多重系统同时极点配置的动态补偿器的设计

本文研究了多重系统同时稳定或极点配置的控制器设计问题。同时稳定或极点配置是出于设计容错控制系统之所需。本文推导了由一个动态补偿器对多重系统进行同时极点配置的充分条件。对于单输入或单输出的情况,上述充分条件也是必要的。文章的最后给出了设计方法以及一个实例。     

Robust receding horizon control of constrained nonlinear systems

We present a method for the construction of a robust dual-mode, receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error. The controller is dual-mode. In a neighborhood of the origin, the control action is generated by a linear feedback controller designed for the linearized system. Outside this neighborhood, receding horizon control is employed. Existing receding horizon controllers for nonlinear, continuous time systems, which are guaranteed to stabilize the nonlinear system to which they are applied, require the exact solution, at every instant, of an optimal control problem with terminal equality constraints. These requirements are considerably relaxed in the dual-mode receding horizon controller presented in this paper. Stability is achieved by imposing a terminal inequality, rather than an equality, constraint. Only approximate minimization is required. A variable time horizon is permitted. Robustness is achieved by employing conservative state and stability constraint sets, thereby permitting a margin of error. The resultant dual-mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear, constrained systems     

Variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator

In this paper, a new variable structure control strategy for exponentially stabilizing chained systems is presented based on the extended nonholonomic integrator model, the discontinuous coordinate transformation and the “reaching law method” in variable structure control design. The proposed approach converts the stabilization problem of an n-dimensional chained system into the pole-assignment problem of an (n−3)-dimensional linear time-invariant system and consequently simplifies the stabilization controller design of nonholonomic chained systems.     

带有稀疏执行器故障的事件触发网络化系统容错控制

针对一类具有事件触发信息传输机制的网络化控制系统,对系统故障执行器个数进行稀疏约束,研究系统在有限个执行器失效情况下的指数稳定及控制器设计问题。将系统故障执行器个数的约束转化为对控制器增益矩阵行的势约束,利用混合整数方法来解决这类稀疏约束的容错控制问题。在此基础上,利用Lyapunov泛函方法,得出闭环系统在有限个执行器失效情况下系统呈指数稳定的充分条件以及具有行稀疏约束的控制器设计方法。最后,通过一个飞行控制系统的数值仿真实例验证所提控制方法的可行性和有效性。     

基于非线性映射的约束系统自适应反推控制

针对基于障碍Lyapunov函数的非线性约束系统反推控制中, 控制器结构复杂、约束量初值选取区间小、会引入额外参数等问题, 提出了一种新的基于非线性映射的自适应反推控制方案. 该方法扩大约束量的初值选取区间为整个约束区间, 增加了系统初值选取和控制器设计的便易性. 约束量被映射至实数空间中, 因此映射后的新系统可以直接应用反推法设计控制器, 简化了控制器结构且不会引入额外参数. 证明了映射前后系统具有一致的收敛性, 保证闭环系统所有信号一致有界, 并且跟踪误差渐近收敛于零. 仿真结果进一步验证了本文方法的有效性.     

Adaptive pole placement control of MIMO systems

An adaptive pole-assignment controller design for an MIMO (multi-input-multi-output) system is with unknown observability indexes or with an overparameterized system model is presented. The controller design algorithm and stability issues are addressed     

Control and simulation of a constrained dynamic two-link system

In this paper a solution to the attitude control problem of a two-link planar system, whose angular momentum about the centre of gravity is constant, is presented. Reference trajectories for simulating the motion of the constrained dynamic system are found by specifying the internal variables of the system and solving for the corresponding external variables. It is shown that the angular momentum constraint has quasi-holonomic character because it can be employed to reduce the dimensionality of the system by eliminating half a degree of freedom. A controller is designed for the reduced dynamic system and tested by digital computer simulation. It is shown that the same controller can be used for the unreduced system if the angular momentum constraint is a linear function of the states of the system. Such an approach, however, cannot be employed if the constraint is a non-linear function of the system state. In this case a controller must be designed which stabilizes both the system and the constraint equation. Computer simulations of the diving motion of a human are presented to illustrate the control approach.     

Robust Hybrid Control of Constrained Robot Manipulators via Decomposed Equations

Basing on a constraint Jacobian induced orthogonal decomposition of the task space and by requiring the force controller to be orthogonal to the constraint manifold, the dynamics of the constrained robots under hybrid control is decomposed into a set of two equations. One describes the motion of robots moving on the constraint manifold, while the other relates the constraint force with the hybrid controller. This decomposition does not require the solution of the constraint equation in partition form. In this setting, the hybrid control of constrained robots can be essentially reduced to robust stabilization of uncertain nonlinear systems whose uncertainties do not satisfy the matching condition. A continuous version of the sliding-mode controller (from Khalil [12]) is employed to design a position controller. The force controller is designed as a proportional force error feedback of high gain type. The coordination of the position controller and the force controller is shown to achieve ultimately bounded position and force tracking with tunable accuracy. Moreover, an estimate of the domain of attraction is provided for the motion on the constraint manifold. Simulation for a planar two-link robot constraining on an ellipse is given to show the effectiveness of a hybrid controller. In addition, the friction effect, viewed as external disturbance to the system, is also examined through simulations.     

Analytical performance prediction for robust constrained model predictive control

This paper presents a new analysis tool for predicting the closed-loop performance of a robust constrained model predictive control (MPC) scheme. Currently, performance is typically evaluated by numerical simulation, leading to an extensive computation when investigating the effect of controller parameters, such as the horizon length, the cost weightings and the constraint settings. The analytic method, in this paper, avoids this computational burden, thus enabling a rapid study of the trades between the design parameters and the performance. Previous work developed an MPC formulation employing constraint tightening to achieve robust feasibility and constraint satisfaction despite the action of an unknown but bounded disturbance. This paper shows that the expected performance of that controller can be predicted using a combination of the gains of two linear systems, the optimal control for the unconstrained system, and a candidate policy used in performing the constraint tightening. The method also accounts for the possible mismatch between the predicted level of disturbance and the actual level encountered. The analytic results are compared with simulation results for several examples and are shown to provide accurate predictions of performance and its variation with the system parameters.     

输入约束系统的滚动时域输出反馈控制方法研究

This paper addresses the H∞ output feedback control problem for discrete-time systems with actuator saturation. Initially, a constrained H∞ output feedback control approach is presented in the framework of linear matrix inequalities (LMI) optimization. Under certain assumptions on the disturbance energy bound, closed-loop H∞ performance is achieved. Furthermore, the moving horizon strategy is applied to an online management of the control performance so that the closed-loop system can satisfy control constraints in the case of unexpected large disturbances. A dissipation constraint is derived to achieve the moving horizon closed-loop system dissipative. Simulation results show that the constrained H∞ controller works effectively under the disturbance assumption and that the moving horizon H∞ controller can trade-off automatically between satisfying control constraints and enhancing performance.     

An extended divide-and-conquer algorithm for a generalized class of multibody constraints

An extension to the divide-and-conquer algorithm (DCA) is presented in this paper to model constrained multibody systems. The constraints of interest are those applied to the system due to the inverse dynamics or control laws rather than the kinematically closed loops which have been studied in the literature. These imposed constraints are often expressed in terms of the generalized coordinates and speeds. A set of unknown generalized constraint forces must be considered in the equations of motion to enforce these algebraic constraints. In this paper dynamics of this class of multibody constrained systems is formulated using a Generalized-DCA. In this scheme, introducing dynamically equivalent forcing systems, each generalized constraint force is replaced by its dynamically equivalent spatial constraint force applied from the appropriate parent body to the associated child body at the connecting joint without violating the dynamics of the original system. The handle equations of motion are then formulated considering these dynamically equivalent spatial constraint forces. These equations in the GDCA scheme are used in the assembly and disassembly processes to solve for the states of the system, as well as the generalized constraint forces and/or Lagrange multipliers.     

A novel approach to the explicit pole assignment self-tuningcontroller design

A recursive algorithm for the controller design phase of the adaptive pole assignment controller is presented. Compared to other pole-assignment adaptive controllers, the computation time to get the controller parameters is drastically reduced and the numerical stability of the controller parameters is increased. If persistent excitation is imposed, the system poles will be located at the desired position in the steady state and the global stability of the system can be easily obtained     

Force/motion control of constrained robots using sliding mode

A sliding mode control algorithm is presented for trajectory tracking of an end-effector on a constrained surface with specified constraint forces by using the theory of variable structure systems. The development of the algorithm is based on a new formulation of the dynamic model and the expansion of sliding surfaces to include the constraint force error. The proposed sliding controller is explicit, which ensures the occurrence of the sliding mode on the intersection of the surfaces. A detailed numerical example is presented to illustrate the method     

Contouring Control for Multi‐Axis Motion Systems With Holonomic Constraints: Theory and Application to a Parallel System

In this paper, the contouring control problem for the constrained multi‐axis motion system is studied. The method of equivalent errors, previously proposed for unconstrained motion systems, is generalized to the system with holonomic constraints. It is shown that the method can be applied to the constrained system provided that the constraints satisfy a proper condition. Because of the constraints, the states in the control law are not completely independent. The unavailable states can be estimated using linear approximation from the constraint equations. As an illustrative example, the proposed method is applied to a parallel motion system with complicated dynamics. A contouring controller is designed using the method of equivalent errors incorporated with integral sliding mode control. Simulation results for contouring circular, elliptic, and square paths verify the effectiveness of the proposed method.     

Optimal regulation of a cable suspended robot equipped with cable interfering avoidance controller

Closed-loop regulation of a spatial cable suspended robot is performed in this paper subject to maximizing the Dynamic Load Carrying Capacity (DLCC) of the end-effector while the cable interference is avoided actively. Optimization is performed between two predefined boundaries and considering the cable interference constraint. This constraint is satisfied by designing a controller which prevents the cables’ collision. The overall formulation of the closed-loop optimal control based on Feedback linearization is derived in this paper for planning the optimal path with the highest load capacity. Then a complementary adaptive controller is designed and implemented to the main controller which is responsible for providing cable interfering avoidance. The efficiency of the designed controller for preventing the cables’ collision is shown by performing and analyzing some comparative simulations conducted on an under constrained cable robot with six cables and six DOFs. All results related to regulation, tracking and DLCC are compared between the simple optimal closed-loop system and the system which is equipped with the proposed cable interfering avoidance controller. It is proved that the planned path satisfies cable interference constraint while its DLCCs are optimized.     

Adaptive pole-assignment subject to saturation constraints

This paper considers a class of type-1 plants and an adaptive pole-assignment control which is constrained by a saturation non-linearity. The adaptive control system is BIBO stable if a constrained parameter estimation algorithm is employed. Also, the desired system performance can be achieved under certain conditions.     

Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets

This paper studies the control of constrained systems whose dynamics and constraints switch between a finite set of modes over time according to an exogenous input signal. We define a new type of control invariant sets for switched constrained systems, called switch–robust control invariant (switch‐RCI) sets, that are robust to unknown mode switching and exploit available information on minimum dwell‐time and admissible mode transitions. These switch‐RCI sets are used to derive novel necessary and sufficient conditions for the existence of a control‐law that guarantees constraint satisfaction in the presence of unknown mode switching with known minimum dwell‐time. The switch‐RCI sets are also used to design a recursively feasible model predictive controller (MPC) that enforces closed‐loop constraint satisfaction for switched constrained systems. We show that our controller is nonconservative in the sense that it enforces constraints on the largest possible domain, ie, constraints can be recursively satisfied if and only if our controller is feasible. The MPC and switch‐RCI sets are demonstrated on a vehicle lane‐changing case study.     

MPC for tracking piecewise constant references for constrained linear systems

In this paper, a novel model predictive control (MPC) for constrained (non-square) linear systems to track piecewise constant references is presented. This controller ensures constraint satisfaction and asymptotic evolution of the system to any target which is an admissible steady-state. Therefore, any sequence of piecewise admissible setpoints can be tracked without error. If the target steady state is not admissible, the controller steers the system to the closest admissible steady state.These objectives are achieved by: (i) adding an artificial steady state and input as decision variables, (ii) using a modified cost function to penalize the distance from the artificial to the target steady state (iii) considering an extended terminal constraint based on the notion of invariant set for tracking. The control law is derived from the solution of a single quadratic programming problem which is feasible for any target. Furthermore, the proposed controller provides a larger domain of attraction (for a given control horizon) than the standard MPC and can be explicitly computed by means of multiparametric programming tools. On the other hand, the extra degrees of freedom added to the MPC may cause a loss of optimality that can be arbitrarily reduced by an appropriate weighting of the offset cost term.     

A unified approach for inverse and direct dynamics of constrained multibody systems based on linear projection operator: applications to control and simulation

This paper presents a unified approach for inverse and direct dynamics of constrained multibody systems that can serve as a basis for analysis, simulation, and control. The main advantage of the dynamics formulation is that it does not require the constraint equations to be linearly independent. Thus, a simulation may proceed even in the presence of redundant constraints or singular configurations, and a controller does not need to change its structure whenever the mechanical system changes its topology or number of degrees of freedom. A motion-control scheme is proposed based on a projected inverse-dynamics scheme which proves to be stable and minimizes the weighted Euclidean norm of the actuation force. The projection-based control scheme is further developed for constrained systems, e.g., parallel manipulators, which have some joints with no actuators (passive joints). This is complemented by the development of constraint force control. A condition on the inertia matrix resulting in a decoupled mechanical system is analytically derived that simplifies the implementation of the force control. Finally, numerical and experimental results obtained from dynamic simulation and control of constrained mechanical systems, based on the proposed inverse and direct dynamics formulations, are documented.     

Position and Force Control of Two Constrained Robotic Manipulators

In this paper, the problem of controlling two robotic manipulators handling a constrained object is addressed. First, a reduced order dynamic model of the system is obtained. Using this model, a controller that guarantees the asymptotic convergence of the position, the internal force, and the constraint force to their desired values is proposed. Simulation results for two three-link planar manipulators moving a constrained object demonstrate the effectiveness of the proposed controller.