A parameter space approach to constrained variance PID controller design

This paper presents a parameter space approach to constrained variance and minimum variance PID controller design for LTI models. The technique is based on rational transfer functions of the plant and noise models. Loci corresponding to a fixed variance can be mapped into parameter planes for PID and PI type controllers to graphically display regions which satisfy the constraint, thereby guiding a design to appropriate controller gains. Requirements for tracking regulation can be readily achieved without excessively increasing the output variance. The usual advantages of parameter space techniques apply where other design criteria may be superimposed, allowing multiple objectives to be achieved non-conservatively. The superposition of the parameter space boundaries from existing robust control techniques thus allows non-conservative robust minimum variance PID design. A design example compares the technique to an algebraic minimum variance design using an integrator when tracking is required.     

Stability regions in the parameter space: D-decomposition revisited

The challenging problem in linear control theory is to describe the total set of parameters (controller coefficients or plant characteristics) which provide stability of a system. For the case of one complex or two real parameters and SISO system (with a characteristic polynomial depending linearly on these parameters) the problem can be solved graphically by use of the so-called D-decomposition. Our goal is to extend the technique and to link it with general M-Δ framework. In this way we investigate the geometry of D-decomposition for polynomials and estimate the number of root invariant regions. Several examples verify that these estimates are tight. We also extend D-decomposition for the matrix case, i.e. for MIMO systems. For instance, we partition real axis or complex plane of the parameter k into regions with invariant number of stable eigenvalues of the matrix A+kB. Similar technique can be applied to double-input double-output systems with two parameters.     

A Hough transform based line recognition method utilizing both parameter space and image space

Hough Transform (HT) is recognized as a powerful tool for graphic element extraction from images due to its global vision and robustness in noisy or degraded environment. However, the application of HT has been limited to small-size images for a long time. Besides the well-known heavy computation in the accumulation, the peak detection and the line verification become much more time-consuming for large-size images. Another limitation is that most existing HT-based line recognition methods are not able to detect line thickness, which is essential to large-size images, usually engineering drawings. We believe these limitations arise from that these methods only work on the HT parameter space. This paper therefore proposes a new HT-based line recognition method, which utilizes both the HT parameter space and the image space. The proposed method devises an image-based gradient prediction to accelerate the accumulation, introduces a boundary recorder to eliminate redundant analyses in the line verification, and develops an image-based line verification algorithm to detect line thickness and reduce false detections as well. It also proposes to use pixel removal to avoid overlapping lines instead of rigidly suppressing the N×N neighborhood. We perform experiments on real images with different sizes in terms of speed and detection accuracy. The experimental results demonstrate the significant performance improvement, especially for large-size images.     

Stable inversion and parameter variations

As part of the process of automatically guiding an aircraft, we have been successful in using stable inversion to compute a desired bounded state trajectory and corresponding bounded control. In addition to this feedforward control, we must also construct a regulator to address modeling errors and disturbances. With respect to modeling errors we find that the stable inversion procedures used are so accurate that the regulator can assume a simple form, say a linear regulator about the desired trajectory. We show that under the appropriate assumptions, the bounded state trajectory and bounded control computed through stable inversion depend continuously on the parameters of the system. This is a consequence of a mathematical result that we prove about the continuous dependence of the “particular solution” of a time varying nonlinear system driven by a bounded input. This is distinct from the usual continuous dependence of the initial value problem for systems.     

Some remarks on a conjecture in parameter adaptive control

A.S. Morse has raised the following question: Do there exist differentiable functions

$\text{f:R}{}^2\text{→ R}\text{and}\text{g:R}{}^2\text{→ R}$

with the property that for every nonzero real number λ and every (x₀, y₀) ∈ $\text{R}$² the solution (x(t),y(t)) of

$\text{x}\text{?}\text{(t) = x(t) + λf(x(t),y(t))}$

,

$\text{y}\text{?}\text{(t) = g(x(t),y(t))}$

,

$\text{x(0) = x}{}_0\text{, y(0) = y}{}_0$

, is defined for all t ? 0 and satisfies

$\text{lim}\text{t → + ∞}$

and y(t) is bounded on [0,∞)? We prove that the answer is yes, and we give explicit real analytic functions f and g which work. However, we prove that if f and g are restricted to be rational functions, the answer is no.     

几种PID控制器参数整定方法的比较研究

本文以一阶惯性加时滞过程为研究对象，通过数字仿真和在实验室的物理对象进行的控制实验，研究了一些比较适合典型工业过程应用的PID整定方法的特点。本文选取了控制工程中常用的4：1衰减法、临界比例度法、鲁棒PID参数整定法和ISTE（Integral Squared Time-weighted Errors）最优参数整定法，从系统跟踪、抗干扰性能和鲁棒性方面进行了分析比较研究。数字仿真和物理对象的实时控制表明了这些方法有各自的优缺点，其中，鲁棒PID参数整定法和ISTE最优参数整定法在综合性能，特别是在系统的鲁棒性方面具有一定的优越性。本文的研究结果对于典型工业过程的PID控制器参数的整定有一定的借鉴作用。     

西门子变频器的应用 第3讲 MM4系列变频器在PID中的应用

PID控制是闭环控制中的一种常见形式。反馈信号取自传动系统的输出端,当输出量偏离所要求的给定值时,反馈信号成比例变化。在输入端,给定信号与反馈信号相比较,存在一个偏差值。对该偏差值,经过PID调节,变频器通过改变输出频率,迅速、准确地消除传动系统的偏差,回复到给定值。本文阐述了MM4系列变频器的PID功能。     

一种模糊PID控制在热工对象中的应用

本文研究一种新型模糊PD控制器在一般热工对象中的应用问题。由于热工对象存在参数时变的问题,因此本文采用仿真方法针对对象参数时变的情况进行了控制器的鲁棒性分析。针对多变量输入,模糊控制规则多而控制器不易实现这一问题,本文提供了一种结构简单、性能优良的一维模糊控制器与PD控制相结合的控制策略。这种控制结构很好的解决了模糊控制不跟踪输入的问题。     

Robust parameter synthesis for planar higher pair mechanical systems

We present a parameter synthesis algorithm for planar, higher pair mechanical systems. The input is a parametric model of a mechanical system (part shapes and configurations) with nominal values and tolerance intervals for the parameters. The output is revised parameter ranges that guarantee correct kinematic function for all system variations. Nominal values are changed when possible and tolerance intervals are shrunk as a last resort. The algorithm consists of a three-step cycle that detects and eliminates system variations with incorrect kinematic function. The first step finds points in parameter space whose kinematic variation is maximal. The maximum of the higher pairs are derived by contact zone construction and are then combined into system maximums. The second step tests the points for correct kinematic function using configuration space matching and kinematic simulation. The third step adjusts the parameter ranges to exclude the points that fail the test. The cycle repeats until every point exhibits correct function. We demonstrate the algorithm on five real-world examples.     

Continuous valuations of temporal logic specifications with applications to parameter optimization and robustness measures

Finding mathematical models satisfying a specification built from the formalization of biological experiments, is a common task of the modeler that techniques like model-checking help solving, in the qualitative but also in the quantitative case. In this article we define a continuous degree of satisfaction of temporal logic formulae with constraints. We show how such a satisfaction measure can be used as a fitness function with state-of-the-art evolutionary optimization methods in order to find biochemical kinetic parameter values satisfying a set of biological properties formalized in temporal logic. We also show how it can be used to define a measure of robustness of a biological model with respect to some temporal specification. These methods are evaluated on models of the cell cycle and of the MAPK signaling cascade.     

Optimization of PID controller with higher-order noise filter

The proposed PID controller optimization is based on the frequency response of a process G_p(s) and maximization of the proportional gain, under constraints on the desired sensitivity to measurement noise, desired maximum sensitivity and desired maximum complementary sensitivity. The set-point and load disturbance step responses with negligible overshoot are obtained for stable processes, processes with oscillatory dynamics, integrating and unstable processes. Simulations, with a band-limited white noise added to the controlled variable, and experimental results, on a laboratory thermal plant with noisy measurements, are used to demonstrate the effectiveness of the proposed PID optimization method.     

Performance and robustness trade-offs in PID control

Control design is a rich problem which requires consideration of many issues such as load disturbance attenuation, set-point tracking, robustness with respect to process variations and model uncertainty, and effects of measurement noise. The purpose of this paper is to provide insight into the trade-offs between performance and robustness explicitly. This is accomplished by introducing plots that show the trade-offs for PI and PID control. These also provide valuable understanding of design compromises used for common PI design methods.     

Basis functions and parameter optimisation in high-order iterative learning control

In this paper a new parameter-optimal high-order Iterative Learning Control (ILC) algorithms is proposed to extend the work of Owens and Feng [Parameter optimisation in iterative learning control. International Journal of Control 14(11), 1059-1069]. If the original plant is positive, this new algorithm will result in convergent learning where the convergence is monotonic to zero tracking error. If the original plant is not positive, it can be shown that by adding a suitable set of basis functions into the algorithm, the tracking error will again converge monotonically to zero. This provides a considerable improvement to earlier work on parameter-optimal ILC as it opens up the possibility of globally convergent algorithms for any linear plant G. The number of parameters needed to ensure convergence could, however, become large. The paper shows that the use of low-order parameterisations is capable of achieving much of the benefit achieved in the ‘ideal’ case.     

数控机床进给伺服系统神经网络自整定PID控制

在介绍BP神经网络结构和学习算法的基础上,给出了一种数控机床进给伺服系统基于BP神经网络的自整定PID控制算法,并设计了基于BP神经网络自整定PID控制器的结构.在Matlab仿真中证实,该算法减小了系统的调节时间,提高了系统的响应速度、抗干扰能力和对被控对象参数变化的适应能力.     

Exact controllability for singular distributed parameter system in Hilbert space

Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space. Necessary and sufficient conditions concerning the exact controllability are given. Relations between exact controllability and stability of singular distributed parameter system are specified.     

Stable on-line parameter identification with general knowledge on level of information noise discrete-time case

An on-line parameter identification problem is posed and solved for discrete-time systems with general knowledge on the level of the inherent information noise. The knowledge can be the bound on either the magnitude or the finite-index ^p norm, pε[1, ∞), of the noise. Based on the knowledge, a switching type gradient algorithm (or called gradient algorithm with dead zone) is proposed to estimate the parameters of the system from the available input-output data. In spite of the existence of the noise, this on-line algorithm guarantees that the estimation error is monotonically decreasing, and the parameter estimate is convergent to a steady-state value under a mild condition. Furthermore, the algorithm is stable in the sense that the estimation error will converge to zero as the bound on the noise gradually diminishes.     

A decomposable parameter space for the detection of ellipses

Hough transform is a well-known method for detecting parametric curves in binary images. One major drawback of the method is that the transform requires time and memory space exponential in the number of parameters of the curves. An effective approach to reduce both the time and space requirement is the parameter space decomposition. In this paper, we present two methods for the detection of ellipses based on the straight line Hough transform (SLHT).

The SLHT of a curve in the θ-π space can be expressed as the sum of two terms, namely, the translation term, and the intrinsic term. One useful property of this representation is that it allows the translation, rotation and intrinsic parametersof the curve be separated easily. Timing performance of the proposed methods compares favorably with the other Hough-based methods.     

一阶参数不确定滞后过程的鲁棒PID控制器设计

提出一种针对一阶参数不确定滞后过程的鲁棒PI／PID控制器优化设计方法。首先基于D-分割法技术,给出确定一阶参数不确定滞后过程的整个PI／PID控制器的可行鲁棒稳定域算法;在定义一个与控制器给定点跟踪性能、鲁棒性能和抗扰动性能相关的目标函数的基础上,给出PI／PID控制器设计的约束优化问题;最后应用一种启发式粒子群优化（PSO）算法对该约束问题进行求解。仿真结果表明,所提出的方法可得到更小的调节时间、更小的超调、较强鲁棒性和更好的抗扰动性能,表明了所提出的方法的有效性。     

参数自调整模糊控制器在空调器中的应用

针对空调系统的复杂情况,介绍了一种在线调整常规模糊控制器的量化因子和比例因子的设计方法,实时对常规模糊控制器进行优化。仿真表明,其动态性能和稳态性能都优于常规模糊控制器,具有良好的控制性能。     

模糊PID复合智能控制参数自整定研究

介绍了一种新的Fuzzy 自适应PID控制器的设计原理及参数自整定方法,该方法充分结合了常规PID与模糊控制的优点,将整个控制过程实施分段控制,通过分析PID参数在偏差调节中的作用,采用模糊控制来实现参数自整定。基于该思想,我们利用STC80C52RC设计了一种智能化温度控制仪,通过实践运行表明,其控制效果比常规单一控制更优越。