Guaranteed robust state feedback controller via constrained optimization using Differential Evolution

For an optimal parametric linear quadratic (LQ) control problem, a design objective is to determine a controller of constrained structure such that the closed-loop system is asymptotically stable and an associated performance measure is optimized. In the presence of system uncertainty, the system obtained by parametric LQ design is further required to be robust in terms of maintaining the closed-loop stability with a guaranteed cost bound. This problem, referred to as robust optimal parametric LQ control with a guaranteed-cost bound, is addressed. A design method is proposed for finding an optimal controller that simultaneously guarantees robust stability and performance over a specified range of parameter variations. A versatile numerical algorithm is given for computing the robust optimal gains. The usefulness of the design method is demonstrated by the design of robust control of a VTOL helicopter. >

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.

Optimal controller properties from closed-loop experiments

This paper is an overview of fundamental linear–quadratic optimal control techniques used for linear dynamic systems. The presentation is suitable for undergraduate and graduate students and practicing engineers. The paper can be used by class instructors as supplemental material for undergraduate and graduate control system courses. The paper shows how to find the solution to a dynamic optimization problem: optimize an integral quadratic performance criterion along trajectories of a linear dynamic system over an infinite time period (steady-state linear–quadratic optimal control problem). The solution is obtained by solving a static optimization problem. All derivations done in the paper require only elementary knowledge of linear algebra and state space linear system analysis. The results are presented also for the observer-driven linear–quadratic steady-state optimal controller, output feedback-based linear–quadratic optimal controller, and the Kalman filter-driven linear–quadratic stochastic optimal controller. Having full understanding of derivations of the linear–quadratic optimal controller, observer-driven linear–quadratic optimal controller, optimal linear–quadratic output feedback controller, and optimal linear–quadratic stochastic controller, students and engineers will feel confident to use these controllers in numerous engineering and scientific applications. Several optimal linear–quadratic control case studies involving models of real physical systems, with the corresponding Simulink block diagrams and MATLAB codes, are included in the paper.

In this work, an Optimal Linear Quadratic (LQR) and optimal Minimax controller is proposed for Wing Rock Motion Control in Delta wing Aircraft model. The nonlinear Wing Rock Motion dynamics were considered. The LQR and Minimax controllers are designed in order to reduce the Wing Rock Motion. Simulations are performed in order to verify the ability of both controllers to reduce the wing rock motion in delta wing aircraft. Results were plotted together in order to show the difference of performance for both controllers for a comparative point of view.

This paper presents the design of a linear quadratic (LQ) optimal controller for a spar-type floating offshore wind turbine (FOWT). The FOWT is exposed to different sea states and constant wind turbulence intensity above rated wind speed. A new LQ control objective is specified for the floater-turbine coupled control, in accordance with standard requirements, to reduce both rotor speed fluctuations and floater pitch motion in each relevant sea state compared with a baseline proportional-integral (PI) controller. The LQ weighting matrices are selected using time series of the wind/wave disturbances generated for the relevant sea states. A linearized state-space model is developed, including the floater surge/pitch motions, rotor speed, collective blade pitch actuation, and unmeasured environmental disturbances. The wind disturbance modeling is based on the Kaimal spectrum and aerodynamic thrust/torque coefficients. The wave disturbance modeling is based on the Pierson–Moskowitz spectrum and linearized Morison equation. A high-fidelity FOWT simulator is used to verify the control-oriented model. The simulation results for the OC3-Hywind FOWT subjected to turbulent wind show that a single LQ controller can yield both rotor speed fluctuation reduction of 32–72% and floater pitch motion reduction of 22–44% in moderate to very rough sea states compared with the baseline PI controller.

The robust exponential stability in mean square for a class of linear stochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we have designed an optimal controller which guarantees the exponential stability of the system. Actually, we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to have shown the robustness of the linear quadratic(LQ) optimal control law. And the algebraic criteria for the exponential stability on the linear stochastic uncertain closed-loop systems are given.

This paper investigates the problem of robust control for a class of systems with both Markovian jumping parameters and parametric uncertainty. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process, and the parameter uncertainty appearing in the state equation is real, time-dependent, and normbounded. A method is proposed for the design of robust state-feedback controllers. Both the cases of finite and infinite horizon are addressed. We show that the problem of robust control for linear systems with Markovian jumping parameters can be solved in terms of the solutions to a set of either coupled Riccati differential equations, or algebraic Riccati equations.

This article investigates the robust optimal output regulation problem for the constrained uncertain nonlinear systems. A two‐step design framework is proposed to overcome the difficulties brought by uncertainties, constraint and performance optimization. First, the feedforward controller is designed by the internal model principle, and the robust output regulation problem is transformed into the robust stabilization problem. Then, the optimal control problem with input saturation is further considered in the robust feedback controller design process. With the help of a non‐quadratic cost functional, actor‐critic algorithm and robust redesign technique are brought together to design the constrained robust optimal feedback controller. Finally, stability analysis based on Lyapunov method shows that all the signals of the closed‐loop system remain bounded, and the tracking error is uniformly ultimately bounded with arbitrarily small ultimate bound. Simulation results illustrate the effectiveness of the proposed methodology.

Linear quadratic (LQ) controller design is considered for continuous-time systems with harmonic signals of known frequencies and it is shown that the design is reducible to an interpolation problem. All LQ optimal loops are parametrized by a particular solution of this interpolation problem and a (free) stable/proper transfer function. The appropriate choice of this free parameter for optimal stability robustness is formulated as a multiobjective design problem and reduced to a Nevanlinna-Pick interpolation problem with some interpolation points on the boundary of the stability domain. Using a related result from the literature, it is finally shown that, if there is sufficient penalization on the power of the control input, the level of optimum stability robustness achievable with LQ optimal controllers is the same as the level of optimum stability robustness achievable by arbitrary stabilizing controllers.

In this work, we propose a new sliding mode controller based on a reference model for controlling data transmission rates in a connection‐oriented communication network. In the proposed approach, we build a model of the network, which is controlled by a linear quadratic (LQ) optimal controller. Then, the sliding variable of the real network is forced to follow the reference sliding variable generated by this model. This method enables us to preserve the favorable properties of the optimal controller, such as reducing and smoothing out the initial flow rates. Moreover, once the reference model attains the vicinity of the desired state, the designed sliding mode controller is able to react more rapidly to changes in the available bandwidth, ensuring better robustness. Due to this fact, the considered controller can ensure full bottleneck link bandwidth utilization with smaller memory buffers than the LQ optimal one. This important advantage is shown both analytically, and in computer simulations

A Linear Quadratic (LQ) optimal controller is proposed in combination with a Functional Electrical Stimulation (FES) system to regulate the quite standing for paraplegic subjects. The lower part of the body (i.e., legs, knees and ankles) is modeled through a double inverted pendulum with user-specific parameters and is driven by two pairs of muscles acting around the ankle and knee joints. For each joint, indeed, extensor and flexor muscles are inserted and their contraction dynamics is described through a three-factor muscle model as in [1]. Trunk, arms, head, hips and pelvis, instead, are described by a point-wise mass placed at the top of the thigh segment. In this study, we present simulation results achieved through a control law based on the linearized dynamics of muscles, joints and body during quite standing.

OPTIMAL CONTROL REDESIGN OF GENERALIZED PREDICTIVE CONTROL

This paper presents the design and implementation of optimal and robust state feedback controller for rotary inverted pendulum system. The Particle Swarm Optimization (PSO) method is used to find the optimal values of the state feedback gains subject to time response specifications and H_∞ constraints. To improve the tracking of the system, a robust state feedback plus integral controller is designed. The simulation results show that the proposed controller can effectively stabilize the pendulum at the upright position. Further, the proposed controller can compensate the variations in system parameters. The effectiveness of the proposed controller is verified experimentally using real rotary inverted pendulum.

In this letter, we study the irregular output feedback linear quadratic (LQ) control problem where the state is measured through a linear system with noise. It is interesting to show that the irregular output feedback control with the standard average LQ cost is unsolvable even if the state feedback LQ control is solvable, which is completely different from the classical regular output feedback LQ control. In order to guarantee the solvability of the irregular output feedback control, the LQ cost is modified at the terminal time with the expectation of terminal state in this letter. In the framework of the modified cost function, it is shown that the separation principle holds and the explicitly optimal controller is given in the feedback form of the Kalman filtering. In particular, the feedback gain is calculated by two Riccati equations, independently of the Kalman filtering. The key technique is the analytical solution of the forward and backward differential equations (FBDEs). We also emphasize that the optimal controller at the terminal time is required to be deterministic.