Finite horizon optimal hybrid reference control for improving transient response of feedback control systems

Hybrid reference control (HRC) has been known to improve transient response of a stabilised closed-loop continuous tracking system. In this paper, an optimal HRC strategy, which minimises a finite horizon quadratic performance index in the control and state error, is investigated based on the assumption that the full plant states are available for measurement. A special case of constrained optimisation problems leads to the optimal deadbeat control strategy. Conditions for asymptotic stability to default reference signal are also derived.     

Multivariable closed-loop deadbeat control: a polynomial-matrix approach

The closed-loop deadbeat servo problem (CDSP), considered in this paper, consists of the synthesis of a linear, output feedback controller such that the control signal and tracking error both vanish, after a finite period of time, for every reference sequence from a prespecified class and for every initial state of a plant and the controller. The closed-loop structure is determined by studying necessary and sufficient conditions for deadbeat tracking performance. A new theorem asserts that if an open-loop deadbeat control strategy exists for every initial state of the plant and every reference function from a given class, then CDSP is solvable and all desired control laws are found in an explicit parametric form by solving simple, unilateral, linear equations in polynomial matrices. On the basis of this theorem a design algorithm is developed. Asymptotic stability of the closed-loop system exhibiting deadbeat properties is demonstrated. A numerical example is given to illustrate the usefulness and computational efficiency of the new design algorithm presented.     

An MPC-based reference governor approach for offset-free control of constrained linear systems

This paper presents a model predictive control (MPC) based reference governor approach for control of constrained linear systems. A nominal closed-loop system is first designed to guarantee that, in the unconstrained case, asymptotic zero-error regulation for (piecewise) constant reference signals is achieved. Then, a couple of exogenous signals are added to the reference signal and to the control variable and their value is determined by formulating a MPC problem in order to guarantee that (i) when the state and control constraints are not active, the nominal closed-loop system is recovered, (ii) in transient conditions the constraints are always satisfied and the difference of the performances between the real and the nominal closed-loop systems is minimised, and (iii) when the reference signal is infeasible, the output is brought to the nearest feasible value. A simulation example is reported to witness the potentialities of the approach.     

A sliding manifold approach to the feedback control of rigid robots

In this paper we propose a sliding manifold approach to the control of rigid robotic manipulators. We design a PD feedback controller via singular perturbation theory which guarantees the tracking of a reference trajectory. The control signal tends during a fast transient to the well-defined equivalent control with fast nonoscillating modes and then it remains close to this in the uniform topology. Then the resulting closed-loop system does not have the drawbacks of high-gain feedback systems, even if it retains robustness properties with respect to disturbances and plant parameter uncertainties. An application of the proposed procedure to a robotic system which includes actuator dynamics and tachometers is presented.     

Computing actuator bandwidth limits for model reference adaptive control

Although model reference adaptive control theory has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, a linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that is not affected by the presence of actuator dynamics. Specifically, we first generalise the hedging approach to cover a variety of cases in which actuator output and the control effectiveness matrix of the uncertain dynamical system are known and unknown. We then show the stability of the closed-loop dynamical system using Lyapunov-based stability analysis tools and propose a linear matrix inequality-based framework for the computation of the minimum allowable actuator bandwidth limits such that the closed-loop dynamical system remains stable. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.     

Robust stability constraints for fuzzy model predictive control

This paper addresses the synthesis of a predictive controller for a nonlinear process based on a fuzzy model of the Takagi-Sugeno (T-S) type, resulting in a stable closed-loop control system. Conditions are given that guarantee closed-loop robust asymptotic stability for open-loop bounded-input-bounded-output (BIBO) stable processes with an additive l₁-norm bounded model uncertainty. The idea is closely related to (small-gain-based) l₁-control theory, but due to the time-varying approach, the resulting robust stability constraints are less conservative. Therefore the fuzzy model is viewed as a linear time-varying system rather than a nonlinear one. The goal is to obtain constraints on the control signal and its increment that guarantee robust stability. Robust global asymptotic stability and offset-free reference tracking are guaranteed for asymptotically constant reference trajectories and disturbances     

Asymptotic stability of digitally redesigned control systems

This paper analyses an asymptotic stability of a digitally redesigned control system when the states of the analogue and the digital control systems are approximately matched at every sampling point. The digital redesign is a simple method of converting a given analogue controller to an equivalent digital controller in the sense of state-matching. The concerned state-matching technique is to minimise the norm distance between the discretised closed-loop system matrix of linear analogue control system and that of linear digital control system. It is shown that (i) there exists an upper bound of the norm distance to guarantee the asymptotic stability of the digitally redesigned control system and (ii) the trajectories of the linear analogue and the linear digital control systems coincide at every sampling point if the norm distance is zero. Also, a robustness result is provided in the case that nonlinear perturbations occur in the analogue and the digital control systems. Moreover, design conditions for the developed stability analysis are proposed in terms of linear matrix inequalities.     

Nonlinear feedback control of multivariable non-minimum-phase processes

A new method of controlling nonlinear processes with a non-minimum-phase delay-free part is presented. Two control laws are derived for stable, multiple-input multiple-output processes. They are obtained by requesting an approximately linear, input–output response and exploiting the connections between model-predictive control and input–output linearization. Conditions under which the closed-loop system is asymptotically stable are given. The application and performance of the control laws are illustrated using numerical simulation of two chemical reactor examples that exhibit non-minimum-phase behavior.     

Discrete model predictive controller design using Laguerre functions

In Model Predictive Controller (MPC) design, the traditional approach of expanding the future control signal uses the forward shift operator to obtain the linear-in-the-parameters relation for predicted output. As a consequence, in case of rapid sampling, complicated process dynamics and/or high demands on closed-loop performance, satisfactory approximation of the control signal requires a very large number of forward shift operators, and leads to poorly numerically conditioned solutions and heavy computational load when implemented on-line. In this paper, by using a performance specification on the exponential change rate of the control signal, a more appropriate expansion, related to Laguerre net-works, is introduced and analyzed. It is shown that the number of terms used in the optimization procedure can be reduced to a fraction of that required by the usual procedure. By relaxing the constraint on the exponential change rate of the control signal and allowing arbitrary complexity in describing the trajectory, the proposed approach becomes equivalent to the traditional approach in MPC design. Closed-loop stability of the proposed model predictive control system is analyzed by using terminal state variable constraints.     

不确定离散系统的输出反馈保性能控制

对一类具有范数有界时变参数不确定性的离散时间系统，研究设计一个输出反馈保性能控制器，使得闭环系统对所有允许的不确定性渐近稳定，且闭环性能指标值不超过某个确定的上界。基于线性矩阵不等式处理方法，证明了保性能控制器的存在性等价于一个线性矩阵不等式的可行性，并用该线性矩阵不等式的可解给出了控制器的构造方法和闭环性能指标的上界。     

2-D奇异系统Roesser模型的鲁棒H∞控制

考虑具有参数不确定性的2-D奇异系统Roesser模型(简称2-D SRM)鲁棒H∞控制问题．在给出界实引理的另一等价形式的基础上,通过求解矩阵不等式,给出了不确定2-D奇异系统鲁棒H∞控制问题可解的充分条件及静态状态反馈控制律设计的代数表达式．最后通过一个仿真算例验证了方法的有效性．     

Improving transient performance in tracking control for linear multivariable discrete-time systems with input saturation

In this paper, we present a composite nonlinear feedback (CNF) control technique for linear discrete-time multivariable systems with actuator saturation. The CNF control law serves to improve the transient performance of the closed-loop system by adding an additional nonlinear feedback. The linear feedback can be designed to yield a quick response at the initial stage, then the nonlinear feedback is introduced to smooth out overshoots when the system output approaches the target reference. As such, the resulting closed-loop system typically has very fast transient response and small overshoots. The goal of this work is to complete the theory for general discrete-time systems. The technique is applied to a magnetic-tape-drive servo system design and yields a huge improvement in settling time compared to that of a purely linear controller.     

Reconfigurable control of Hammerstein systems after actuator failures: stability,tracking, and performance

A new method for the reconfigurable control of stable Hammerstein systems with sector-bounded static nonlinear input characteristics subject to actuator failures is described. It aims at the recovery of the nominal stability, setpoint tracking, disturbance rejection and performance properties by the reconfigured closed-loop system. This article extends the virtual actuator from linear systems to Hammerstein systems and provides sufficient linear matrix inequality conditions for closed-loop stability, and a corresponding synthesis algorithm. It is shown that the approach is robust against uncertainties of the static input nonlinearity in a small-gain sense, and universal in a certain sense. Feasible setpoints for the reconfigured closed-loop system are characterised, and infeasible setpoints are projected to feasible ones. An extension guarantees minimum performance loss. The method is successfully experimentally evaluated using a system of interconnected tanks.     

临界状态下三维仿射控制系统的局部光滑镇定

讨论三维仿射非线性控制系统,在具有零和一对共轭纯虚数特征值的临界状态下的局部光滑镇定性.首先,应用非奇异线性状态变换和时间尺度变换,将系统转化成标准形式.之后,运用形式级数法的思想和扩展正则判别函数法,构造多组线性方程组,给出确定光滑控制律和闭环系统李雅普诺夫函数的一种方法,从而得到该标准化系统局部光滑镇定的充分条件.示例说明该方法是有效的.     

Multisensor switching control strategy with fault tolerance guarantees

In this paper we propose a novel fault tolerant multisensor switching strategy for feedback control. Each sensor of the proposed multisensor scheme has an associated state estimator which, together with a state feedback gain, is able to individually stabilise the closed-loop system. At each instant of time, the switching strategy selects the sensor-estimator pair that provides the best closed-loop performance, as measured by a control-performance criterion. We establish closed-loop stability of the resulting switching scheme under normal (fault-free) operating conditions. More importantly, we show that closed-loop stability is preserved in the presence of faulty sensors if a set of conditions on the system parameters (such as bounds on the sensor noises, maximum and minimum values of the reference signal, etc.) is satisfied. This result enhances and broadens the applicability of the proposed multisensor scheme since it provides guaranteed properties such as fault tolerance and robust closed-loop stability under sensor fault. The results are applied to the problem of automotive longitudinal control.     

Sensitivity analysis of linear control systems with random plan parameters

Abstract-The effects of random variations of the plant parameters in multivariable linear control systems are analyzed in terms of stochastic sensitivity operators. Both tie-varying and time-invariant control systems are analyzed. Conditions are derived for the stochastic sensitivity operator which are sufficient to guarantee that the closed-loop realization of the control system is less sensitive to the random parameter variations than the nominally equivalent open-loop system.     

一类时滞广义非线性系统H_∞可靠跟踪控制

讨论一类Lipschitz时滞非线性广义系统的H∞可靠跟踪控制问题.分别给出了执行器失效和传感器失效两种模型下可靠控制器存在的充分条件,使得闭环系统正则无脉冲并且指数稳定,同时系统输出跟踪预先给定的可测参考模型的输出,且满足H∞性能指标,并利用线性矩阵不等式技巧给出了可靠控制器的设计方法.最后给出了一个数值例子,说明了本文所给出方法的有效性.     

Neural network-based control design: an LMI approach.

We address a neural network-based control design for a discrete-time nonlinear system. Our design approach is to approximate the nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin. A linear difference inclusion representation is then established for this class of approximating neural networks and is used to design a state feedback control law for the nonlinear system based on the certainty equivalence principle. The control design equations are shown to be a set of linear matrix inequalities where a convex optimization algorithm can be applied to determine the control signal. Further, the stability of the closed-loop is guaranteed in the sense that there exists a unique global attraction region in the neighborhood of the origin to which every trajectory of the closed-loop system converges. Finally, a simple example is presented so as to illustrate our control design procedure.     

On fractional order composite model reference adaptive control

This paper presents a novel composite model reference adaptive control approach for a class of fractional order linear systems with unknown constant parameters. The method is extended from the model reference adaptive control. The parameter estimation error of our method depends on both the tracking error and the prediction error, whereas the existing method only depends on the tracking error, which makes our method has better transient performance in the sense of generating smooth system output. By the aid of the continuous frequency distributed model, stability of the proposed approach is established in the Lyapunov sense. Furthermore, the convergence property of the model parameters estimation is presented, on the premise that the closed-loop control system is stable. Finally, numerical simulation examples are given to demonstrate the effectiveness of the proposed schemes.     

Robust synergetic control design under inputs and states constraints

In this paper, a novel robust-constrained control methodology for discrete-time linear parameter-varying (DT-LPV) systems is proposed based on a synergetic control theory (SCT) approach. It is shown that in DT-LPV systems without uncertainty, and for any unmeasured bounded additive disturbance, the proposed controller accomplishes the goal of stabilising the system by asymptotically driving the error of the controlled variable to a bounded set containing the origin and then maintaining it there. Moreover, given an uncertain DT-LPV system jointly subject to unmeasured and constrained additive disturbances, and constraints in states, input commands and reference signals (set points), then invariant set theory is used to find an appropriate polyhedral robust invariant region in which the proposed control framework is guaranteed to robustly stabilise the closed-loop system. Furthermore, this is achieved even for the case of varying non-zero control set points in such uncertain DT-LPV systems. The controller is characterised to have a simple structure leading to an easy implementation, and a non-complex design process. The effectiveness of the proposed method and the implications of the controller design on feasibility and closed-loop performance are demonstrated through application examples on the temperature control on a continuous-stirred tank reactor plant, on the control of a real-coupled DC motor plant, and on an open-loop unstable system example.