Reference output tracking control for a flexible air‐breathing hypersonic vehicle via output feedback

This paper addresses the problem of reference output tracking control for the longitudinal model of a flexible air‐breathing hypersonic vehicle (FAHV) by utilizing the output feedback control approach. The dynamic characteristics of the FAHV along with the aerodynamic effects of hypersonic flight make the flight control of such systems highly challenging. Moreover, there exist some intricate couplings between the engine and flight dynamics as well as complex interaction between rigid and flexible modes in the longitudinal model. These couplings bring difficulty to the flight control design for the intractable hypersonic vehicle systems. This paper deals with the problem of reference output tracking control for the longitudinal model of the FAHV. By utilizing the trim condition information including the state of altitude, velocity, angle of attack, pitch angle, pitch rate and so on, the linearized model is established for the control design objective. Then, the reference output velocity and altitude tracking control design problem is proposed for the linearized model. The flexible models of the FAHV system are hardly measured because of the complex dynamics and the strong couplings of the FAHV. Thus, by using only limited flexible model information, the reference output tracking performance analysis criteria are obtained via Lyapunov stability theory. Then, based on linear matrix inequality optimization algorithm, the static output feedback controller is designed to stabilize the closed‐loop systems, guarantee a certain bound for the closed‐loop value of the cost function, and can make the control output achieve the reference velocity and altitude tracking performance. Subsequently, the condition of dynamic output feedback controller synthesis is given in terms of linear matrix inequalities and a numerical algorithm is developed to search for a desired dynamic output feedback controller which minimizes the cost bound and obtains the excellent reference altitude and velocity tracking performance simultaneously. The effectiveness of the proposed reference output tracking control method is demonstrated in simulation part. Furthermore, the superior reference velocity and altitude performance commands could be achieved via using static and dynamic output feedback controllers under lacking some unmeasured flexible states information in the measurement output vector. Copyright © 2011 John Wiley & Sons, Ltd.     

An optimal control approach to spacecraft rendezvous on elliptical orbit

In this paper, we consider a linear quadratic regulator control problem for spacecraft rendezvous in an elliptical orbit. A new spacecraft rendezvous model is established. On the basis of this model, a linear quadratic regulator control problem is formulated. A parametric Lyapunov differential equation approach is used to design a state feedback controller such that the resulting closed‐loop system is asymptotically stable, and the performance index is minimized. By an appropriate choice of the value of a parameter, an approximate state feedback controller is obtained from a solution to the periodic Lyapunov differential equation, where the periodic Lyapunov differential equation is solved on the basis of a new numerical algorithm. The spacecraft rendezvous mission under the controller obtained will be accomplished successfully. Several illustrative examples are provided to show the effectiveness of the proposed control design method. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust reliability method and reliability‐based performance optimization for non‐fragile robust control design of dynamic system with bounded parametric uncertainties

An efficient robust reliability method for non‐fragile robust control design of dynamic system with bounded parametric uncertainties is presented systematically, in which the uncertainties existing in the controlled plant and controller realization are taken into account simultaneously in an integrated framework. Reliability‐based design optimization of non‐fragile robust control for parametric uncertain systems is carried out by optimizing the H₂ and H_∞ performances of the closed‐loop system, with the constraints on robust reliabilities. The non‐fragile robust controller obtained by the presented method may possess a coordinated optimum performance satisfying the precondition that the system is robustly reliable with respect to the uncertainties existing in controlled plant and controller. Moreover, the robustness bounds of uncertain parameters can be provided. The presented formulations are within the framework of linear matrix inequality and thus can be carried out conveniently. It is demonstrated by a numerical example that the presented method is effective and feasible. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal reduced‐order LQG synthesis: Nonseparable control and estimation design

The optimal linear‐quadratic‐Gaussian synthesis design approach and the associated separation principle are investigated for the case where the observer design model is a reduced model of the underlying system model. Performance of the resulting reduced‐order controller in the full‐state system environment is formulated in terms of an augmented state vector consisting of the system state vector and the reduced model state vector. Considering explicitly separated linear control and estimation laws, a calculus of variations/Hamiltonian approach is used to determine the necessary conditions for the optimal controller and observer gains for the simplified algorithms. Results show that the optimal gains are not separable, ie, the optimal controller and observer gains are coupled and cannot be computed independently. Numerical examples of an infinite‐horizon and finite‐horizon control and estimation large‐scale multiagent system problem clearly show the advantages of using the nonseparable coupled solutions.     

Optimal trajectory control for a two‐link rigid‐flexible manipulator with ODE‐PDE model

In this paper, the optimal trajectory control problem for a two‐link rigid‐flexible manipulator is considered. Since the two‐link rigid‐flexible system is a distributed system, an ordinary differential equation and partial differential equation (ODE‐PDE) dynamic model of the manipulator is established by Hamilton's principle. Based on the ODE‐PDE model, an optimal trajectory controller is proposed in this paper, which includes 2 stages. In the first stage, the optimal trajectory is created by using the differential evolution algorithm. Energy consumption and deflection of the flexible link are chosen as performance indexes. Cubic spline interpolation is applied to obtain the continuous trajectory. In the second stage, the aim is to regulate 2 joints to follow the optimal trajectory and simultaneously suppress vibration of the flexible link. To achieve it, boundary control laws are designed and the stability analysis is given. In simulations, the effectiveness of the optimal controller is verified by MATLAB.     

Single network adaptive critic aided dynamic inversion for optimal regulation and command tracking with online adaptation for enhanced robustness

To combine the advantages of both stability and optimality‐based designs, a single network adaptive critic (SNAC) aided nonlinear dynamic inversion approach is presented in this paper. Here, the gains of a dynamic inversion controller are selected in such a way that the resulting controller behaves very close to a pre‐synthesized SNAC controller in the output regulation sense. Because SNAC is based on optimal control theory, it makes the dynamic inversion controller operate nearly optimal. More important, it retains the two major benefits of dynamic inversion, namely (i) a closed‐form expression of the controller and (ii) easy scalability to command tracking applications without knowing the reference commands a priori. An extended architecture is also presented in this paper that adapts online to system modeling and inversion errors, as well as reduced control effectiveness, thereby leading to enhanced robustness. The strengths of this hybrid method of applying SNAC to optimize an nonlinear dynamic inversion controller is demonstrated by considering a benchmark problem in robotics, that is, a two‐link robotic manipulator system. Copyright © 2013 John Wiley & Sons, Ltd.     

Quantitative feedback design for a variable-displacement hydraulic vane pump

In this paper the model development, problem specification, constraint formulation, and optimal feedback controller design for a variable-displacement hydraulic pump system are shown using the Quantitative Feedback Theory (QFT) technique. The use of variable-displacement pumps in hydraulic system applications has become widespread due to their efficiency advantages; however, this efficiency gain is often accompanied by a degradation of system stability. Here we develop a QFT controller for a variable-displacement pump based upon a linear, parametrically uncertain model in which some of this uncertainty reflects variation in operating point-dependent parameters. After presentation of a realistic non-linear differential equation model, the linearized model is developed and the effect of parametric uncertainty is reviewed. From this point, closed-loop performance specifications are formulated and the QFT design technique is carried out. An initial feasible controller is designed, and this design is optimized via a non-linear programming technique. In conclusion, a non-linear closed-loop system response is simulated. This paper is intended to have tutorial value, both in terms of the detailed hydraulic system model development, as well as in terms of the detailed exposition of the QFT controller design and optimal loop shaping processes. © 1998 John Wiley & Sons, Ltd.     

Joint control for flexible‐joint robot with input‐estimation approach and LQG method

In this work, the input‐estimation (IE) algorithm and the linear quadratic Gaussian (LQG) controller are adopted to design a control system. The combined method can maintain higher control performance even when the system variation is unknown and under the influence of disturbance input. The IE algorithm is an on‐line inverse estimation method involving the Kalman filter (KF) and the least‐square method, which can estimate the system input without additional torque sensor, while the LQG control theory has the characteristic of low sensitivity of disturbance. The design and analysis processes of the controller will also be discussed in this paper. The joint control of the flexible‐joint robot system is utilized to test and verify the effectiveness of the control performance. According to the simulation results, the IE algorithm is an effective observer for estimating the disturbance torque input, and the LQG controller can effectively cope with the situation that the disturbance exists. Finally, higher control performance of the combined method for joint control of the robotic system can be further verified. Copyright © 2007 John Wiley & Sons, Ltd.     

Optimal control strategy–based AGC of electrical power systems: A comparative performance analysis

This study extensively addresses the application of optimal control approach to the automatic generation control (AGC) of electrical power systems. Proportional‐integral structured optimal controllers are designed using full‐state feedback control strategy employing performance index minimization criterion. Some traditional single/multiarea and restructured multiarea power system models from the literature are explored deliberately in the present study. The dynamic performance of optimal controllers is observed superior in comparison to integral/proportional‐integral controllers tuned using some recently published modern heuristic optimization techniques. It is observed that optimal controllers show better system results in terms of minimum value of settling time, peak overshoot/undershoot, various performance indices, and oscillations corresponding to change in area frequencies and tie‐line powers along with maximum value of minimum damping ratio in comparison to other controllers. The results are displayed in the form of tables for ease of comparison. Sensitivity analysis affirms the robustness of the optimal feedback controller gains to wide variations in some system parameters from their nominal values.     

Quantized feedback fault‐tolerant H ∞ controller design for linear systems with adaptive mechanism

This paper addresses the design problem of fault‐tolerant H _∞ controller for linear systems with state quantization. By combining linear matrix inequality technique and indirect adaptive method, a new method is proposed to design a fault‐tolerant controller against actuator faults via quantized state feedback. The controller gains are updating according to the online estimation of eventual faults, which are dependent on the quantized state signals. Meanwhile, the proposed designs conditions with variable gains can be proved to be less conservative than those of the traditional controller with fixed gains. A numerical example is presented to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Design of adaptive controllers using partial certainty equivalence principle

Optimal stochastic control problem for general non‐linear dynamic system with unknown parameters is considered. An approximative assumption, which has been named partial certainty equivalence (PCE) principle, is suggested for design of adaptive controllers of non‐linear and linear stochastic systems. For derivation of a suboptimal controller with the PCE principle the certainty equivalence (CE) assumption is used only for the part of the system states and unknown parameters. The PCE control policy has a simple form for linear systems with unknown parameters. It is suggested in the present paper to design adaptive dual control using the PCE assumption and bicriterial optimization to derive the adaptive controller with the optimal persistent excitation. Simulated examples are used to demonstrate the potential of the suggested method and its superiority over the generally used CE‐controllers. Copyright © 2004 John Wiley & Sons, Ltd.     

State estimation for a networked control system with packet delay,packet dropouts,and uncertain observation in S-E and C-A channels

In this work, a minimum variance estimator is designed for a networked system with inherent network imperfections in both sensor to estimator (S-E) and controller to actuator (C-A) channels simultaneously. The channels are affected by packet delays, dropouts, and uncertain observations. These effects are modeled using five Bernoulli distributed random variables. Correlation of noise at neighboring time caused by random delay is avoided by introducing two additional variables in the augmented stochastic model. The developed augmented stochastic model can handle network imperfections in both the S-E and C-A channels simultaneously. A minimum variance recursive linear estimator is designed using an innovation approach and projection theorem. Furthermore, sufficient condition is presented for the existence of steady state property of the proposed estimator. Simulation studies are carried out for the proposed estimator using a numerical example and a single link robot arm. Finally, performance comparison with other popular filters shows the effectiveness of the designed estimator.     

Model predictive control of blood sugar in patients with type‐1 diabetes

In this article, two adaptive model predictive controllers (AMPC) are applied to regulate the blood glucose in type 1 diabetic patients. The first controller is constructed based on a linear model, while the second one is designed by using a nonlinear Hammerstein model. The adaptive version of these control schemes is considered to make them more robust against model mismatches and external disturbances. The least squares method with forgetting factor is used to update the model parameters. For simulation study, two well‐known mathematical models namely, Puckett and Hovorka which describe the dynamical behavior of patient's body have been selected. The performances and robustness of the proposed controllers are tested for regulating the blood glucose of diabetic patients in presences of model mismatches and measurement noises. Simulation results indicate that the non‐linear model predictive controller (NMPC) outperforms the linear one. To improve the performance of the NMPC in rejecting the meal disturbances, two different feedforward control strategies have been considered. Simulation results indicate that the combined adaptive NMPC with feedforward controller has a better performance over the other considered control schemes. Copyright © 2015 John Wiley & Sons, Ltd.     

Design of an optimal feedback linearizing‐based controller for an experimental flexible‐joint robot manipulator

This paper presents the design of an optimal non‐linear position tracking controller for a two‐link flexible joint robot manipulator. The controller is designed based on the concept of exact feedback linearization and LQG/LTR techniques. It is shown that the non‐linear robot model is feedback linearizable and a characterization of the set, over which the linearizing transformation is diffeomorphic, is provided. The proposed control approach reduces the number of required measurement sensors and takes into account the effects of measurement noises. A new method for computing the non‐linear state estimate is also presented. It takes advantage of the linear structure of the transformed system. Simulation results demonstrate the potential benefits of the proposed control approach in reaching the desired performance with minimum control effort. Copyright © 1999 John Wiley & Sons, Ltd.     

Simultaneous fault detection and control design for switched linear systems based on dynamic observer

The problem of simultaneous fault detection and control (SFDC) for linear continuous‐time switched systems is addressed in this paper. An H _∞ formulation of the SFDC problem using dynamic observer is presented. In essence, a single unit called detector/controller depending on the system modes is designed, where the detector is a dynamic observer, and the controller is a state feedback controller based on the dynamic observer. It is shown that the dynamic observer can be used effectively to tackle the drawbacks of the existing methods of SFDC design. Extended linear matrix inequalities (LMIs) characterization is used to reduce the conservativeness by introducing additional matrix variables, so as to eliminate the coupling of Lyapunov matrices with the system matrices. Indeed, the idea presented in this paper is based on average dwell time and conservatism reduction approaches and applying the advantages of dynamic observers, which leads to some sufficient conditions for solvability of the SFDC problem in terms of LMI feasibility conditions. Simulation results illustrate the effectiveness of the proposed design methodology. Copyright © 2011 John Wiley & Sons, Ltd.     

A practical approach to control of nonlinear discrete-time state-delay systems

The robust feedback stabilization of a class of nonlinear discrete-time systems with unknown constant state-delay and uncertain function of nonlinear perturbations is considered based on linear matrix inequality (LMI)-based analysis and design procedures. In both cases of nominal and resilient feedback designs, the trade-off between the size of the controller gains and the bounding factors is illuminated and incorporated into the design formalism. A dynamic output feedback controller is then designed for this class of systems. Seeking computational convenience, all the developed results are cast in the format of LMIs and several numerical examples are presented throughout the paper to demonstrate the advantages of the design methods. Copyright © 2007 John Wiley & Sons, Ltd.     

H∞ tracking control of two-dimensional fuzzy networked systems

In this article, the H_∞ tracking control problem is first considered for two-dimensional fuzzy networked control systems. The system is described by fuzzy blending of the so-called second Fornasini-Marchesini local linear state-space model. Based on the fuzzy model, an observer-based state feedback controller is employed to guarantee the H_∞ tracking performance. The separation property is established in the case of observer-based H_∞ tracking control framework, that is, the controller gains and observer gains can be simultaneously obtained by solving two sets of linear matrix inequalities. A simulation example is given to illustrate the effectiveness of the proposed method.     

The effect of sample period on optimally designed servomechanism control systems

A uniform approach for comparing sampled-data servomechanism control systems with respect to the sample period is formulated such that a quadratic performance measure of the augmented continuous system states and discrete controller states is used both for controller design and performance evaluation. The structure of the controller and performance cost is optimally designed as a function of the sample period and converges to an optimal continuous control system as the sample period approaches zero. Extensive simulation reveals that the performance cost increases and that the norm of the controller gains decreases monotonically with the sample period.     

Optimal control of a magnetic bearing without bias flux using finite voltage

Conventional active magnetic bearings (AMB) are operated using a bias current (or flux) to achieve greater linearity and dynamic capability. Bias, however, results in undesirable rotating losses and consequent rotor heating. While control without bias flux is an attractive alternative, it is considerably more complex due to both force slew rate limitations and actuator non-linearity. In this paper, optimal control of a magnetic bearing without bias is investigated. A single-degree-of-freedom system consisting of a mass and two opposing electromagnets is considered. The optimal control problem is examined for a cost function that penalizes both poor regulation and rotational energy lost. Though a standard optimization procedure does not directly yield an analytical solution, it does show that the optimal control is always bang–bang including possibly a singular arc. First, the minimum time problem is solved for a simple switching law in three dimensional state space. A non-standard, physics-based approach is then employed to obtain an optimal solution for the general problem. The final result is an optimal variable structure feedback controller. This result provides a benchmark which can be used for evaluation of the performance of a practical feedback controller designed via other methods. The practical controller will be designed to support a flexible rotor and achieve robustness and optimally reject disturbance. This result may also be applied to many other applications which contain opposing quadratic actuators. © 1998 John Wiley & Sons Ltd.     

Optimal control of a flexible manipulator and controller order reduction

Presented is a control system design study for a flexible manipulator. The device consists of a DC electric motor drive connected via two flexible links to an end effector for position control. The paper details in tutotrial fashion optimal control designs using both H₂ and H_∞ methods with dynamic weighting. The resulting controller is found to be fairly of high order for implementation and so controller order reduction is considered. It is observed that reduction of the controller order beyond a nominal amount cannot be done. A reason for this is postulated using novel perturbation models where it is found that the controller reduction problem is, in this case, a roadblock to practical implementation of the control. Copyright © 1998 John Wiley & Sons, Ltd.