A method for control of an implantable rotary blood pump for heart failure patients using noninvasive measurements

We propose a deadbeat controller for the control of pulsatile pump flow (Q(p) ) in an implantable rotary blood pump (IRBP). Noninvasive measurements of pump speed and current are used as inputs to a dynamical model of Q(p) estimation, previously developed and verified in our laboratory. The controller was tested using a lumped parameter model of the cardiovascular system (CVS), in combination with the stable dynamical models of Q(p) and differential pressure (head) estimation for the IRBP. The control algorithm was tested with both constant and sinusoidal reference Q(p) as input to the CVS model. Results showed that the controller was able to track the reference input with minimal error in the presence of model uncertainty. Furthermore, Q(p) was shown to settle to the desired reference value within a finite number of sampling periods. Our results also indicated that counterpulsation yields the minimum left ventricular stroke work, left ventricular end diastolic volume, and aortic pulse pressure, without significantly affecting mean cardiac output and aortic pressure.     

Controller design for optimal tracking response in discrete‐time systems

The problem of designing a controller, which results in a closed‐loop system response with optimal time‐domain characteristics, is considered. In the approach presented in this paper, the controller order is fixed (higher than pole‐placement order) and we seek a controller that results in closed‐loop poles at certain desired and pre‐specified locations; while at the same time the output tracks the reference input in an optimal way. The optimality is measured by requiring certain norms on the error sequence—between the reference and output signals—to be minimum. Several norms are used. First, l₂‐norm is used and the optimal solution is computed in one step of calculations. Second, l_∞‐norm (i.e. minimal overshot) is considered and the solution is obtained by solving a constrained affine minimax optimization problem. Third, the l₁‐norm (which corresponds to the integral absolute error‐(IAE)‐criterion) is used and linear programming techniques are utilized to solve the problem. The important case of finite settling time (i.e. deadbeat response) is studied as a special case. Examples that illustrate the different design algorithms and demonstrate their feasibility are presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Optimal control of first-order plants by dead-beat techniques

The design of optimal dead-beat controllers for first-order plants is considered. The simple nature of these plants leads to ripple-free step response, a property that is highly desirable. The minimum energy and minimum effort control problems are formulated and solved with an analytical and generalized approach. Analytical expressions for the digital controller pulse transfer functions along with the resulting control sequences are derived. Generalized curves for the maximum control signals appearing in the system are also presented. The latter can be used for the determination of the minimum sampling period when the maximum control signal is specified. © 1997 John Wiley & Sons, Ltd.     

Tracking control of Wiener models with hierarchical and switching model predictive control

A tracking problem is considered for a Wiener model. A two‐layer hierarchical control structure is designed: the upper level controller operates at a slow rate and computes the inputs to be ideally provided to the system; the effective control actions are provided by actuators placed at the lower layer and having faster dynamics. Model predictive control (MPC) laws are synthesized for both layers. In order to cope with the discrepancy between the ideal and the effective control action, a robust MPC controller is designed at the upper level. Such a controller can switch among different operating conditions ensuring different level of robustness. In doing so, the overall controller guarantees steady‐state zero error regulation for constant reference signals while trading off robustness versus system performance. A numerical example is reported. Copyright © 2011 John Wiley & Sons, Ltd.     

A predictive control framework for 3‐phase induction motors modeled in natural variables

This paper presents a nonlinear control approach for 3‐phase induction motors. The proposed structure combines a 3‐phase predictive controller with an integrative reference filter. The predictive controller is designed based on an induction motor model established in natural variables (without using transformations), which is a nonlinear and time‐variant one. This model enables the controller to work independently with the supply voltages, considering unbalanced situations. A dynamic evaluation of the state equation coefficients is used to perform the process variables prediction, thereby executing a point‐to‐point linearization. The conversion of the rotation speed and stator flux modulus reference values is realized by a integrative 3‐phase referrer, which acts as a reference filter, expressing the references as 3‐phase signals and acting as an integrator to eliminate steady‐state errors. Also, a constraint feature is implemented, to reduce the currents. Simulation results satisfactorily show the proposed control architecture characteristics for various reference values and for motor operation as a brake and with load variation.     

Auto-weighted minimum-variance self-tuning controller

A self-tuning controller which automatically assigns weightings to control and set-point following is introduced. This discrete-time single-input single-output controller is based on a generalized minimum-variance control strategy. The automatic on-line selection of weightings is very convenient, especially when the system parameters are unknown or slowly varying with respect to time, which is generally considered to be the type of systems for which self-tuning control is useful. This feature also enables the controller to overcome difficulties with non-minimum phase systems.     

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.     

Asynchronous control of T-S fuzzy chaotic systems via a unified model using the hidden Markov model subject to strict dissipativity

The asynchronous control for the unified model of chaotic systems with Markovian jumping parameters is considered via the Takagi-Sugeno (T-S) fuzzy approach in this paper. According to jumping modes for chaotic systems and modes for the asynchronous controller, a double-mode process is generated. By introducing the hidden Markov model (HMM), the asynchronization phenomenon is represented between the controller and chaotic systems. By linear matrix inequalities (LMIs), some conditions are received to guarantee the stochastic stability and the strict dissipativity for chaotic systems. Based on the stochastic stability theory and the dissipativity theory, the asynchronous controller is discussed. The proposed method can be applied to the mode-independent controller and the synchronous controller. Finally, the effectiveness of the proposed controller is illustrated by two examples.     

Optimal synchronization of n identical double-integral plants with identical inputs but different initial conditions

In this paper automatic error elimination between outputs of n identical double-integral plants (K/s²) with different output initial conditions will be studied with two distinct objectives: (1) making all the identical steady-state outputs to be the double integral of any common input x(t); (2) having all the identical steady-state outputs track perfectly a reference input r(t). Thus fulfilment of objective (1), which can be viewed as a synchronization problem, commands that the whole MIMO system work on a closed-loop principle during the transient time in order to eliminate the errors between the n outputs; and on an open-loop basis during the steady-state phase in order to preserve the operation of the plant transfer functions (i.e. double integration) upon their inputs x(t). We shall see that objective (1) can always be attained if, once and for all, the plants are interconnected through identical PD-controllers (1 + Ts), no matter what form the common inputs x(t) may have. This is a far cry from the orthodox feedback control systems in which the type of input always plays a decisive role in selecting the appropriate controller. Having arranged the system for achievement of objective (1), we will show, with a unique technique, that objective (2) can be achieved through use of only one replaceable controller H(s), which operates on the difference between the reference input r(t) and any one of the n outputs. That is, each time r(t) is changed with the possible necessary change of controller H(s), we can make any number of outputs follow the reference input. This second objective can be considered as both synchronization and tracking, which in the text we shall refer to as tracking. We shall also show, without any alteration in the arrangements of our MIMO system, that objective (1) can also be achieved for identical plants of transfer functions [K/s²(T_fs + 1)]. Through two examples, various observations discussed in the text will be demonstrated. Finally, armed with our previous results for simple-integral plants (K/s) and the results obtained in this paper, we shall briefly discuss triple-integral plants (K/s³) and q-integral plants (K/s^(q)).     

Some experiences with the application of multivariable adaptive control in chemical and electromechanical plants

Based on a new unified theory, multivariable adaptive generalized minimum variance and model reference adaptive control are applied to three different types of processes. The improvement of control quality in a foil coating process using adaptive control is significant. Reduced energy costs can be really achieved on distillation columns as shown on a production column. The tuning of a multivariable controller for a turbogenerator can be done automatically and yields satisfactory disturbance rejection. The examples illustrate that adaptive control using these techniques has reached a high degree of maturity, making it a powerful tool for the control engineer.     

Design of a Symmetry Controller for Cycling Induced by Electrical Stimulation: Preliminary Results on Post‐Acute Stroke Patients

This study deals with the design of a controller for cycling induced by functional electrical stimulation. The controller will be exploitable in the rehabilitation of hemiparetic patients who need to recover motor symmetry. It uses the pulse width as the control variable in the stimulation of the two legs in order to nullify the unbalance between the torques produced at the two crank arms. It was validated by means of isokinetic trials performed both by healthy subjects and stroke patients. The results showed that the controller was able to reach, and then maintain, a symmetrical pedaling. In the future, the controller will be validated on a larger number of stroke patients.     

Fully autonomous preload-sensitive control of implantable rotary blood pumps

A pulsatility-based control algorithm with a self-adapting pulsatility reference value is proposed for an implantable rotary blood pump and is to be tested in computer simulations. The only input signal is the pressure difference across the pump, which is deduced from measurements of the pump's magnetic bearing. A pulsatility index (PI) is calculated as the mean absolute deviation from the mean pressure difference. As a second characteristic, the gradient of the PI with respect to the pump speed is derived. This pulsatility gradient (GPI) is used as the controlled variable to adjust the operating point of the pump when physiological variables such as the systemic arterial pressure, left ventricular contractility, or heart rate change. Depending on the selected mode of operation, the controller is either a linear controller or an extremum-seeking controller. A supervisory mechanism monitors the state of the system and projects the system into the region of convergence when necessary. The controller of the GPI continuously adjusts the reference value for PI. An underlying robust linear controller regulates the PI to the reference value in order to take into account changes in pulmonary venous return. As a means of reacting to sudden changes in the venous return, a suction detection mechanism was included. The control system is robustly stable within a wide range of physiological variables. All the clinician needs to do is to select between the two operating modes. No other adjustments are required. The algorithm showed promising results which encourage further testing in vitro and in vivo.     

Stochastic control of networked control systems with packet dropout and time‐varying delay

This paper studies the stochastic stabilization problem for discrete‐time networked control systems with time delay and packet dropout. The message losses and time delay from the sensor to the controller and from the controller to the actuator are considered simultaneously. A two‐state Markov chain is used to model the correlated packet dropout process. By introducing free weighting matrices, the sufficient condition on the stochastic stability of such networked control system is obtained. An improved criterion is found by introducing the delay fractioning method and a new Lyapunov–Krasovskii functional. On the basis of the stability condition, the mode‐dependent controller is given in terms of linear matrix inequalities. A simulation example is given to show the proposed results. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

The advantages of robust control of pulse amplitude modulation series–parallel load induction heating inverters

The goal of this paper is to present to the research community the benefit of utilizing advanced control methods for induction heating inverters in comparison with the existing classical control methods and to promote their application. For this purpose, a robust controller and a classical PI controller for application in a high‐power series–parallel load induction heating inverter has been designed. For the robust controller designed, the series–parallel load inverter model is augmented with additive and multiplicative uncertainties for nonmagnetic material heating, and the H_∞ algorithm is utilized. To highlight the advantages of the robust controller designed in this research study, a comparison is made with the classical PI controller system. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

A decomposition approach to suboptimal control of discrete-time systems

A suboptimal controller for a class of discrete-time systems is presented. The controller is derived by first solving ‘off-line’ a simplified optimal control problem obtained by neglecting part of the system state and by considering a larger time step, then by solving ‘on-line’ at each time step an optimization problem based on the results of the previously solved ‘off-line’ problem. A simple numerical example is presented to illustrate the control scheme.     

A novel hybrid model predictive control design with application to a quadrotor helicopter

In this paper, a novel control design strategy based on a hybrid model predictive control in combination with fuzzy logic control is presented for a quadrotor helicopter system. In the proposed scheme, a 2‐part control structure is used. In the first part, a linear model predictive controller with receding horizon design strategy is combined with a nonlinear model predictive controller, which is applied as the main controller. In the second part, a 2‐level fuzzy logic controller is utilized to assist the first controller when the error exceeds a predefined value. The proposed nonlinear predictive control method utilizes a novel approach in which a prediction of the future outputs is used in the modeling stage. Using this simple technique, the problem can be solved using linear methods and, thereby, due to considerable reduction in the computational cost, it will be applicable for the systems with fast dynamics. Moreover, the fuzzy logic controller is used as a supervisor to adjust a proportional‐integral‐derivative controller to enhance the system performance by decreasing the tracking error. The proposed scheme is applied to a model of quadrotor system such that the difference between the predicted output of the system and the reference value is minimized while there are some constraints on inputs and outputs of the nonlinear quadrotor system. Simulation results demonstrate the efficiency of the proposed control scheme for the quadrotor system model.     

Dissipative control for singular Markovian jump systems with time delay

This paper focuses on the problem of dissipative control for continuous‐time singular time‐delayed systems with Markovian jump parameters. Different from usually mode‐dependent or mode‐independent controller design methods, a partially mode‐dependent dissipative controller is firstly proposed via using a mode‐dependent Lyapunov function. The stochastic property of the mode available to a controller operation is taken into consideration in the corresponding controller design. Moreover, the existence of the established controller is given in terms of strict linear matrix inequalities. Finally, numerical examples are used to demonstrate the effectiveness of the given theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

ℋ︁∞ control of discrete‐time Markov jump systems with bounded transition probabilities

This paper deals with the class of discrete‐time linear systems with random abrupt changes and unknown transition probabilities but varying between known bounds for each mode. The ℋ︁_∞ control problem of this class of systems is revisited and new sufficient conditions are developed in the linear matrix inequality (LMI) setting to design the state‐feedback controller that stochastically stabilizes the system under consideration and at the same time guarantees the disturbance rejection with a desired level γ . Sufficient conditions for existence of the state‐feedback controller are developed. It is shown that the addressed problem can be solved if the corresponding developed LMIs are feasible. Numerical examples are employed to show the usefulness of the proposed results. Copyright © 2008 John Wiley & Sons, Ltd.