Optimum placement of actuators in structural and control design using Stackelberg games

We study the problem of actuator and sensor placement in a linear advection partial differential equation (PDE). The problem is motivated by its application to actuator and sensor placement in building systems for the control and detection of a scalar quantity such as temperature and contaminants. We propose a gramian based approach to the problem of actuator and sensor placement. The special structure of the advection PDE is exploited to provide an explicit formula for the controllability and observability gramian in the form of a multiplication operator. The explicit formula for the gramian, as a function of actuator and sensor location, is used to provide test criteria for the suitability of a given sensor and actuator location. Furthermore, the solution obtained using gramian based criteria is interpreted in terms of the flow of the advective vector field. In particular, the almost everywhere uniform stability property and ergodic properties of the advective vector field are shown to play a crucial role in deciding the location of actuators and sensors. Simulation results are performed to support the main results of this paper.

This thesis focuses on the development of robust control solutions for linear time-invariant interconnected systems affected by polytopic-type uncertainty. The main issues involved in the control of such systems, e.g. sensor and actuator placement, control configuration selection, and robust fixed-structure control design are included. The problem of fixed-structure control is intrinsically nonconvex and hence computationally intractable. Nevertheless, the problem has attracted considerable attention due to the great importance of fixed-structure controllers in practice. In this thesis, necessary and sufficient conditions for fixed-structure H_inf control of polytopic systems with a single uncertain parameter in terms of a finite number of bilinear matrix inequalities (BMIs) are developed. Increasing the number of uncertain parameters leads to sufficient BMI conditions, where the number of decision variables grows polynomially. Convex approximations of robust fixed-order and fixed-structure controller design which rely on the concept of strictly positive realness (SPRness) of transfer functions in state space setting are presented. Such approximations are based on the use of slack matrices whose duty is to decouple the product of unknown matrices. Several algorithms for determination and update of the slack matrices are given. It is shown that the problem of sensor and actuator placement in the polytopic interconnected systems can be formulated as an optimization problem by minimizing cardinality of some pattern matrices, while satisfying a guaranteed level of H_inf performance. The control configuration design is achieved by solving a convex optimization problem whose solution delivers a trade-off curve that starts with a centralized controller and ends with a decentralized or a distributed controller. The proposed approaches are applied to inverter-interfaced microgrids which consist of distributed generation (DG) units. To this end, two important control problems associated with the microgrids are considered: (i) Current control of grid-connected voltage-source converters with L/LCL filters and (ii) Voltage control of islanded microgrids. The proposed control strategies are able to independently regulate the direct and quadrature (dq) components of the converter currents and voltages at the point of common couplings (PCC) in a fully decoupled manner and provide satisfactory dynamic responses. The important problem of plug-and-play (PnP) capability of DGs in the microgrids is also studied. It is shown that an inverter-interfaced microgrid consisting of multi DGs under PnP functionality can be cast as a system with polytopic-type uncertainty. By virtue of this novel description and use of the results from theory of robust control, the stability of the microgrid system under PnP operation of DGs is preserved. Extensive case studies, based on time-domain simulations in MATLAB/SimPowerSystems Toolbox, are carried out to evaluate the performance of the proposed controllers under various test scenarios, e.g., load change, voltage and current tracking. Real-time hardware-in-the-loop case studies, using RT-LAB real-time platform of OPAL-RT Technologies, are also conducted to validate the performance of the designed controllers and demonstrate their insensitivity to hardware implementation issues, e.g., noise and PWM non-idealities. The simulation and experimental results demonstrate satisfactory performance of the designed controllers.

One of the fundamental problems in feedback control design is the ability of the control system to maintain stability and performance in the face of system uncertainties. To this end, elegant multivariable robust control design frameworks such as /spl Hscr//sub /spl infin// control, /spl Lscr//sub 1/ control, and /spl mu/ synthesis have been developed to address the robust stability and performance control problem. An implicit assumption inherent in these design frameworks is that the controller will be implemented exactly. In a paper by Keel and Bhattacharyya (1996) it was shown that even though such frameworks are robust with respect to system uncertainty, they are extremely fragile with respect to errors in the controller coefficients. In this paper, we extend the fixed-structure controller synthesis approach to develop non-fragile or resilient controllers to controller gain variations.

In this paper, we investigate the problem of the discrete-time adaptive control design of robotic manipulators by utilizing the characteristic model theory. Different from the traditional plants manipulated by the characteristic model-based control strategy, the Coriolis matrix in the robotic dynamics makes the bound of the characteristic model coefficients rely on the state information, proposing great challenge for the controller design and stability analysis. To conquer this problem, we develop a projection estimation algorithm depending on the state information, and propose an adaptive control law via introducing a discrete-time sliding vector. A new stability analysis framework is proposed by use of the recursive induction methodology, giving rise to the asymptotic convergence of joint positions. Simulations are performed to test the effectiveness of our methodology. Our design extends the characteristic model theory frame by proposing the control design and stability analysis methods for the the characteristic model with the state-relevance coefficients.

In this study, a two‐dimensional (2D) H ∞ ‐based method is presented for the iterative learning control (ILC) design problem of a class of linear discrete‐time systems with iteratively periodic factors, including initial states, parametric uncertainties, disturbances, measurement noises, and reference trajectories. First, the ILC design problem of the linear systems is described as a controller design problem of 2D uncertain Roesser models. Second, the H ∞ performance of 2D Roesser models is studied under a general boundary condition. Third, an ILC design criterion is presented to achieve the perfect tracking and specified H ∞ performance by using linear matrix inequality approaches. Finally, a numerical example is given to illustrate the efficiency of the proposed ILC design method.

This paper is concerned with control design for a generalized discrete-time Takagi-Sugeno fuzzy system. The Takagi-Sugeno fuzzy system generally describes nonlinear systems by employing local linear system representations. It is a great tool to analyze a nonlinear system and to design a stabilizing controller for it. However, there is a case where a controller design for a nonlinear system based on the Takagi-Sugeno fuzzy system becomes difficult due to its representation. A generalized fuzzy system to be considered in this paper describes even a wider class of nonlinear systems by representing locally nonlinear systems, and gives a different representation from the standard Takagi-Sugeno fuzzy system, which leads to a rather easy controller design. For such a generalized system, a stabilizing controller design method is proposed by introducing a new class of nonlinear controllers. Then, the resulting closed-loop system becomes a fuzzy system with linear system structures locally, which makes the control design easier. Stabilizing controller design conditions are given in terms of a set of linear matrix inequalities(LMIs), which are easily numerically solvable. A relaxation method is used to reduce the conservatism of design conditions. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.

ROBUST NETWORKED OUTPUT FEEDBACK PREDICTIVE CONTROLLER DESIGN

To solve the problem of transient control design with uncertainties and degradation in the life cycle, a design method for a turbofan engine’s transient controller based on reinforcement learning is proposed. The method adopts an actor–critic framework and deep deterministic policy gradient (DDPG) algorithm with the ability to train an agent with continuous action policy for the continuous and violent turbofan engine state change. Combined with a symmetrical acceleration and deceleration transient control plan, a reward function with the aim of servo tracking is proposed. Simulations under different conditions were carried out with a controller designed via the proposed method. The simulation results show that during the acceleration process of the engine from idle to an intermediate state, the controlled variables have no overshoot, and the settling time does not exceed 3.8 s. During the deceleration process of the engine from an intermediate state to idle, the corrected speed of high-pressure rotor has no overshoot, the corrected-speed overshoot of the low-pressure rotor does not exceed 1.5%, and the settling time does not exceed 3.3 s. A system with the designed transient controller can maintain the performance when uncertainties and degradation are considered.

In this paper, the problems of exponential stability and control design for switched systems with time-varying delay are investigated. Under a class of switching signals counting with average dwell time, a new less conservative stability condition is proposed for the systems. To facilitate controller design for the switched systems with time-varying input delay, a new state transformation method is developed, with which the non-linear term in matrix inequality is removed. The method is also applicable to the existing stability conditions for controller design, while the existing methods may be not able to obtain computational control procedures from the stability conditions. In this paper, the computational algorithms are established for the stability analysis and control synthesis. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed techniques.

A modal H∞-norm-based performance requirement for damage-tolerant active controller design

Control design in the longitudinal-vertical channel is studied for tilt-rotor aircraft at low speed flight. The famous XV-15 tilt-rotor aircraft is used as a prototype. A model predictive control (MPC) design is developed based on a state-space model in a cascaded architecture. The MPC algorithm considers a terminal cost in its objective function so as to ensure close-loop stability, and an error-rate term is introduced in order to improve transient performance. By transforming constraints, the controller designed based on a linearized model at single operating point is applied to the whole stage at low speed flight. It means that there is not switching as gain scheduling in the realization of the longitudinal control. The simulation results show that the flight control system presents satisfied performance and robustness.

H∞ and L1 control of a teleoperation system via LMIs

This paper is concerned with the quantized control design problem for a class of semi-Markovian jump systems with repeated scalar nonlinearities. A semi-Markovian system of this kind has been transformed into an associated Markovian system via a supplementary variable technique and a plant transformation. A sufficient condition for associated Markovian jump systems is developed. This condition guarantees that the corresponding closed-loop systems are stochastically stable and have a prescribed $H_{\infty} $ performance. The existence conditions for full- and reduced-order dynamic output feedback controllers are proposed, and the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one, which can be solved efficiently with existing optimization techniques. Finally, an application to cognitive-radio systems demonstrates the efficiency of the new design method developed.

In a recent paper a unification of the L/sub 2/ (LQG) and H/sup infinity / control design problems was obtained in terms of modified algebraic Riccati equations. In this study these results are extended to guarantee robust L/sub 2/ and H/sup infinity / performance in the presence of structured real-valued parameter variations in the state-space model. For design flexibility the authors consider two distinct types of uncertainty bounds, for both full- and reduced-order dynamic compensation. An important special case of these results generates L/sub 2//H/sup infinity / controller designs with guaranteed gain margins. >

This paper deals with a digital controller and observer design problem for the ball and beam system which is extended version of the previous investigated result. The controller is an extension of robust integral tracking controller. In the discrete-time system, it cannot perform integration and differentiation operation, so we introduce a difference system to design controller for the distance subsystem between reference and output. The observer is designed using dual system LQ design method. The observer gain is able to obtain as the result of robust control design problem of dual system. Each design problem is solved by the guaranteed cost control method. Through the numerical result, we validity and effectiveness of our proposed method.