Quantitative non-linear compensation design for saturating unstable uncertain plants

Consider an unstable uncertain plant controlled by an element Np, which saturates when its input |x| ≥ M. The system can be stabilized by means of feedback, which, however, is absent during Np saturation. If the saturation interval is long enough, it is impossible to recover system stability via Np. This paper presents a synthesis technique for ensuring that Np does not saturate despite very large command inputs. The basic idea is to prevent |x|>M, via an added saturating element N with saturation level m, which in turn is determined by |x|. A systematic, quantitative design technique is presented for unstable plants with large uncertainty, to achieve (a) desired performance tolerances over the linear range (small command inputs) and (b)acceptable but unavoidably slower response for large command inputs. Both (a) and (b) are achieved over the specified extent of plant uncertainty. The design technique makes use of several previously developed quantitative synthesis theories for minimum- and non-minimum-phase uncertain plants in linear operation, and for uncertain minimum-phase stable plants subject to saturation.     

The design of servomechanism controllers for uncertain plants

The design of multivariable servomechanism controllers is considered here for plants whose parameters are uncertain or perturbed within a cone-bounding criterion. The solution comes from a controller design problem as an LQ optimal control problem in which the gain matrices result in a quadratic performance upper bound (similar to that described by Gilman and Rhodes (1976() which depends on the uncertainty. Under conditions on the nominal plant and on the uncertainty, a resulting linear time-invariant controller is guaranteed to achieve the objectives of robust tracking and regulation with closed-loop stability.     

Quantitative design for SISO non-minimum-phase unstable plants by the singular-G method

It has been shown how a single-input-single-output (SISO) plant can be converted by several independent samplings of the output, into an equivalent multiple-input-multiple-output one, with respect to feedback system stability. The singular-G method may then be used to stabilize the system despite plant uncertainty. Only qualitative properties were previously presented. This paper presents a quantitative design procedure for such uncertain SISO plants with right half-plane poles and zeros, and some of the costs thereby incurred. The inherently large loop sensitivity is transferred from the plant to the compensators. Plant disturbances are greatly amplified rather than attenuated. But for a large class of such uncertain plants, stabilization and reasonable command response are possible.     

逆向物流流量不确定闭环供应链鲁棒运作策略设计

考虑一类同时具有再分销、再制造和再利用的闭环供应链在逆向物流流量不确定环境下的运作问题.采用具有已知概率的离散情景描述逆向物流流量的不确定性,利用基于情景分析的鲁棒线性优化方法建立该闭环供应链的多目标运作模型.设计了一个数值算例,其结果验证了运作策略的鲁棒性.在该算例基础上,分析了逆向物流流量的大小对闭环供应链系统运作性能的影响.     

QFT design for uncertain non-minimum phase and unstable plants revisited

Design method for uncertain non-minimum phase and unstable plants in the quantitative feedback theory (QFT) developed by Horowitz and Sidi is revisited in this paper. It is illustrated that the existing method may not work since some design rules have not been clearly specified by several examples including non-minimum phase plants and unstable plants. Then stability of a new nominal plant is carefully examined and analysed, and an improved design method is presented. The result in this paper provides mathematical justification of the QFT design procedure for nonminimum phase and unstable plants in Horowitz and Sidi (1978) and Horowitz (1992).     

The design of servomechanism controllers for uncertain plants and input signals

This paper summarizes a methodology for the design of servomechanism controllers for multivariate plants and reference/disturbance signals which may be uncertain or weakly non-linear. This framework represents a departure from the idealized tracking/disturbance rejection problem in the direction of realistic design considerations. The objective becomes ‘good’, though not exact, error regulation for applied signals which may be unknown or random in nature.     

A method to design multirate controllers for plants sampled at alow rate

Classical discrete control systems allow control of the output of a plant at sampling instants. If control of the output between sampling instants is required, a multirate controller can be used. An analytical procedure is developed that allows feedforward control of the output at multirate instants and feedback control at sampling instants. The method proposed is a practical approach to the model-matching problem and takes into account the intersampling dynamics of the system     

Equivalent transfer function method for PI/PID controller design of MIMO processes

In this paper, a novel engineering oriented control system design method for multivariable processes is presented. By employing the concepts of energy transmission ratio and effective relative gain, an equivalent transfer function matrix for closed loop control system can be obtained. Based on the equivalent transfer function matrix, both off-diagonal decoupling controllers and main loop diagonal controllers can be easily designed using the existing PI/PID tuning rules. The main advantages of the method are that: (1) the overall control system performance is better compared with the existing decoupling control methods; (2) it is very simple which can be easily understood and implemented by field control engineers; and (3) the control system is robust, it can still work with satisfactory performance even under significant model mismatches. Several multivariable industrial processes with different interaction characteristics are employed to demonstrate the simplicity and effectiveness of the design method.     

时变不确定系统鲁棒控制器设计的新方法

基于包含两个二次项的分段Lyapunov函数,研究了线性时变不确定系统的鲁棒控制器设计问题.所考虑的系统由两个矩阵的凸组合构成,通过引入一个附加矩阵,推导出鲁棒控制器存在的充分条件.该控制器的状态反馈增益的求解问题可以转化为一组带有两个比例参数的线性矩阵不等式的凸优化问题.最后的数值示例说明了该设计方法的可行性.     

An LMI-based switching surface design method for a class of mismatched uncertain systems

In this note, we consider the problem of designing linear sliding surfaces for multivariable uncertain systems with mismatched uncertainties in the state matrix. In terms of linear matrix inequalities, we give a new invariance condition guaranteeing the existence of a linear switching surface such that the reduced-order equivalent sliding mode dynamics restricted to the switching surface is not only stable but completely invariant to mismatched uncertainties. We also give an explicit formula of such linear switching surfaces, together with a design example.     

An analysis and design method for uncertain variable structure systems with bounded controllers

We present a method for estimating the asymptotic stability region(ASR) of uncertain variable structure systems with bounded switching feedback controllers. Using linear matrix inequalities(LMIs) we estimate the ASR and we show the exponential stability of the closed-loop control system in the estimated ASR. We also give a simple LMI-based method for designing switching surfaces that will make the estimated ASR big. Finally, we give numerical examples in order to show the effectiveness of our method.     

Time-varying sliding mode control for a class of uncertain MIMO nonlinear system subject to control input constraint

To solve the regulator problem of a class of uncertain MIMO nonlinear systems subject to control input constraint, three types of time-varying sliding mode control laws are proposed. The sliding surfaces pass the initial value of the system at the initial time, and are shifted/rotated towards the predetermined ones. The controller parameters are optimized by genetic algorithm (GA). Lyapunov method is adopted to prove the stability and robustness to the parameter uncertainties and external disturbance. By me...     

Decomposed control design for non-stationary plants subject to disturbances

This paper combines the block (Luk'yanov and Utkin 1982, 1998), sliding mode and high gain control techniques (Utkin 1992) to form a new decomposed control law suitable for general multivariable non-stationary plants. Different versions of the control law are developed with various dependencies on plant parameters and state variables. The new control law is demonstrated by simulation of its application to an electrical drive employing a dc motor with controlled flux.     

An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems

In this paper, an optimal adaptive robust PID controller based on fuzzy rules and sliding modes is introduced to present a general scheme to control MIMO uncertain chaotic nonlinear systems. In this control scheme, the gains of the PID controller are updated by using an adaptive mechanism, fuzzy rules, the gradient search method, and the chain rule of differentiation in order to minimize the sliding surfaces of sliding mode control. More precisely, sliding mode control is used as a supervisory controller to provide sufficient control inputs and guarantee the stability of the control approach. To ascertain the parameters of the proposed controller and avoid trial and error, the multi-objective genetic algorithm is employed to augment the performance of proposed controller. The chaotic system of a Duffing-Holmes oscillator and an industrial robotic manipulator are the case studies to evaluate the performance of the proposed control approach. The obtained results of this study regarding both systems are compared with the outcomes of two notable studies in the literature. The results and analysis prove the efficiency of the proposed controller with regard to MIMO uncertain systems having challenging external disturbances in terms of stability, minimum tracking error and optimal control inputs.     

An LMI approach to design robust fault detection filter for uncertain LTI systems

In this paper, the robust fault detection filter design problem for uncertain linear time-invariant (LTI) systems with both unknown inputs and modelling errors is studied. The basic idea of our study is to use an optimal residual generator (assuming no modelling errors) as the reference residual model of the robust fault detection filter design for uncertain LTI systems with modelling errors and, based on it, to formulate the robust fault detection filter design as an H_∞ model-matching problem. By using some recent results of H_∞ optimization, a solution of the optimization problem is then presented via a linear matrix inequality (LMI) formulation. The main results include the development of an optimal reference residual model, the formulation of robust fault detection filter design problem, the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the LMI solution parameters, the determination of adaptive threshold for fault detection. An illustrative design example is employed to demonstrate the effectiveness of the proposed approach.     

A型漏电保护器脱扣电流一致性的创新设计

提出了一种减小A型漏电保护器最小脱扣电流离散性的创新方法,在一个周期中采用不同的连续时间段检测,识别剩余电流的类型和判断它的均方根值是否超过了额定值。在开始计时后,0~3 ms时间内检测±135°的漏电电流,3~7 ms内检测±90°的漏电电流,7~12 ms内检测±0°的漏电电流,3~7 ms以及12~16 ms时间内检测AC型的漏电电流。芯片采用0.5μm数模混合COMS工艺制作。测试结果表明,A型漏电保护器的脱扣电流的离散减小到了2.8 m A,极大地提高了芯片的可靠性和抗干扰性。     

防止OFDM天线放大器峰值削波的AMAPR帧加权方法

OFDM系统由于子载波数目庞大,具有较大的动态信号范围和非常高的峰均功率比(PAPR),往往造成天线放大器的非线性失真和峰值削波,从而增加系统的误码率。较为先进的算法是利用峰值因数PAR对输入信号进行加权,降低了峰均功率比PAPR,但该算法使得输入信号大幅衰减,信噪比迅速减小,误码率增加。基于上述问题,提出新的,利用AMAPR(信号峰值与天线放大器极大值比)进行帧加权的计算方法,当某一帧最大功率大于放大器的线性区间,再对该帧实现线性补偿方法。逐帧计算加权系数,尽最大可能提高输入信号的信噪比。通过仿真,验证了AMAPR帧加权算法能防止峰值削波,改进误码率性能,防止信号的大幅度衰减,实现了低成本天线放大器的线性补偿。     

A new approach to adaptive control design without overparametrization for a class of uncertain nonlinear systems

This paper considers the globally stabilizing adaptive controller design for a class of more general uncertain high-order nonlinear systems with unknown control coefficients.Although the existing literature has solved the problem,for n-dimensional systems,the existing methods need at least n + 1 dynamic updating laws for the unknown parameters to construct the stabilizing adaptive controller;that is,the dimension of the dynamic compensator is not less than n + 1,and therefore,there exists serious overparame...     

一类不确定非线性系统无过参数自适应控制设计新方法

文中研究了一类控制系数未知的更一般高阶不确定非线性系统的全局稳定自适应控制设计问题.尽管现有文献已解决了该问题,但对于n维系统,现有构造稳定自适应控制的方法至少需要设计n+1个未知参数的动态调节律,即动态补偿器的维数至少为n+1,存在较为严重的过参数问题.文中通过定义新的需动态调节的未知参数,运用增加幂积分和有关自适应技术,成功地解决了已有方法中的过参数问题,给出了构造只含有一个参数调节律的稳定自适应控制设计新方法.仿真算例验证了文中所给方法的有效性.