Linear multivariable control of two-link robots

Several simple multivariable controllers such as proportional (P), proportional-derivative (PD), proportional-integral (PI), and proportional-integral-derivative (PID) are investigated and designed for stabilization and regulation of a two-link planar robot. A new multivariable controller is introduced in this article to achieve command matching. The multivariable controllers are designed on the basis of a linearized model of the robot dynamics. Numerous simulation results are presented to evaluate the performance of the multivariable controllers for the two-link planar robot.     

Exact and inexact LQG model matching problems

The design of discrete-time LQG (linear-quadratic-Gaussian) controllers that yield closed-loop systems that match a provided model is addressed. The solution is in the form of a two-degree-of-freedom controller having feedback and feedforward paths that independently provide the optimal actions for disturbance rejection and model matching. Exact and approximate model matching cases are discussed in a unified fashion     

Model matching for asynchronous sequential machines with adversarial inputs using state bursts

Asynchronous sequential machines are referred to as finite state machines in which state changes are not governed by a global clock. This paper presents model matching for asynchronous sequential machines where an unobservable adversarial input can infiltrate and provoke unauthorized state transitions. The objective is to build an automatic state feedback controller so that the closed-loop system can match a prescribed model and all the unauthorized transitions by adversarial inputs can be invalidated. We address reachability and detectability properties of the asynchronous machine with adversarial intervention, and present necessary and sufficient conditions for the existence of appropriate controllers that realize model matching. Whenever controllers exist, algorithms for their design are outlined and an experimental verification is provided.     

Block multirate input-output model for sampled-data control systems

A model for multirate sampled-data systems is presented. A detailed analysis of nonconventional sampled-data control systems (SDCS) is performed. The block multirate input-output model illustrates the control possibilities of multirate SDCS. It is obtained from either a transfer function matrix or a state variable representation. The model provides a direct way to represent, design, and understand either periodic or predictive controllers. A controller design methodology suitable for multivariable, multirate, nonsynchronous SDCS is also presented. The main feature is the freedom to achieve important objectives such as structure assignment, decoupling, and desired transient behavior, as well as reference matching, optimal control, or disturbance rejection     

A new software tool for synthesis of linear PID controllers

A new versatile software utility for synthesis of linear PID controllers is described, and the software listing is presented. The software is in the MATLAB environment. Closed-form PID controller gain design equations are developed. The design approach is systematic, and it is based on frequency matching technique with a model matching criteria. The objective is to design a closed-loop feedback system with a PID controller whose dynamic and static behavior would mimic a user-defined reference linear model. The design procedure is automated via a new MATLAB command. The software also has applications in synthesis of nonlinear PID controllers. Because the design equations are of a closed form, the speed of calculations is high; therefore, design software may be used in designing self-tuning adaptive PID controllers.     

Robust ℋ2/ℋ∞/reference model dynamic output-feedback control synthesis

This article presents a new strategy to design robust model matching dynamic output-feedback controllers that guarantee tracking response specifications, disturbance rejection and noise attenuation. The proposed synthesis methodology, based on a multi-objective optimisation problem, can be applied to uncertain continuous or discrete-time linear time-invariant systems with polytopic uncertainty, leading to both full-order and reduced-order robust-performance dynamic controllers. The objective functions represent the ?_∞-norm of the difference between the closed-loop transfer function matrix, from the reference signals and the plant outputs and the reference model matrix, the ?_∞-norm of the closed-loop transfer function matrix from the disturbances and the plant outputs and the ?₂-norm of the closed-loop transfer function matrix from the measurement noises and the control inputs. An integral control action is also introduced in order to achieve zero steady-state error. In the case of MIMO systems, the proposed strategy can be applied to decouple the closed-loop control system choosing an appropriated reference model matrix. Two examples are presented to illustrate both SISO and MIMO systems control synthesis.     

On improving control-loop robustness of model-matching controllers

This note first characterizes the class of all stabilizing controllers for a two-degree-of-Freedom control system which achieve a prescribed achievable transfer function. The characterization is in terms of an arbitrary proper stable transfer function. With this characterization, robust model matching is formulated as a standard H^∞-optimization problem. This means that standard controller designs for a nominal plant, such as linear-quadratic Gaussian ones, can be enhanced to give improved robustness properties using H^∞-design techniques.     

Suboptimal exact model matching for multivariable systems withmeasurement noise

This paper describes a method for the design of discrete-time model matching control systems for a multivariable plant with measurement noise. This method uses a new parametrization for model matching controllers. Simulation results are presented which confirm the validity of the design method     

Minimal inversion,command matching and disturbance decoupling in multivariable systems

This paper addresses the two basic and related problems of minimal inversion and perfect output control in linear multivariable systems. A simple analytical expression is obtained for the inverse of the transfer-function matrix of a square multivariable system. This expression is then used to construct a minimal-order inverse of the system. It is shown that the poles of the minimal-order inverse are the transmission zeros of the system. As a result, necessary and sufficient conditions for existence and stability of the inverse system are stated simply in terms of the zero polynomial of the original system. Furthermore, the minimal-order inverse is shown to be proper provided the original system has a full rank feedthrough matrix. The related problem of perfect output control, namely command matching and disturbance decoupling, in linear multivariable systems by means of feedforward controllers is also formulated and solved in a transfer-function setting. It is shown that a necessary and sufficient condition for existence of the required controllers is that the plant zero polynomial is not identical to zero or unstable. The order of the required controllers is equal to the number of plant transmission zeros. The control scheme proposed in this paper is composed of a feedback controller to enhance system stability and robustness, a feedforward controller to ensure command matching, and another feedforward controller to achieve disturbance decoupling. The three controllers have no effect on each other and can therefore be designed independently. A number of numerical examples are discussed for illustration.     

内模统一预测控制的进一步分析

统一预测控制克服了一般预测控制器设计时难以比较每种控制器效果的缺点,将每 个问题的设计统一在一种框架下进行,设计费用也显著降低.对单输入单输出系统,统一预测 控制是一种优越的预测控制方法.采用内模结构就设计参数和模型匹配性对统一预测控制闭 环系统的跟踪性能和鲁棒性能的影响作更为详细的分析.从中可以看出内模结构在预测控制 中的独特优点.本文最后对一些结论给出了仿真结果.     

Model matching for finite-state machines

The problem of model matching for finite state machines (FSMs) consists of finding a controller for a given open-loop system so that the resulting closed-loop system matches a desired input-output behavior. In this paper, a set of model matching problems is addressed: strong model matching (where the reference model and the plant are deterministic FSMs and the initial conditions are fixed), strong model matching with measurable disturbances (where disturbances are present in the plant), and strong model matching with nondeterministic reference model (where any behavior out of those in the reference model has to be matched by the closed-loop system). Necessary and sufficient conditions for the existence of controllers for all these problems are given. A characterization of all feasible control laws is derived and an efficient synthesis procedure is proposed. Further, the well-known supervisory control problem for discrete-event dynamical systems (DEDSs) formulated in its basic form is shown to be solvable as a strong model matching problem with measurable disturbances and nondeterministic reference model     

Control of a grinding mill circuit using fractional order controllers

This paper presents the design and application of fractional single-input–single-output (SISO) controllers to a grinding mill circuit, which is a multiple-input–multiple-output (MIMO) process. Two kinds of controllers are presented: fractional order proportional-integral (FOPI) controllers, and a combination of FOPI and fractional order model reference adaptive controllers (FOMRAC). The parameters of the controller are tuned using off-line particle swarm optimization. In the presence of disturbances and process noise, the SISO fractional controllers achieve similar or better performance compared to linear model predictive control (LMPC).     

Design of linear time-invariant controllers for multirate systems

In this paper we discuss a frequency domain approach to model multirate single-input single-output (SISO) systems which facilitates design of linear time-invariant (LTI) controllers operating at the fast rate. To illustrate the approach we consider a dual-rate system with slow output measurements and fast control actions. We obtain necessary and sufficient conditions for the existence of stabilizing linear time-invariant (LTI) controllers for which model matching is also achieved at the fast rate with a desired single-rate system. Moreover, a solution to the problem of parameterizing the set of such LTI controllers is also given.     

Decentralized supervisory control with communicating controllers

The decentralized control problem for discrete-event systems addressed in this paper is that of several communicating supervisory controllers, each with different information, working in concert to exactly achieve a given legal sublanguage of the uncontrolled system's language model. A novel information structure model is presented for dealing with this class of problems. Existence results are given for the cases of when controllers do and do not anticipate future communications, and a synthesis procedure is given for the case when controllers do not anticipate communications. Several conditions for optimality of communication policies are presented, and it is shown that the synthesis procedure yields solutions, when they exist for this class of controllers, that are optimal with respect to one of these conditions     

Periodic sampling: maximising the sampling period

The process of periodic sampling is investigated for a class of nonlinear systems. The objective is to achieve the longest sampling period that is compatible with a specified error bound. It is shown that there are robust optimal controllers that achieve this objective. It is also shown that the performance of such optimal controllers can be approximated by bang-bang controllers – controllers that are relatively easy to design and implement.     

Universal controllers in model matching optimal control problems for unknown external signals

Linear-quadratic model matching optimal control problems are studied for unknown external signals and noise in the control plant. Given natural assumptions for two practically significant classes of external signals (stochastic with an unknown, rapidly decreasing spectral density and polyharmonic with the known spectrum and unknown amplitudes), controllers universal in the sense that they generate an optimal or approximately optimal process in the problem for any signal from the stated class are proved to exist. Linear controllers are shown to exist among them, with the class of linear universal controllers described exhaustively.     

Decentralized and adaptive control of multiple nonholonomic robots for sensing coverage

This work deals with decentralized control of multiple nonholonomic mobile sensors for optimal coverage of a given area for sensing purposes. We assume a density function over the region to be covered, which can be viewed as a probability density of the phenomena to be sensed. The density function is unknown but assumed to be linearly parameterized with unknown parameter weights. We consider a second‐order dynamic model for the mobile agents and derive decentralized adaptive control laws to achieve optimal coverage of the region. We then consider the case where the dynamic model of the agents are not fully known, and then develop parameter adaptation laws to achieve the optimal coverage objective. We test the derived algorithms using simulations and compare our proposed controllers with kinematics‐based controllers. We find that the feedback control design based on the dynamic model performs significantly better than controllers solely relying on kinematic models. Furthermore, for the unknown dynamics case, our controller outperforms the nonadaptive controller with poor initial parameter estimates.     

Design of sliding mode controllers for bilinear systems with time varying uncertainties.

Sliding mode controllers for the bilinear systems with time varying uncertainties are developed in this paper. The bilinear coefficient matching condition which is similar to the traditional matching condition for linear system is defined for the homogeneous bilinear systems. It can be seen that the bilinear coefficient matching condition is very limited and is not generally applicable to the nonhomogeneous bilinear system. Thus, the sliding coefficient matching condition is also considered for the bilinear systems with time varying uncertainties. Then, the sufficient conditions are provided for the reaching mode of the time varying uncertain bilinear systems to be guaranteed by the designed sliding mode controllers. Moreover, the stability of the uncertain bilinear systems with the sliding mode controller is discussed. Simulation results are included to illustrate the effectiveness of the proposed sliding mode controllers.     

Bio-inspired behaviour-based control

The design and development of conventional controllers for robot platforms are sometimes too complex to achieve due to the fact that they require an exact model of the system and of the operating environment. The ability to pre-account for unknown operating environments is an important task for the controller to be robust. In contrast, biological controllers are model free and are based on simple working principles. Due to natural biological principles these controllers are adaptive and more robust than their conventional counterparts. In this paper, a behaviour-based controller has been developed, inspired by the concept of spinal fields found in frogs and rats. The performance of the controller has been verified on a Khepera robot platform.     

Stabilization of sampled-data nonlinear systems via backstepping on their Euler approximate model

Two integrator backstepping designs are presented for digitally controlled continuous-time plants in special form. The controller designs are based on the Euler approximate discrete-time model of the plant and the obtained control algorithms are novel. The two control laws yield, respectively, semiglobal-practical stabilization and global asymptotic stabilization of the Euler model. Both designs achieve semiglobal-practical stabilization (in the sampling period that is regarded as a design parameter) of the closed-loop sampled-data system. A simulation example illustrates that the obtained controllers may sometimes be superior to backstepping controllers based on the continuous-time plant model that are implemented digitally.