基于非线性PID的非最小相位系统控制

提出一种新型非线性PID控制器简单结构，利用非线性PID控制器的非线性特性，抑制非最小相位系统的右半平面零点所造成的负调问题，克服非最小相位系统的超凋、负调和调整时间之间的矛盾。数值仿真结果表明，由非线性PID控制器构成的非最小相位系统具有良好的动静态性能、高的控制精度和较强的鲁棒性。数值结果说明方法有效，算法简单，易于实时实现。     

Singularly perturbed implicit control law for linear time‐varying delay MIMO systems

This paper proposes a control scheme for the problem of stabilizing partly unknown multiple‐input multiple‐output linear time‐varying retarded systems. The control scheme is composed by a singularly perturbed controller and a reference model. We assume the knowledge of a number of structural characteristics of the system as the boundedness and the knowledge of the bounds for the unknown parameters (and their derivatives) that define the system matrices, as well as the structure of these matrices. The results presented here are a generalization of previous results on linear time‐varying Single‐Input Single‐Output (SISO) and multiple‐input multiple‐output systems without delays and linear time‐varying retarded SISO systems. The closed‐loop system is a linear singularly perturbed retarded system with uniform asymptotic stability behavior. The uniform asymptotic stability of the singularly perturbed retarded system is guaranteed. We show how to design a control law such that the system dynamics for each output is given by a Hurwitz polynomial with constant coefficients. Copyright © 2015 John Wiley & Sons, Ltd.     

Transient tracking performance improvement for nonlinear nonminimum phase systems: an additive-state-decomposition-based control method

To study the problem of improving transient tracking performance for nonlinear systems, this paper proposes an additive-state-decomposition-based control method for a class of nonlinear nonminimum phase (NMP) systems. This method ‘additively’ decomposes the original problem into two more tractable problems, namely a tracking problem for a linear time-invariant NMP ‘primary’ system and a state stabilisation problem for a certain nonlinear ‘secondary’ system. Then, controller for each system is designed respectively by employing existing methods, i.e. the linear quadratic regulator (LQR) method for the primary system and the backstepping method for the secondary system. Next, these two controllers are combined together to achieve the original tracking goal. Furthermore, the adjustment of weighting matrix Q in the LQR regulates the transient response of the closed-loop nonlinear system. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed method.     

Fractional-order unstable pole-zero cancellation in linear feedback systems

As a very well-known classical fact, non-minimum phase zeros of the process put some limitations on the performance of the feedback system. The source of these limitations is that non-minimum phase zeros cannot be cancelled by unstable poles of the controller since such a cancellation leads to internal instability. The aim of this paper is to propose a method for fractional-order cancellation of non-minimum phase zeros of the process and studying its properties. It is specially shown that the proposed cancellation strategy increases the phase and gain margin without leading to internal instability. Since the systems with higher gain and phase margin are easier to control, the proposed method can be used to arrive at more effective controls, which is also verified by the simulation results.     

All‐Stabilizing Proportional Controllers for First‐Order Bi‐Proper Systems with Time Delay: An Analytical Derivation

In this paper, a simple derivation for an all‐stabilizing proportional controller set for first‐order bi‐proper systems with time delay is proposed. In contrast to proper systems, an extremely limited number of studies are available in the literature for such bi‐proper systems. To fill this gap in the literature, broader aspects of the stabilizing set are taken into consideration. The effect of zero on the stabilizing set is clearly discussed and we also prove that, when their zeros are placed symmetrically to the origin, the stabilizing set of non‐minimum phase plant is always smaller than that of the minimum phase one. Moreover, for an open‐loop unstable plant, maximum allowable time delay (MATD) is explicitly expressed as a function of the locations of the pole and zero. From that function, it is shown that for a minimum phase plant, the supremum of the MATD is two times that of the time constant of the plant and the infimum of the MATD is the time constant of the plant. We also prove that the supremum is the time constant and the infimum is zero for a non‐minimum phase plant.     

Discrete output feedback sliding‐mode control with integral action

This paper presents a novel approach to the problem of discrete time output feedback sliding‐mode control design. The method described applies to uncertain systems (with matched uncertainties) which are not necessarily minimum phase or relative degree one. A new sliding surface is proposed, which is associated with the equivalent control of the output feedback sliding‐mode controller. Design freedom is available to select the sliding surface parameters to produce an appropriate reduced‐order sliding motion. In order for this to be achieved, a static output feedback condition associated with a certain reduced‐order system obtained from the original plant must be solvable. The practicality of the results are demonstrated through the implementation of the controller on a small DC motor test rig. Copyright © 2005 John Wiley & Sons, Ltd.     

Variable Structure Predefined‐Time Stabilization of Second‐Order Systems

A controller that stabilizes second‐order vector systems in predefined‐time is introduced in this paper. That is, for second‐order systems a controller is designed such that the trajectories reach the origin in a time defined in advance. The proposed controller is a variable structure controller that first drive the system trajectories to a linear manifold in predefined time and then drives the system trajectories to a non‐smooth manifold with the predefined‐time stability property, in predefined time also; this is done in order to avoid the differentiability problem that inherently appears when stabilizing high‐order systems in finite time under the block control principle technique. The proposal is applied to the predefined‐time exact tracking of fully actuated mechanical systems. As an example, the proposed solution is applied to a two‐link planar manipulator, and numerical simulations are conducted to show its performance.     

Feedback limitations of linear sampled‐data periodic digital control

We present a set of feedback limitations for linear time‐invariant systems controlled by periodic digital controllers based upon an analysis of the inter‐sample response of the closed‐loop system to sinusoidal inputs. Fundamental sensitivity and complementary sensitivity functions govern the fundamental and harmonic components of the continuous closed‐loop response. The continuous and discrete response of the system is sensitive to variations in the analog plant at frequencies integer multiples of ω_s/N away from the excitation frequency, where ω_s is the sampling frequency and N is the period of the controller. These functions satisfy interpolation and integral constraints due to open‐loop non‐minimum phase zeros and unstable poles. In addition, the use of periodic digital control may result in a reduction in closed‐loop bandwidth. Copyright © 2000 John Wiley & Sons, Ltd.     

DISCRETIZING CONTINUOUS‐TIME CONTROLLERS WITH FUZZY LOGIC SYSTEMS AND ITS STABILITY ANALYSIS

In this paper, a new method, applying the fuzzy logic system, is proposed to discretize the continuous‐time controller in computer‐controlled systems. All the continuous‐time controllers can be reconstructed by the proposed method under the Sampling Theorem. That is, the fuzzy logic systems are used to add nonlinearity and to approximate smooth functions. Hence, the proposed controller is a new smooth controller that can replace the original controller, independent of the sampling time under the Sampling Theorem. Consequently, the proposed controller not only can discretize the continuous‐time controllers, but also can tolerate a wider range of sampling time uncertainty. Besides, the input‐output stability is proposed for discretizing the continuous‐time controller of the fuzzy logic systems. Finally, computer simulation shows that the proposed method can easily reconstructthe continuous‐time controller and has very good robustness for different sampling times.     

Robust compensation of time delayed plant by continuous‐time high frequency periodic controller with negligible output ripples

The present work addresses the problem of ensuring robust stability to time delayed plants, compensated with continuous‐time high frequency periodic controller. An efficient design methodology is proposed to synthesize the periodic controller for robust compensation of time delayed linear time‐invariant plants. The periodic controller, by virtue of its loop zero‐placement capability, is shown to achieve superior gain as well as phase/delay margin compensation, especially for non‐minimum phase plants having right half plane poles and zeros in close vicinity to each other. The periodic controller is considered in the observable canonical form which results in realizable bounded control input as well as ensuring insignificant periodic oscillations in the plant output. As a consequence, this paper, furthermore, establishes the fact that the periodic controller designed and synthesized with the proposed methodology can be implemented in real‐time with an assurance of model matching and robust zero‐error tracking. Simulation and experimental results are illustrated to establish the veracity of the claims. The closed‐loop system comprising of time‐delayed linear time‐invariant plant with the periodic controller is analyzed employing the averaging principle and presented here explicitly in a meticulous approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Sampled‐data output feedback stabilization for a class of switched stochastic nonlinear systems

This paper investigates a global sampled‐data output feedback stabilization problem for a class of switched stochastic nonlinear systems whose output and system mode are available only at the sampling instants. An observer is designed to estimate the unmeasurable state and thus a sampled‐data controller is constructed with the sampled estimated state. As a distinctive feature, a merging virtual switching signal is introduced to describe the asynchronous switching generated by detecting the system mode via a sampler. By choosing an appropriate piecewise Lyapunov function, it is proved that the proposed sampled‐data controller with allowable sampling period can stabilize the considered switched stochastic nonlinear systems under an average dwell‐time condition. Finally, two simulation results are presented to illustrate the effectiveness of the proposed method.     

Finite‐time consensus of Euler‐Lagrange agents without velocity measurements via energy shaping

Motivated by the energy‐shaping framework and the properties of homogeneous systems, this paper deals with the problem of achieving consensus of multiple Euler‐Lagrange (EL) systems using the energy shaping plus damping injection principles of passivity‐based control. We propose a method to derive a novel family of decentralized controllers that is capable of solving the leaderless and the leader‐follower consensus problems in finite‐time in networks of fully actuated EL systems without employing velocity measurements. As in the energy‐shaping methodology, the controller is another EL system and the plant‐controller interconnection is the gradient of a suitable defined potential function. The potential energy and dissipation functions, of the controller, are provided with some homogeneous properties in order to achieve finite‐time convergence. This paper provides several simulations that corroborate the performance of different controllers.     

Exponential Stability for Multi‐Area Power Systems with Time Delays Under Load Frequency Controller Failures

This paper investigates the exponential stability problem for a class of multi‐area power systems with time delays under load frequency controller failures (LFCFs). For describing the phenomenon of LFCFs, the considered multi‐area power system is rewritten as a switched system with multiple time delays. By adopting the switching technique, the exponential stability conditions for multi‐area power systems are developed when the controller failure frequency and the unavailability ratio of the controller are restricted. Finally, one example is given to show the applicability of the proposed method.     

A multilevel sampled‐data approach for resilient navigation and control of autonomous systems

Autonomous systems are rapidly becoming an integrated part of the modern life. Safe and secure navigation and control of these systems present significant challenges in the presence of uncertainties, physical failures, and cyber attacks. In this paper, we formulate a navigation and control problem for autonomous systems using a multilevel control structure, in which the high‐level reference commands are limited by a saturation function, whereas the low‐level controller tracks the reference by compensating for disturbances and uncertainties. For this purpose, we consider a class of nested, uncertain, multiple‐input–multiple‐output systems subject to reference command saturation, possibly with nonminimum phase zeros. A multirate output‐feedback adaptive controller is developed as the low‐level controller. The sampled‐data (SD) design of this controller facilitates the direct implementation on digital computers, where the input/output signals are available at discrete time instances with different sampling rates. In addition, stealthy zero‐dynamics attacks become detectable by considering a multirate SD formulation. Robust stability and performance of the overall closed‐loop system with command saturation and multirate adaptive control are analyzed. Simulation scenarios for navigation and control of a fixed‐wing drone under failures/attacks are provided to validate the theoretical findings.     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

Fast terminal sliding‐mode finite‐time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems

This paper presents a fast terminal sliding‐mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states combined with time‐varying disturbances. Fast terminal sliding‐mode finite‐time tracking systems based on differential evolution algorithms incorporate an integral chain differentiator (ICD) to feedback systems for the estimation of the unknown system states. The differential evolution optimization algorithm using ICD is also applied to a tracking controller, which provides unknown parametric estimation in the limitation of unknown system states for trajectory tracking. The ICD in the tracking systems strengthens the tracking controller robustness for the disturbances by filtering noises. As a powerful finite‐time control effort, the fast terminal sliding‐mode tracking control guarantees that all tracking errors rapidly converge to the origin. The effectiveness of the proposed approach is verified via simulations, and the results exhibit high‐precision output tracking performance in uncertain nonlinear systems.     

Global asymptotic tracking for nonminimum‐phase nonlinear systems in output feedback form

The problem of global asymptotic tracking by output feedback is studied for a class of nonminimum‐phase nonlinear systems in output feedback form. It is proved that the problem is solvable by an n‐dimensional output feedback controller under the two conditions: (a) the nonminimum‐phase nonlinear system can be rendered minimum‐phase by a virtual output; and (b) the internal dynamics of the nonlinear system driven by a desired signal and its derivatives has a bounded solution trajectory. With the help of a new coordinate transformation, a constructive method is presented for the design of a dynamic output tracking controller. An example is given to validate the proposed output feedback tracking control scheme.     

Fuzzy‐Neuron Intelligent Coordination Control Fora Unit Power Plant

A novel fuzzy‐neuron intelligent coordination control method for a unit power plant is proposed in this paper. Based on the complementarity between a fuzzy controller and a neuron model‐free controller, a fuzzy‐neuron compound control method for Single‐In‐Single‐Out (SISO) systems is presented to enhance the robustness and precision of the control system. In this new intelligent control system, the fuzzy logic controller is used to speed up the transient response, and the adaptive neuron controller is used to eliminate the steady state error of the system. For the multivariable control system, the multivariable controlled plant is decoupled statically, and then the fuzzy‐neuron intelligent controller is used in each input‐output path of the decoupled plant. To the complex unit power plant, the structure of this new intelligent coordination controller is very simple and the simulation test results show that good performances such as strong robustness and adaptability, etc. are obtained. One of the outstanding advantages is that the proposed method can separate the controller design procedure and control signals from the plant model. It can be used in practice very conveniently.     

UNIVERSAL OUTPUT‐FEEDBACK SISO CONTROLLERS

It is proved in the paper that practically all known higher‐order sliding controllers can be combined with recently developed 2‐sliding‐mode‐based differentiators yielding universal output‐feedback Single‐Input‐Single‐Output (SISO) controllers. These controllers can be applied at least locally, whenever the system relative degree is known. The convergence is global, provided the system relative degree is permanent and few boundedness restrictions hold. No detailed mathematical model of the system is needed. The proposed output‐feedback controller provides for the exact finite‐time‐convergent output tracking of real‐time‐given smooth signals if the output measurements are exact. Otherwise the tracking accuracy is proportional to the magnitude of the sampling noise. The control may be made arbitrarily smooth, thereby removing the chattering effect. The theoretical results are illustrated by computer simulation.     

Finite‐time stability and stabilization of semi‐Markovian jump systems with time delay

Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method.