flight control design method is proposed for a generic air-breathing hypersonic vehicle based on a state-dependent Riccati equation technique and a nonlinear disturbance observer. The highly nonlinear dynamics of the hypersonic vehicle are firstly brought to a linear structure having a state-dependent coefficient form. And then a state-dependent Riccati equation is solved at each sampling moment to obtain a nonlinear feedback optimal control law. In order to enhance robustness of the closed-loop system, a nonlinear disturbance observer is introduced to estimate the uncertainty caused by parametric variations and external disturbances. The resulting composite controller achieves not only promising robustness and disturbance rejection performance but also flexible adjustment in the response time. Compared to a Kriging controller, the proposed controller has great advantages in the system response time and robustness. The feasibility of the proposed method is validated by simulation results.

A Simplified Robust Control Design Method for Wide Area Damping Controllers

In this work a simplified robust control design method is proposed for Wide-Area Damping Control (WADC). Several challenges are considered during the control design such as output-feedback, low order controllers as well as robustness to time variation communication delay and operating point (load level). The methods main goal is to minimize the spectral abscissa with minimum damping constraints using a non-convex optimization algorithm. The use of spectral abscissa simplifies the method application making it an alternative to the H_∞ minimization approach proposed in the literature. The modal analysis and time-domain simulations of a Brazilian equivalent system is performed to assess the control robustness and performance.

Output Information Based Fault-Tolerant Iterative Learning Control for Dual-Rate Sampling Process with Disturbances and Output Delay

For a class of single-input single-output (SISO) dual-rate sampling processes with disturbances and output delay, this paper presents a robust fault-tolerant iterative learning control algorithm based on output information. Firstly, the dual-rate sampling process with output delay is transformed into discrete system in state-space model form with slow sampling rate without time delay by using lifting technology; then output information based fault-tolerant iterative learning control scheme is designed and the control process is turned into an equivalent two-dimensional (2D) repetitive process. Moreover, based on the repetitive process stability theory, the sufficient conditions for the stability of system and the design method of robust controller are given in terms of linear matrix inequalities (LMIs) technique. Finally, the flow control simulations of two flow tanks in series demonstrate the feasibility and effectiveness of the proposed method.

Multi-criteria Optimization of PD Controllers for Plants including Integral Action

A simple design method for robust PD controllers is presented for systems including integral action. The design method is based on a multi-criteria optimal control formulation, which is easily solved by a few lines of MATLAB code. Most criteria are based on H∞ measures, but since the focus is on reference signal tracking and not load disturbance compensation, the settling time is also included as a relevant performance measure. Since a PD controller is equivalent to a lead filter, the optimal PD controller is compared with ordinary text book design rules for lead filters. More specifically, it is shown that the common recommendation to place the mid frequency of the lead filter at the desired gain crossover frequency often gives bad servo performance. The suggested optimal solution, still including robustness and control activity adjustments, is on the other hand a simple and flexible design method for arbitrary plants including integral action.

Robust PID Controller Design for Both Delay-Free and Time-Delay Systems

Robust PID controller design methods are proposed for linear single-input single-output systems. Non-parametric models represented by a finite number of frequency responses are used for them. Sufficient conditions for closed-loop stability are derived based on the Nyquist stability criterion and the sufficient conditions are reduced to convex constraints. Together with the convex constraints and closed-loop model matching problems the robust PID controller design problems are formulated as convex optimization problems. A important feature of the proposed design methods is that they can be applied to delay-free and time-delay systems in the same manner. Moreover, the proposed methods are extended to two-degree-of-freedom PID controller design methods.

Robust controller design method for linear systems with parametric uncertainty using minimum eigenvalue approach

In this paper, a static state feedback robust controller design method for linear systems with parametric uncertainty is presented. The closed-loop stability analysis is carried out in the sense of Lyapunov and the controller design parameters with constraints are formulated in linear matrix inequality (LMI) framework. A less conservative robust stability result is obtained by introducing a new set of sufficient conditions developed which contains the information of minimum eigenvalue of the perturbation matrices. The control effort is also reduced by imposing additional constraints in the designed framework. The proposed design technique is illustrated by considering several numerical examples that show the superiority of the proposed technique over the existing methods.

Energy‐based stabilisation and robust stabilisation of stochastic non‐linear systems

This study proposes a constructive stabilisation and H ∞ robust controller design method for stochastic non-linear systems from a novel dissipation analysis and energy point of view. First, the authors propose a sufficient condition for the dissipation of stochastic Hamiltonian systems and discuss the energy property of the systems, which will be used for the stability analysis and feedback controller design. Then, the authors show that the system is (asymptotically) stable in probability if it is (strictly) dissipative. By completing the Hamiltonian realisation of the stochastic non-linear systems, a feedback controller is proposed to stabilise the system under the condition of dissipation and zero state detectability. For stochastic non-linear systems subjected to external disturbances, an energy-based H ∞ controller was proposed by choosing the Hamiltonian function to construct a solution of Hamiltonian–Jacobi inequality. Finally, the effectiveness of the proposed method was illustrated via the inverted pendulum systems.

H∞ control of nonlinear systems with positive input with application to antiangiogenic therapy

Abstract There are many systems in practice that can have only positive (nonnegative) input, typical examples for such systems are physiological systems. Moreover, the parameters of these systems are usually not known exactly or may vary over time, thus application of robust controllers represents a reasonable possibility. Most model-based controller design methods are developed for systems that can (or must) have negative and positive inputs as well, thus a dynamical extension is given here to the original system that ensures that the input of the original system is positive but the extended system can have negative input as well. The current paper investigates a robust control design method with positive input for an automatic therapy possibility in the case of antiangiogenic targeted molecular therapy using a recently published tumor growth model based on mice experiments. The extended system is transformed into an integrator series that is further modified using state-feedback to prepare the system for H∞ norm-based controller synthesis. The simulations demonstrate the robustness of the controller and the positivity of the input.

Once-through Circulating Fluidized Bed Boiler Control Design with the Dynamic Relative Gain Array and Partial Relative Gain

Combustion power plants currently face major performance challenges, which require robust control design methods. Extensive relative gain analysis was conducted in this paper to generate plantwide control structures for a full-scale once-through circulating fluidized bed boiler. No such study has been reported before for steam boilers. The partial relative gain was employed to generate decentralized control structures based on integral controllability with integrity. The approach provided feasible control structures and verified that basic turbine-following boiler control is preferable in terms of controllability. The steady-state results were extended with the dynamic relative gain array for higher frequencies, which revealed that boiler-following control becomes feasible for faster disturbances. The results highlight the complex interactions between steam pressure and output electrical power control, as well as the loop interactions caused by the feedwater flow in the once-through steam path.

ℓ2 Gain Estimation and Visualization of A Control Parameter Set in 3D Space Using Plant Response Data

AbstractIn this paper, a novel parameter space approach that uses volume rendering is proposed to visualize controller parameter sets that consist of three controller parameters. An off‐line design method for robust control using plant response data is also studied. A solution set with equal ℓ2 gain can be visualized as isosurfaces in three‐dimensional space, and the designer can visually select an appropriate parameter. This numerical method is applicable to many practical specifications, in contrast to analytical methods based on solving equations. An estimation method based on the extension theorem and a method using bandpass filters are both considered as possible methods for estimating the ℓ2 gain of the sensitivity functions when using grid points on the order of tens of thousands to create the volume data.The former method is superior to the latter with respect to accuracy but impractical with respect to computational load. The latter method is hence practical, because the computing time is reduced to less than 0.05 s for about 300,000 grid points by parallel computation with a graphical processing unit.

A study of robust controller and observer design method for a rolling object and beam system

This paper deals with a robust control problem for a ball and beam system with an uncertainty. At first, we clarify the effect of a measurement error in the beam rotational angle and its differential value. It is expressed as additional terms in the state and input matrix of the state equation, which is called as a structured uncertainty. For this system, a robust tracking controller and a robust state observer are applied. Both components are designed based on a robust control, which is called guaranteed cost control. This is a kind of cost minimization method for designing problem of a linear feedback system. The controller is obtained as the solution of the matrix algebraic Riccati like equation, which is referred to as stochastic algebraic Riccati equation. The nominal system performance is degraded due to the influence of the uncertainty, but it is able to design a system with robustness for disturbance. Next, we consider the design problem of a state observer to estimate all state variables form the output signal easy to measure, like rotation angle of the beam. For the design problem of the state observer, we consider dual problem of the original system. Consequently, our proposed system estimates the whole state vector, and using estimated state values, it controls the ball to the desired position. Both components have robustness for the uncertainty. Numerical result shows the validity of our proposed method.

Advanced Droop Control in Islanded Microgrids Using Dynamic Phasor Models

Abstract A dynamic phasor model for low- and medium-voltage distribution grids is presented. This model accurately represents the transient dynamics of this type of grid, and its low order makes it well suited for control design. A novel fixed-structure, robust control design method based on convex optimization is then used to design a decentralized low-order controller that shows a significantly improved transient performance compared to classical droop controllers. The performance of the designed controller is then validated in a simulation example for voltage and frequency control of an islanded medium-voltage distribution grid.

ROBUST FUZZY CONTROL DESIGN USING GENETIC ALGORITHM OPTIMIZATION APPROACH: CASE STUDY OF SPARK IGNITION ENGINE TORQUE CONTROL

In the case of widely-uncertain non-linear system control design, it was very difficult to design a single controller to overcome control design specifications in all of its dynamical characteristics uncertainties. To resolve these problems, a new design method of robust fuzzy control proposed. The solution offered was by creating multiple soft-switching with Takagi-Sugeno fuzzy model for optimal solution control at all operating points that generate uncertainties. Optimal solution control at each operating point was calculated using genetic algorithm. A case study of engine torque control of spark ignition engine model was used to prove this new method of robust fuzzy control design. From the simulation results, it can be concluded that the controller operates very well for a wide uncertainty.

A robust fixed point transformation-based approach for type 1 diabetes control

Modeling and control of diabetes mellitus (DM) are difficult due to the highly nonlinear attitude, time-delay effects, the impulse kind input signals and the lack of continuously available blood glucose (BG) level to be regulated. Regarding the mentioned problems, identification of DM model is crucial. Furthermore, due to the lack of information about the internal states (which cannot be measured in everyday life) and because the BG level is not available in every moment over time, adaptive robust control design method regardless exact model dependency would successfully handle these unfavorable effects without simplifications. The recently developed nonlinear robust fixed point transformation (RFPT)-based controller design method requires only a roughly approximate model in order to realize the controller structure. Moreover, parallel simulated approximate models—in order to provide additional internal information—can be used with the method. In this paper, the usability of the novel RFPT-based technique is demonstrated on the physiological problem of diabetes.

Space robot active collision avoidance maneuver under thruster failure

The problem of robust control for space robot collision avoidance maneuver under constant thrust is studied in this paper. Firstly, based on the Clohessy–Wiltshire (C–W) equations and by considering uncertainties and thruster failure in radial direction, the dynamic model for space robot is proposed. Then, based on the established model, a parametric design method of robust controller is given by using the eigenstructure assignment theory and the model reference theory. Next, a new constant thrust switching algorithm is proposed by using the impulse compensation method. Finally, simulation results and performance analysis validate the effectiveness of the proposed approach.

Fixed-order loop shaping robust controller design for parametric models to damp inter-area oscillations

The inter-area oscillations are common in power systems and can occur due to the changes in the load or generating power especially in long transmission lines. This paper presents the design of a robust fixed-order loop shaping controller to damp out the inter-area oscillations and to enhance the stability of the power system. The proposed loop shaping method is based on the shaping of the open-loop transfer function in the Nyquist diagram through minimizing the quadratic error between the actual and the desired open loop transfer functions in the frequency domain. The proposed method is robust with respect to multi-model uncertainty. Despite other robust controller design methods, the proposed approach deals with the entire system i.e. there is no need to reduce the system and still leads to a lower order controller. In addition, most of the robust methods are heavily dependent on selecting some weight filters which is not required in the proposed approach. This method is applied to the two-area four-machine system and 68 bus system and the effectiveness and robustness of the proposed method in damping inter-area oscillations are validated using case studies.

HDD 磁気ヘッド位置決め制御系における RBode Plot を用いた H∞制御器の改善法

In this paper, we present a design method of a robust controller for the magnetic-head positioning system in HDDs based on the H ∞ control theory and the Robust Bode (RBode). The RBode plot represents robust performance criteria as allowable and forbidden areas on Bode diagrams. Using the RBode plot, we can easily improve an existing feedback controller with visualized guidelines in order to compensate for disturbances against plant perturbations for a magnetic-head positioning system in a hard disk drive. With the RBode plot method, we need frequency characteristics data of the controlled object and weighting functions. Thus, there is no need to construct transfer function models of controlled objects. Simulation results with the HDD benchmark problem showed that the proposed method enable us to improve the positioning accuracy from the initial H ∞ controller by about 11% without losing stabilities of the control system.

A novel strategy to design enhanced performance robust controller for standalone VSI

A novel methodology for enhanced performance robust controller design is presented in this paper. The proposed method provides an efficient way to design a controller with an improved performance in terms of higher convergence rate of the system for the allowable uncertainties. The method is applied for the control design of standalone voltage source inverter. The control objective is to regulate its output voltage and frequency with an uncertain RL load. The dynamic equations of the system are used for uncertainty structure modelling. Then using Sylvester’s criterion, new uncertainty conditions are developed. Assisting with these conditions and intelligent technique differential evolution (DE), the optimum robust controller is designed. For reference tracking, this robust control law is augmented with integral control, which is also designed using DE. Furthermore, to guarantee the robustness of the augmented control law, a numerical approach is proposed. The effectiveness of the methodology is illustrated by means of simulations and real time hardware in the loop experiments. A comparison of the proposed method with existing robust control design method is also presented to demonstrate the improvement in performance.