Using stable input-output inversion for minimum-time feedforward constrained regulation of scalar systems

The paper approaches the feedforward minimum-time smooth control of non-minimum-phase linear scalar systems for set-point regulation. The aim is to synthesize a bounded input subject to non-saturating constraints on the input and its derivatives till a prespecified arbitrary order. The provided solution relies on a stable input-output dynamic inversion technique and an ad hoc parameterized family of output transition functions. The synthesized minimum-time input that exhibits pre- and post-actuation is determined by means of easily-implementable closed-form expressions. Examples are given to illustrate the methodology.     

Inversion-based feedforward and reference signal design for fractional constrained control systems

In this paper we propose a solution for the synthesis of a feedforward control action for a fractional control system. In particular, an input–output inversion based methodology is devised in order to determine the open-loop signal that provides a predefined process variable transition from a steady-state value to another. The transition time is then minimized subject to constraints on the process and control variables and their derivatives. Simulation results show the effectiveness of the technique.     

Robust output regulation by observer-based feedforward control

In this paper, a new method for the design of disturbance and reference feedforward controllers with disturbance observers is presented for systems, where the disturbance input location is unknown. The resulting controller achieves asymptotic tracking in the presence of the disturbances despite plant parameter variations and changing disturbance input locations, and is therefore robust. It is shown that the new controller design method is dual to Davison's approach for the application of the internal model principle. However, different from the latter one, the new design procedure allows a simple and complete prevention of controller windup by driving the disturbance observer with the saturated input. Furthermore, a straightforward separate reference channel design is possible in order to improve the tracking behaviour if the types of the reference and the disturbance signals differ. A simple example demonstrates the advantages of the new design method.     

Experimental-based feedforward control for a DoD inkjet printhead

Markets demand continuously for higher quality, higher speed, and more energy-efficient professional printers. Drop-on-Demand (DoD) inkjet printing is considered as one of the most promising printing technologies. It offers many advantages including high speed, quiet operation, and compatibility with a variety of printing media. Nowadays, it has been used as low-cost and efficient manufacturing technology in a wide variety of markets. Although the performance requirements, which are imposed by the current applications, are tight, the future performance requirements are expected to be even more challenging. These print requirements are related to the jetted drop properties, namely, drop velocity, drop volume, drop velocity consistency, productivity, and reliability. Meeting these performance requirements is restricted by several operational issues that are associated with the design and the operation of inkjet printheads. Major issues that are usually encountered are residual vibrations and crosstalk among ink channels. These result in a poor printing quality for high-speed printing. The main objective is to design a feedforward control strategy such that variations in the velocity and volume of the jetted drops are minimized. In this article, an experimental-based feedforward control scheme is proposed to improve the performance of a professional inkjet printer.     

Feedback stabilization of $N$-dimensional stochastic quantum systems based on bang-bang control

For an $N$-dimensional quantum system under the influence of continuous measurement, this paper presents a switching control scheme where the control law is of bang-bang type and achieves asymptotic preparation of an arbitrarily given eigenstate of a non-degenerate and degenerate measurement operator, respectively. In the switching control strategy, we divide the state space into two parts: a set containing a target state, and its complementary set. By analyzing the stability of the stochastic system model under consideration, we design a constant control law and give some conditions that the control Hamiltonian satisfies so that the system trajectories in the complementary set converge to the set which contains the target state. Further, for the case of a non-degenerate measurement operator, we show that the system trajectories in the set containing the target state will automatically converge to the target state via quantum continuous measurement theory; while for the case of a degenerate measurement operator, the corresponding system trajectories will also converge to the target state via the construction of the control Hamiltonians. The convergence of the whole closed-loop systems under the cases of a non-degenerate and a degenerate measurement operator is strictly proved. The effectiveness of the proposed switching control scheme is verified by the simulation experiments on a finite-dimensional angular momentum system and a two-qubit system.     

Model based feedforward control of an industrial glass feeder

This article presents the automation of set point changes of an industrial glass feeder in container glass production. A model is proposed consisting of multiple first order partial differential equations (PDEs). Based on the derived model a feedforward control approach is presented. The approach allows for the calculation of control inputs out of reference trajectories of the system outputs and is used to perform automated set point changes with short transition time. Finally, the approach is implemented at an industrial glass feeder. Measurement results from the Thüringer Behälterglas GmbH (Schleusingen, Germany) are included.     

Adaptive control for nonlinear nonnegative dynamical systems

Nonnegative and compartmental models are widespread in engineering systems and life sciences and play a key role in the understanding of these systems. In this paper, we develop a direct adaptive control framework for nonlinear uncertain nonnegative and compartmental dynamical systems. The proposed framework is Lyapunov-based and guarantees partial asymptotic set-point regulation; that is, asymptotic set-point regulation with respect to part of the closed-loop system states associated with the plant. In addition, the adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space.     

A Riccati approach for constrained linear quadratic optimal control

An active-set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. A Riccati-based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure. The solution of each subproblem requires computations that scale linearly with the horizon length. The algorithm is illustrated with numerical examples.     

Separation theorem for linearly constrained LQG optimal control

We solve the linearly constrained linear-quadratic (LQ) and linear-quadratic-Gaussian (LQG) optimal control problems. Closed-form expressions of the optimal controls are derived, and the Separation Theorem is generalized.     

Robust one-step receding horizon control for constrained systems

This paper proposes a robust receding horizon control scheme for discrete-time uncertain linear systems with input and state constraints. The control scheme is based on the minimization of the worst-case one-step finite horizon cost with a finite terminal weighting matrix. It is shown that the proposed receding horizon control robustly asymptotically stabilizes uncertain constrained systems under some matrix inequality conditions on the terminal weighting matrices. This robust receding horizon control scheme has a larger feasible initial-state set and a more general structure than existing robust receding horizon controls for uncertain constrained systems under the same design parameters. The proposed controller is obtained using semidefinite programming. Copyright © 1999 John Wiley & Sons, Ltd.     

Global sampled-data output feedback control for a class of feedforward nonlinear systems

This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Nonlinear minimum-time control with pre- and post-actuation

This article studies the time-optimal output transition problem to change the system output, from an initial value (for all time ) to a final value (for all time ), for invertible nonlinear systems. The main contribution of the article is to show that the use of pre- and post-actuation input outside the transition interval I_T=[0,T] can reduce the transition time T beyond the standard bang–bang-type inputs for optimal state transition. The advantage of using pre- and post-actuation is demonstrated with an illustrative nonlinear example.     

Max-plus-linear model-based predictive control for constrained hybrid systems: linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the (max, +) algebra, a typical subclass of hybrid systems called max-plus-linear (MPL) systems is obtained. And then, model predictive control (MPC) framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem (ELCP) were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling (MMPS) functions (using the operations maximization, minimization, addition and scalar multiplication) with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.     

Max-plus-linear model-based predictive control for constrained hybrid systems：linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the （max, ＋） algebra, a typical subclass of hybrid systems called max-plus-linear （MPL） systems is obtained. And then, model predictive control （MPC） framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem （ELCP） were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling （MMPS） functions （using the operations maximization, minimization, addition and scalar multiplication） with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.     

Stochastic model predictive control for constrained discrete-time Markovian switching systems

In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the SMPC law under very weak assumptions. In the special but important case of constrained MJLS we present an algorithm for computing explicitly the SMPC control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization.     

Generalized feedforward tuning rules for non-realizable delay inversion

This paper describes the problem of load disturbance rejection using feedforward for the case when perfect compensation is not realizable due to processes delays inversion. First, a new generalized open-loop design tuning rule for feedforward compensators is proposed. Simple and intuitive guidelines are given for aggressive, moderate, and conservative performance results. Moreover, a switching feedforward compensator is proposed to be used when oscillations are not allowed in the process output. Simulation results show important improvements in disturbance rejection, reference tracking error and control effort.     

Constraint feedforward control for thermal processing of quartz photomasks in microelectronics manufacturing

A feedforward control scheme is designed to improve performance of conductive heating systems used for lithography in microelectronics processing. It minimizes the loading effects induced by the common processing condition of placement of a quartz photomask at ambient temperature on a bake plate at processing temperature. The feedforward control strategy is a model-based method using linear programming to minimize the worst-case deviation from a nominal temperature set-point during the load disturbance condition. This results in a predictive controller that performs a pre-determined heating sequence prior to the arrival of the substrate as part of the resulting feedforward/feedback strategy to eliminate the load disturbance. This procedure is based on an empirical model generated from data obtained during closed-loop operation. It is easy to design and implement for conventional thermal processing equipment. Experimental results are performed for two commercial bake plates and depict an order-of-magnitude improvement in the settling time and the integral-square temperature error between the optimal predictive controller and a feedback controller for a typical load disturbance.     

Generalized predictive control for non-uniformly sampled systems

In this paper, we study digital control systems with non-uniform updating and sampling patterns, which include multirate sampled-data systems as special cases. We derive lifted models in the state-space domain. The main obstacle for generalized predictive control (GPC) design using the lifted models is the so-called causality constraint. Taking into account this design constraint, we propose a new GPC algorithm, which results in optimal causal control laws for the non-uniformly sampled systems. The solution applies immediately to multirate sampled-data systems where rates are integer multiples of some base period.     

Robust model predictive control for constrained continuous-time nonlinear systems

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.     

Robust set‐point constrained regulation via dynamic inversion

In this paper we present a novel methodology, based on dynamic system inversion, for the set‐point constrained regulation of a scalar plant in presence of structured uncertainties. The approach consists in choosing a polynomial as the output function and then designing both the controller and the reference input in order to minimize the worst‐case settling‐time of the set‐point regulation, with constraints on the maximum absolute value of the control variable and on the maximum overshoot of the output. A comparison with a traditional methodology, which is based on the step‐response, shows how the overall design is significantly simplified and how the worst‐case settling‐time can be greatly reduced. Optimization has been performed by means of genetic algorithms. Copyright © 2001 John Wiley & Sons, Ltd.