Digital controller design for multivariable systems with structural closed-loop performance specifications

The problem of the direct design of the closed-loop transfer function matrix is addressed for multivariable discrete systems. The limitations imposed by unstable zeros, time delays and the structure associated with these are quantified. A design procedure is formulated that provides the designer with quantitative measures for evaluating the tradeoffs between different closed-loop interaction structures and durations. The problem of intersample rippling is also considered. The procedure requires only linear-algebra operations, includes the eventual construction of the feedback controller in state space, and is presented in a way that allows its straightforward computer implementation.     

Balanced performance preserving controller reduction

Two methods for controller reduction based on the closed-loop system performance-preserving criterion are proposed. They are the closed-loop block balanced and the closed-loop structurally balanced truncating methods. Reduced-order controllers are obtained directly by solving the closed-loop system reduction problem with performance-preserving weights.     

Switching supervisory control based on controller falsification and closed-loop performance inference

The paper addresses two of the basic issues of switching supervisory control (SSC): controller falsification (CF) and inference of candidate loop behaviour (ICLB). CF is approached as a statistical fault detection problem in that the currently operating controller is falsified as soon as a divergence trend is detected. This is achieved by considering a statistic (or residual) in the form of a ratio of closed-loop variables, and the falsification test is carried out by comparing at each time the ratio statistic with a threshold. It is constructively shown that the thresholds can be fixed, irrespective of the disturbance intensity, in such a way that faults are detected with probability one while probability of false alarms can be made as small as we wish. The ICLB issue is approached by the virtual reference approach. This allows one to obtain an inference of the performance of a candidate loop via a mean-square average of suitably filtered prediction errors. It is shown how a supervisory logic can be built by combining the results on CF with those on ICLB.     

Performance preserving controller reduction via additiveperturbation of the closed-loop transfer function

An H_∞ performance preserving controller order reduction method is proposed. Here performance preservation indicates that the H_∞ norm bound of the closed loop transfer function with reduced-order controller is not greater than the H_∞ norm bound of the closed loop transfer function with full order controller. We assume additive perturbations to the closed-loop transfer function and obtain a sufficient condition for performance preservation. Two kinds of useful weightings are derived, and the controller reduction problem is solved via a frequency weighted model reduction problem     

一种检测闭环控制器及全温稳定性验证

提出一种基于比例—积分和相位超前校正的闭环控制器设计,并验证电路在全温状态下的稳定性。分析闭环控制器的工作原理和电路的设计方案,并对闭环控制器的电路进行了仿真,得到了比较理想的结果。在不同温度状态下检测电路的性能,实验结果显示温度不会影响控制器的稳定性,但会影响控制器的带宽。证明了在驱动回路和检测回路较小频率差的前提下,可通过控制系统的优化达到拓展带宽的目的,进一步提高了陀螺的动态性能。     

A controller perturbation technique for transferring closed-loop stability between systems

This brief paper presents a perturbation technique with which a controller stabilizing one plant may be modified so that it stabilizes a second, related plant. The proposed technique produces an internally stable loop for a broad class of linear systems without requiring any further calculations on the part of the designer. Four seemingly different examples are described in terms of this result.     

Synthesis of a closed-loop combined plant and controller model

In practice, a controlled system consists of two distinct entities: the plant and the controller. These two entities are coupled by a feedback mechanism to give the closed-loop behavior of the controlled system. Under this structure, the controlled behavior of the system can be analyzed by simulation which is costly and time consuming. In this study, we synthesize a combined plant and controller model. We consider the practical issues and propose a method which combines the advantages of Petri nets (PN) and the supervisory controller design based on Formal Language Theory. The resultant combined model is a PN and represents the controlled closed-loop behavior of the system. This model can be used for the functional and the performance analysis of the system, verification of the controller and the control code generation.     

MPC for tracking with optimal closed-loop performance

In the recent paper [Limon, D., Alvarado, I., Alamo, T., & Camacho, E.F. (2008). MPC for tracking of piece-wise constant references for constrained linear systems. Automatica, 44, 2382-2387], a novel predictive control technique for tracking changing target operating points has been proposed. Asymptotic stability of any admissible equilibrium point is achieved by adding an artificial steady state and input as decision variables, specializing the terminal conditions and adding an offset cost function to the functional.In this paper, the closed-loop performance of this controller is studied and it is demonstrated that the offset cost function plays an important role in the performance of the model predictive control (MPC) for tracking. Firstly, the controller formulation has been enhanced by considering a convex, positive definite and subdifferential function as the offset cost function. Then it is demonstrated that this formulation ensures convergence to an equilibrium point which minimizes the offset cost function. Thus, in case of target operation points which are not reachable steady states or inputs for the constrained system, the proposed control law steers the system to an admissible steady state (different to the target) which is optimal with relation to the offset cost function. Therefore, the offset cost function plays the role of a steady-state target optimizer which is built into the controller. On the other hand, optimal performance of the MPC for tracking is studied and it is demonstrated that under some conditions on both the offset and the terminal cost functions optimal closed-loop performance is locally achieved.     

Simplified procedure for classical controller design for linear closed-loop system with transport delay

For the servo designer who occasionally encounters transport delays in the linear stationary control loop, this note presents an easy-to-apply design guide that permits him to continue to equalize his control system with Bode plots and simple design equations. The results are generally very good.     

An approximate minimal time closed-loop controller for processes with bounded control amplitudes and rates

This paper presents a method for designing an approximate minimal time closed-loop controller for linear systems with bounded control amplitudes and rates. The method is based on obtaining an approximate functional expression (explicitly in terms of the state variables) that describes the minimal time isochrones of the system. This expression is obtained by a series of least-squares fits to the computed system states on the various isochrones. The computation of the system states on the isochrones and the determination of the approximate expressions are achieved off-line. For on-line operation, it is only required to store a limited number of coefficients of the approximate expressions, and to compute the closed-loop control function by some algebraic manipulation. Consequently, the on-line computer storage requirement as well as the on-line computation requirement is relatively small. Thus, the method is feasible for high-order practical systems. To evaluate its usefulness in applications, the scheme is used to design a fourth-order Ranger Block III Attitude Control System. The results are compared to those obtained by applying the minimal time open-loop control.     

Sampled-data controller reduction procedure

The problem of controller order reduction aimed at preserving the closed-loop performance of a sampled-data closed-loop system is investigated. Past sampling of the system at a multiple of the sampling frequency followed by lifting allows capturing of the system's intersample behavior and yields a time-invariant single-rate system; this then permits standard order-reduction ideas to be applied. Special weighting functions aimed at preserving the closed-loop transfer function are obtained, and weighted balanced truncation is used to reduce the controller, An example shows that without the use of fast-sampling, an unstable closed loop can result from the reduction     

HPP controller: a system controller for high performance computing

This paper introduces the design of a hyper parallel processing (HPP) controller, which is a system controller used in heterogeneous high performance computing systems. It connects several heterogeneous processors via HyperTransport (HT) interfaces, a commercial Infiniband HCA card with PCI-express interface, and a customized global synchronization network with self-defined high-speed interface. To accelerate intra-node communication and synchronization, global address space is supported and some dedicated hardware is integrated in the HPP controller to enable intra-node memory and shared I/O resources. On the prototype system with the HPP controller, evaluation results show that the proposed design achieves high communication efficiency, and obvious acceleration to synchronization operations.     

PID controller design for robust performance

This note is devoted to the problem of synthesizing proportional-integral-derivative (PID) controllers for robust performance for a given single-input-single-output plant in the presence of uncertainty. First, the problem of robust performance design is converted into simultaneous stabilization of a complex polynomial family. An extension of the results on PID stabilization is then used to devise a linear programming design procedure for determining all admissible PID gain settings. The most important feature of the proposed approach is that it computationally characterizes the entire set of the admissible PID gain values for an arbitrary plant.     

Accuracy-enhancing methods for balancing-related frequency-weighted model and controller reduction

We consider the solution of the balancing-related frequency-weighted model and controller reduction problems using accuracy enhanced numerical algorithms. We propose first new stability-enforcing choices of the frequency-weighted grammians which can guarantee the stability of reduced models for two-sided frequency weights. Then we show that for the frequency-weighted controller reduction problems with standard stability and performance-enforcing frequency weights the computation of the frequency-weighted grammians can be done by solving reduced order Lyapunov equations. For both frequency-weighted model and controller reduction problems we indicate how to compute the grammians directly in terms of their Cholesky factors. This allows the extension of the square-root and balancing-free accuracy-enhancing techniques to the frequency-weighted case.     

An improved closed-loop stability related measure forfinite-precision digital controller realizations

The pole-sensitivity approach is employed to investigate the stability issue of the discrete-time control system, where a digital controller implemented with finite word length (FWL), is used. A stability related measure is derived, which is more accurate in estimating the closed-loop stability robustness of an FWL implemented controller than some existing measures for the pole-sensitivity analysis. This improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output-feedback and observer-based controllers. A numerical example is used to verify the theoretical analysis and to illustrate the design procedure     

A closed-loop mass flow controller based on static solid-state devices

A mass flow controller, based on an integrated flow sensor and a thermally actuated solid state regulator, is presented. The sensor is a miniaturized differential calorimeter obtained by postprocessing a silicon chip fabricated by a standard microelectronic process. The regulator consists in a microchannel etched into the surface of a silicon substrate and sealed with a glass plate, joined to the silicon die using anodic bonding. Flow regulation is achieved by varying the channel temperature by means of a chromium resistor. The two devices are connected in closed-loop through a low noise-low offset electronic circuit. Experimental data, demonstrating the effectiveness of the flow controller, are presented. Limitations of the proposed approach and possible improvements are discussed.     

Characterization of allowable perturbations of a closed-loop systemwith pole-placement controller

The problem of determining stability of a closed-loop transfer function in the presence of coefficient perturbations is considered. The results of interval polynomial theory are used to characterize the allowable interval of variation     

连续搅拌反应釜过程的闭环增益成形PID控制器设计

针对连续搅拌反应釜（CSTR）系统控制问题,设计了一种基于闭环增益成形算法的PID控制器,以提高PID控制器设计的简洁性和鲁棒性。首先假设期望闭环回路传递函数有一阶形式,同时将受控对象的一阶传递函数和PID控制器构成实际闭环回路传递函数。然后,比较期望闭环回路传递函数和实际闭环回路传递函数,即可确定PID参数。最后,以某CSTR系统为例,利用该方法设计了PID控制器,并通过仿真结果比较,检验了该方法所得PID控制器的良好鲁棒稳定性和动态品质。     

Sensor and controller location problems for distributed parameter systems

Optimal location of point sensors and controllers in stochastic regulator problems for evolution equations is considered using a semigroup approach and the separation principle. The existence of an optimal location is established under very general hypotheses. The theory is illustrated by specializing to a diffusion equation and some computational results are presented.