Design of dynamic programming feedback controllers for multivariable time-invariant linear systems†

6 - Design and Performance of Feedback Controllers

This paper addresses reduced-order design of dynamic partial-state feedback controllers for uncertain nonlinear systems. The design objective is to achieve disturbance attenuation and global stabilization in spite of nonlinear static and dynamic uncertainties arising from various locations of the system. Since only a part of the plant state is measured and the reduced-order dynamic controller does not have the mechanism to rebuild the full state vector, the design problem is much harder than state-feedback and full-order observer/state-feedback design. The design problem is tackled by the pair of state-dependent scaling and diffeomorphism which are newly tailored to the reduced-order partial-state feedback successfully. The paper not only shows a state-dependent scaling characterization of controllers and an analytical solution, but also suggests numerical computation.

Optimal load clipping with time of use rates

Dynamic feedback control strategies are proposed for the asymptotic stabilization and asymptotic output tracking problems, associated with the operation of flexible joint manipulators. Smooth dynamical linearizing feedback controllers, as well as dynamical sliding mode regulators, are derived within the context of M. Fliess's (1989) generalized observability canonical form (GOCF). The GOCF is obtained by means of a state elimination procedure, carried out on the system of differential equations describing the manipulator dynamics. The remarkable feature of this new approach lies in the fact that a truly effective smoothing of the sliding mode controlled responses is possible while substantially reducing the chattering in the control input torque. Simulation examples are given that illustrate the performance of the proposed controllers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dynamic feedback control of day-to-day traffic disequilibrium process

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

The mathematical model of optimal water quantity allocation for a single main canal in a large-scale irrigation area was constructed that took the minimal sum of the squared deviation of water shortage for water receiving areas controlled by the single main canal in one given irrigation period as the study target, and the total irrigation quantity of the single main canal as a constraint condition. Taking the optimal allocation of water quantity of each branch canal as decision variables, and several branch canals under the irrigation sequence of the main canal as a state variable, this model was solved by the one-dimensional dynamic programming (DP) method, by which the minimal water shortage and corresponding optimal water quantity allocation of each branch canal was calculated. The proposed method could provide a decision-making reference for optimal water resources allocation of single main canal irrigation areas, and also provide the theoretical basis for optimal water quantity allocation of a main canal with rotation irrigation by strips or with segmented rotation irrigation mode in China’s large-scale irrigation areas. Taking Hengliu Main Canal of Zhouqiao Irrigation Area in Jiangsu Province as a study case, optimization results showed that in a medium drought year (p = 75%) and a special drought year (p = 95%), minimal water shortage for water receiving areas controlled by Hengliu Main Canal was respectively 2.57 × 104 m3 and 23.31 × 104 m3 during the ponding period of rice. The corresponding water quantity allocation for each branch canal has reflected a compellent model solution precision and efficiency.

The aim of this paper is to develop a new approach for a solution of the model following control (MFC) problem with a dynamic compensator by using linear matrix inequalities (LMIs). TheH1 model following control problem is derived following LMI formulation. First, the H1 optimal control problem is revisited by referring to Lemmas assuring all admissible controllers minimizing the H1 norm of the transfer function between the exogenous inputs and the outputs. Then, the solvability condition and a design procedure for a two degrees of freedom (2 DOF) dynamic feedback control law is introduced. The existence of a 2 DOF dynamic output feedback controller for the model following control is proven and the stability of the closed-loop system is satisfied by assuring the Hurwitz condition. The benchmark thermal process (PT-326) as the first order process with timedelay is regulated by the presented 2 DOF dynamic output feedback controller. The simulation results illustrate that the presented controller regulates a system with dead-time as a large set of generic industrial systems and the H1 norm of the closed-loop system is assured less than the H1 norm of the desired model system.

International audience

Design of feedback control, for a system with slow and fast eigenvalue modes, using single sampling rate results in either information loss (for a larger sampling period) or increased computations (for a smaller sampling period). This paper contributes to designing multirate state feedback controllers for such systems. In this, it is shown that the feedback control for a linear time-invariant system, having slow and fast eigenvalue modes, can be successfully designed by multirate sampling of states in two stages. Multirate sampling refers to sampling slow- and fast-varying states at different rates, that is sampling slow states at a lower rate than the fast states. Here, two approaches for multirate sampling of states are presented, depending on the sampling sequence. In the first approach, fast subsystem states are sampled initially, and then, slow subsystem states are sampled, whereas in the second approach, slow subsystem states are sampled before sampling the fast subsystem states. As far as the two-stage design is concerned, the first stage of the design of feedback control is initiated just after sampling the first subsystem. Then, the left subsystem is sampled, and the second stage of the design of feedback control is accomplished. It is proved that the feedback controls derived with the multirate sampling of states stabilize the full-order system in both approaches. The design and implementation aspects of both approaches are compared. Finally, the applicability of the proposed control is demonstrated by simulating two examples. Simulations are also compared with other methods proposed in the literature.

This paper presents as its main result a new and efficient method for the design of optimal dynamic compensators for linear multivariable control systems. The discussion starts with a fresh look into the design of optimal constant gain output feedback. In this context, three new ideas are introduced that prove their usefulness particularly in the dynamic compensator case: (1) deterministic measurement disturbances are included in the formulation of the underlying optimization problem, (2) the relationship between a deterministic and a stochastic optimal control problem is shown, (3) by proper modifications of the quadratic cost function, the effort involved in the numerical solution of the optimal output feedback problem is considerably reduced. Furthermore, a canonical form is introduced for the dynamic compensator and an algorithm is developed for the numerical computation of its free parameters. It is based on quasi-newtonian gradient methods and an efficient line search procedure. Some features of the new design method are demonstrated by means of a non-trivial benchmark taken from the literature.

A 24-GHz power amplifier (PA) for 5G communication is implemented with a 65-nm bulk CMOS process, which adopts analog linearization techniques of dynamic feedback control (DFC) and an adaptive bias control (ADB). The DFC decreases feedbacks and the ADB increases a gate bias of common sources (CSs) with an increase of the input signal power so that the DFC improves gain flatness and peak efficiency, and the ADB increases high power gain, saturation power, and peak efficiency. These analog linearization techniques lower the IMD3 by improving the AM-AM and AM-phase modulation (PM) of the PA. The proposed PA shows a saturation power of 18.7 dBm, a 1-stage PA gain of 15.3 dB, and a peak PAE of 37.2% with the 24.29-GHz continuous wave signal measurement. It also shows a linear power of 12.9 dBm and a linear PAE of 14.8% with a two-tone signal measurement that has a center frequency of 24.49 GHz and a bandwidth of 80 MHz.

This paper is devoted to the finite‐time local piecewise control for parabolic partial differential equations (PDEs) by using dynamic output feedback control strategy, where the controller is designed as an ordinary differential equation (ODE). This makes the closed‐loop system PDE‐ODE coupled, which is employed to accurately describe the dynamics of the PDE system. According to the constructed PDE‐ODE coupled model, a local piecewise dynamic feedback control law is first proposed. Sufficient conditions on finite‐time stabilisation of the parabolic PDE‐ODE coupled system by the suggested feedback controller are then developed in the sense of both complete spatial measurement and incomplete spatial measurement of the observed output of the PDE system, respectively. Finally, the issues regarding the finite‐time stabilisation of the closed‐loop system is converted into the feasibility of matrix inequalities, and some simulation studies are provided to verify the effectiveness of the proposed results.

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.

Sliding control consists of ans dynamics and an error dynamics where thes dynamics filters the uncertainties. The filtered uncertainties are further filtered by the error dynamics to obtain a desired system response. Thes dynamics rejects the uncertainties and affect the system response significantly. In this article, a SISO sliding control enhances the control of thes dynamics, and the desired system response may be obtained with a straight-forward tuning procedure. The dynamics of the sliding control is analyzed, and a tuning mechanism is presented. Thes dynamics is derived from a first-order plus integral sliding condition. The lower bound of the damping ratio and the equivalent spring constant in thes dynamics are two control parameters. The bandwidth of thes dynamics is determined by the selection of the equivalent spring constant, and the thickness of the boundary layer is controlled by the choice of the lower bound of the damping ratio. The integral ofs in thes dynamics guarantees zero steady-states, and therefore zero steady-state error is warranted.