Design of stable proportional-integral-plus controllers

There are a number of reasons why, in practical situations, implementation of an unstable dynamic controller may be undesirable. In particular, sensor failure can result in a forward path which is unstable and might severely damage the plant. As with many dynamic controller design techniques, the PIP design philosophy may produce controllers which stabilize the closed-loop system, but are themselves unstable. This paper builds upon the existing PIP design philosophy, introducing a design step which stabilizes the PIP controller. This design strategy not only stabilizes the controller, but also ensures that the equivalent closed-loop transfer function of the system remains identical (in the absence of model mismatch) to that of the original PIP closed-loop system.     

On the design of linear multivariable feedback systems via constrained nondifferentiable optimization in H/sup infinity / spaces

The design discussed is of linear, lumped, time-invariant, multivariable feedback systems, subject to various frequency and time-domain performance specifications. The approach is based on the use of stabilizing controller parametrizations which result in the formulation of feedback system design problems as convex, nondifferentiable optimization problems. These problems are solvable by recently developed nondifferentiable optimization algorithms for the constrained minimization of regular, uniformly locally Lipschitz continuous functions in R/sup N/.<>     

Remarks on strong stabilization and stable H/sup /spl infin// controller design

A state space based design method is given to find strongly stabilizing controllers for multiple-input-multiple-output plants (MIMO). A sufficient condition is derived for the existence of suboptimal stable H/sup /spl infin// controller in terms of linear matrix inequalities (LMIs) and the controller order is twice that of the plant. A new parameterization of strongly stabilizing controllers is determined using linear fractional transformations (LFTs).     

Robust and reliable H infinity controllers for discrete-time systems with parameter uncertainty and actuator failure

New robust and reliable H infinity control algorithms are suggested for discrete-time uncertain systems with time-varying norm-bounded parameter uncertainty in the state matrix as well as with actuator failure among a pre-specified subset of actuators. State feedback controllers can be obtained by deriving and solving modified parameter-dependent Riccati equations, which can stabilize the plant and guarantee a given H infinity-norm bound on attenuation of augmented disturbances - all admissible uncertainties as well as actuator failure. Two robust and reliable H infinity whether the process of fault accommodation is used or not. Performances of two controllers are evaluated through simulation studies for various failures. controllers are derived according to     

Design of stable decentralized adaptive model-following controllers for large-scale systems

A decentralized model reference adaptive control for a class of large-scale inter-connected systems is developed. The proposed scheme does not require identification of the system parameters, or satisfaction of perfect model-following conditions (PMFC). The boundedness of the output error and the controller parameters is guaranteed using Lyapunov stability theory. The effectiveness of the developed algorithm is demonstrated using a numerical example.     

Design of globally stable controllers for a class of chaotic systems

A simple method to design chaos suppressors for a class of chaotic systems that can be decomposed into a linear subsystem and a nonlinear subsystem whose states can be decoupled is presented. The method yields a constant state feedback controller and global stability of the controlled system. The proposed methodology is demonstrated on three well-known chaotic systems, the third-order Chua circuit, the fourth-order hyperchaotic Chua circuit and the hyperchaotic Ro¨ssler oscillator.     

离散对象的降阶H∞控制器设计

基于LMI方法,考虑了离散对象的阶数不超过广义对象阶的降阶H∞控制器存在性问题.通过3LMIs可解性条件的等价变换,给出了一个降阶控制器的上界.该上界可适用于奇异和非奇异对象两种情形,且在奇异情形不为已有结果蕴涵.证明是构造性的,当降阶控制器存在时,可以设计出这种控制器.最后给出了两个简单的算例,说明文中方法的可行性.     

Reduced-complexity nonlinear H/sup /spl infin// control of discrete-time systems

In this note, we describe a reduced-complexity solution to the nonlinear H/sup /spl infin// control problem. This reduction applies to systems where some of the states are perfectly known, and is an intermediate problem between full state feedback and the standard measurement feedback problem. The reduction of computational complexity is significant and of practical importance. Online implementation is feasible with 2003 computer technology for a range of practical engineering design problems.     

H/sub /spl infin// design with first-order controllers

The problem of determining all first order controllers (C(s)=(x/sub 1/s+x/sub 2//s+x/sub 3/)) which stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) plant of arbitrary order has been recently solved. In this note, these results are extended to determine the subset of controllers which also satisfy various robustness and performance specifications which can be formulated as specific H/sub /spl infin// norm constraints. The problem is solved by converting the H/sub /spl infin// problem into the simultaneous stabilization of the closed-loop characteristic polynomial and a family of related complex polynomials. The stability boundary of each of these polynomials can be computed explicitly for fixed x/sub 3/ by solving linear equations. The union of the resulting stability regions yields the set of all x/sub 1/ and x/sub 2/ which simultaneously satisfy the H/sub /spl infin// condition and closed-loop stability for a fixed x/sub 3/. The entire three-dimensional set meeting specifications is obtained by sweeping x/sub 3/ over the stabilizing range.     

A gradient method for computing the optimal H/sub infinity / norm

A fast algorithm for computing the optimal H/sub infinity / norm is presented. The algorithm is based on certain explicit computations of gradients. Examples are given to show that the gradient method is much faster than the bisection method. The gradient method can be used without the upper and lower bound computations. This could be a substantial additional saving because computing these bounds requires the computation of the H/sub infinity / norm.<>     

基于遗传算法的混合H 2 öH ∞状态反馈控制器

提出了应用遗传算法设计混合H2/H∞状态反馈控制器的一种方法.通过遗传算法对H∞控制器进行H2性能优化,从而设计出鲁棒性强并满足系统性能要求的混合H2/H∞状态反馈控制器.该方法采用实数编码、排序选择与最佳个体保存相结合的选择算子、实值中间重组的交叉算子和实值变异的变异算子,并在适应度函数中添加惩罚约束.对国产某型飞机进行仿真,结果表明得到的混合H2/H∞状态反馈控制器具有良好的H∞性能和H2性能.     

Design of pole placing controllers for stable and unstable systems with pure time delay

Based on improved low order dead time approximants or starting from an overall approximation of linear time invariant systems with pure time delay, pole placing controller design is applied. This procedure yields excellent results for stable and unstable systems. The main advantage of this approach is the use of well-known state feedback control methods which can be used to shape the closed-loop response in a desired manner. As long as the approximations are of sufficient quality, the closed loop transients of model and original loop coincide within small error limits.     

A parameterization of reduced stable models and controllers

This note addresses the problem of instability in both model and controller reduction methods based on similarity transformations. For a given model (controller) a general framework is proposed that parameterizes a large set of reduced models (controllers) that preserve the stability of the original model (closed loop system). In addition, a sufficient condition for the existence of such a framework is derived. As an application of the main results, it is shown how different reduction methods can be modified, if they fail to maintain stability.     

Reduced-order solutions for the singular H/sup /spl infin// filtering problem

We consider the filtering H/sup /spl infin// problem for linear time-varying systems. This problem has been already solved in the case when the direct feedthrough matrix F between the disturbance and the output vectors is full-row rank. Here, we consider the case when the problem is singular, that is when this feedthrough matrix is not full-row rank. We show that in this case a reduced-order observer can be designed to meet the desired performance. Moreover, we apply the obtained results to solve a particular H/sup /spl infin// singular output feedback problem.     

Design of robot controllers

The decoupling method is applied to the design of position-speed-acceleration and force/position-speed-acceleration robot controllers. For this purpose, the Cartesian approach and the decoupling method are used to derive the generating rules of the control laws to be implemented in these systems. In this paper, only the case of non-redundant robots is considered.     

Design of low‐order controllers satisfying sensitivity constraints for unstructured uncertain plants

This paper presents a simple analytically based algorithm for the design of reduced‐order controllers satisfying frequency‐dependent sensitivity specifications for SISO plants having unstructured uncertainty. The uncertainties can be additive as well as multiplicative, and can take the form of circles, polygons or sectors located around a nominal plant. Moreover, the circle radius and polygon and sector sizes may depend on the frequency. The proposed method is applicable to both continuous and discrete designs. Copyright © 2004 John Wiley & Sons, Ltd.     

Design of dynamic suboptimal low-order controllers on basis of the H∞-criterion

A design problem of dynamic reduced-dimension controllers according to the boundedness condition of the H_∞-norm of a transfer matrix of a closed system is studied. The problem of controller deflation is related to the solution to degenerate filtering problems (no noise of measuring) and to degenerate control problems (no control in a manipulated output). It was demonstrated that these problems can be solved on basis of the modified 2-Riccati approach, in which the “filtrating” (for a singular filtrating problem) or the “control” (for a singular control problem) Lurie-Riccati equations have a low order. An example of an optimal reduced-dimension controller design is given that illustrates the obtained results.     

Robust control of flexible structures with stable bandpass controllers

In this paper, a control law for the active vibration control of mechanical flexible systems is considered. The proposed strategy minimizes an index and results in a stable stabilizing controller with bandpass frequency shape, due to the presence of zeros at the origin. The control authority is thus effective in a chosen band of frequency, resulting in a selective broadband control action, as opposed to narrow-band (tonal) vibration reduction. Moreover, the explicit closed-form solution of the controller is also obtained, thus avoiding numerical calculation of the solution of the Riccati equations, which can be ill-conditioned in the case of very high-order, poorly damped flexible systems. The parametrization of all the controllers is also given and a family of controllers with the above properties is deduced. The case is also obtained as a byproduct. The controller is based on a colocated actuators/sensors pair strategy and numerical simulations are presented, showing the robustness of the proposed approach even for systems with zero damping. Finally, experimental results on a skin panel of a Boeing 717 aircraft also prove the effectiveness of the proposed approach in practical complex applications, with global vibration reduction performances.     

Nonlinear H/sub /spl infin// controllers for electromagnetic suspension systems

This note presents a unified framework to derive nonlinear H/sub /spl infin// state and output feedback controllers for magnetically levitated (Maglev) vehicles with controlled dc electromagnets, referred to as electromagnetic suspension systems. The theoretical exposition, based on the Taylor series expansion solution to the Hamilton-Jacobi-Isaacs inequality, is followed by an assessment of some of the practical issues in realizing the nonlinear controllers with a digital signal processor and embedded hardware. A select set of experimental results from a single-degree-of-freedom suspension system is included to highlight the effectiveness of the proposed nonlinear stateand output-feedback H/sub /spl infin// controllers to suppress guideway-induced disturbances.     

Design of PID controllers satisfying gain margin and sensitivity constraints on a set of plants

This paper presents a method for the design of PID-type controllers, including those augmented by a filter on the D element, satisfying a required gain margin and an upper bound on the (complementary) sensitivity for a finite set of plants. Important properties of the method are: (i) it can be applied to plants of any order including non-minimum phase plants, plants with delay, plants characterized by quasi-polynomials, unstable plants and plants described by measured data, (ii) the sensors associated with the PI terms and the D term can be different (i.e., they can have different transfer function models), (iii) the algorithm relies on explicit equations that can be solved efficiently, (iv) the algorithm can be used in near real-time to determine a controller for on-line modification of a plant accounting for its uncertainty and closed-loop specifications, (v) a single plot can be generated that graphically highlights tradeoffs among the gain margin, (complementary) sensitivity bound, low-frequency sensitivity and high-frequency sensor noise amplification, and (vi) the optimal controller for a practical definition of optimality can readily be identified.