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.     

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.     

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.     

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.     

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.     

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.     

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.     

On the constrained small-time controllability of linear systems

This note presents a necessary and sufficient condition for small-time controllability of a linear system with respect to a cone. This result extends the controllability conditions for linear systems to the case of control and phase constraints.     

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.     

A note on the value function for constrained control problems

We consider the Mayer optimal control problem with dynamics given by a nonconvex differential inclusion, whose trajectories are constrained to a given set and we obtain a relation between the costate function that appears in the maximum principle and the value function. This relation extends the known conditions existing in the literature for unconstrained problems to those for problems under state constraints.     

Dynamic programming for constrained optimal control of discrete-time linear hybrid systems

In this paper we study the solution to optimal control problems for constrained discrete-time linear hybrid systems based on quadratic or linear performance criteria. The aim of the paper is twofold. First, we give basic theoretical results on the structure of the optimal state-feedback solution and of the value function. Second, we describe how the state-feedback optimal control law can be constructed by combining multiparametric programming and dynamic programming.     

Generalized control systems,boundary control systems,and delayed control systems

We investigate the relationships between the three classes of systems mentioned in the title: we show that systems with delays in control are a special instance of boundary control systems, and a boundary control system produces a generalized control system when projected onto its (unstable) eigenspaces. We use this observation to investigate the action of feedback on the dynamical behavior of systems with boundary controls. In particular, the well-known fact that spectral controllability is necessary and sufficient for a system with delays in control to be stabilizable is derived from a general rather than from anad hoc method. This paper was written according to the programs of the GNAFA-CNR group, with the financial support of the Italian “Ministero della Pubblica Istruzione.”     

滑模等式约束的时滞系统广义预测控制

提出了一种滑模等式约束的广义预测控制方法.该方法将广义预测控制与离散滑模控制结合起来用于具有大惯性、大时滞、时变和非线性的热力站换热机组的供水温度控制系统中,并采用柔化输入信号的方法,可避免广义预测控制算法中的矩阵求逆,有效缩短了预测时域,减小计算量.最后给出了稳定性分析并通过仿真验证了该方法的有效性.     

Task space decomposition for invariant control of constrained robots

An approach, motivated by analytical mechanics and linear algebra methods, is proposed for task space decomposition. The approach relies on the introduction of a new set of kinematic parameters describing the constrained motion of the end-effector, using the analytical forms of material and program constraints. These parameters define a new basis in the end-effector configuration space. A general inner product characterized by the unity matrix is introduced in this basis and in its dual, which gives rise to the definition of a new set of metrics for the end-effector configuration space. The vectors defined in these bases are considered as pseudo-orthogonal. Returning to the original bases of the configuration space, the symmetric matrices for the vanishing bilinear forms can be defined. In this way, the freedom and constraint subspaces can be defined in a rigorous, analytical way. The physical meaning of the resulting metrics is explained. It is shown that the task space decomposition is invariant, although non-Euclidean metrics are being used. To illustrate the application of the methodology and to explain further the properties of the task space decomposition, two examples are presented. In the first example, the robot end-effector tracks a planar surface. A particular definition of the program constraint gives rise to the introduction of skewed bases, which better explains the inherent features of the approach. In the second example, a task of operating a planar joystick, with constrained orientation of the end-effector, is considered. The relevant bases of the task space are translated in this case and it is possible to explain other features of the method.     

Predictor-based sampled-data output-feedback control for feedforward nonlinear time-delay systems

This paper studies global stabilization via predictor-based sampled-data output feedback for a class of feedforward nonlineartime-delay systems. Note that the traditional sampled-data observer via zero-order holder may result in the performancedegradation of the observer. In this paper, an improved predictor-based observer is designed to compensate for the influenceof the unmeasurable states, sampling errors and output delay. In addition, a sampled-data output-feedback controller is alsoconstructed using the gain scaling technique. By the Lyapunov–Krasovskii functional method, the global exponential stabilityof the resulting closed-loop system can be guaranteed under some sufficient conditions. The simulation results are providedto demonstrate the main results.     

Tracking in nonlinear differential-algebraic control systems with applications to constrained robot systems

We consider the design of a feedback control law for control systems described by a class of nonlinear differential-algebraic equations so that certain desired outputs track given reference inputs. The nonlinear differential-algebraic control system being considered is not in state variable form. Assumptions are introduced and a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential-algebraic equations is expressed in a familiar normal form. A nonlinear feedback control law is then proposed which ensures, under appropriate assumptions, that the tracking error in the closed loop differential-algebraic system approaches zero exponentially. Applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints, constrained robot systems with joint flexibility, and constrained robot systems with significant actuator dynamics are discussed.     

LQ control for constrained continuous-time systems

A design method of LQ optimal control law is considered for constrained continuous-time systems. By introducing singular value decomposition for finite-time horizon linear systems, the sequence of LQ sub-optimal control laws, which converges to the exact solution, is obtained based on quadratic programming. It is also shown that the nonlinear sub-optimal feedback gain is found by the union of affine state functions.