Feedforward Matrix Research Articles

Linear Quadratic Optimal Robust Multivariable Proportional-Integral Control Design for a Boiler-Turbine Unit

Abstract Boiler-turbine unit is a highly nonlinear, coupled, and ill-conditioned system. Moreover, the presence of physical constraints, such as actuator magnitude and rate limits, makes the system difficult to control. This paper employs a fixed multivariable proportional-integral (PI) controller of the I–P structure for robust linear quadratic (LQ) compensation of a nonlinear boiler-turbine benchmark. In order to ensure that a single PI controller works for the whole operating region of this nonlinear system, the linearized model of the system is represented as a norm-bounded, time-varying uncertain system. The ranges of the uncertain parameters of this linearized model are determined from different operating points of the nonlinear system. To design the PI controller for the uncertain system, first, it is transformed into a state feedback design for an augmented uncertain system and then the state feedback gains satisfying some LQ performance limit are computed by solving a linear matrix inequality (LMI) problem. As the uncertainty in the feedforward matrix of the linearized model cannot be considered in the above design process, an LMI-based method is developed to check if the designed PI controller performance in H∞ sense is close to the one if the neglected uncertainty is included. The performance of the controller is tested on the nonlinear boiler-turbine unit under several operating conditions and physical constraints. Comparisons are also made with some existing PI controllers, to show the superiority of the proposed robust PI controller.

Learning-Ability of Discrete-Time Iterative Learning Control Systems with Feedforward

This paper considers the learning-ability for discrete-time iterative learning control (ILC) systems with feedforward. More specifically, the relation between the output realizability and the feedforward matrix is first established. Then, the learning-ability of four ILC systems is considered. It is shown that the proportional type (P-type) update law can only ensure the fully asymptotic learning-ability. By only using the feedforward matrix, a more efficient point-wise P-type update law is developed, which can ensure the fully -step learning-ability, where is the trial length. In the case that the state is measurable and controllable, it is proven that the update law with current state feedback can ensure the fully monotone learning-ability and the fully 2-step learning-ability, respectively. In addition, by only using the output data at the previous trial, a full output feedback update law is proposed, which can respectively ensure the fully 2-step learning-ability and the fully monotonic learning-ability.

A linear Bayesian filter for input and state estimation of structural systems

AbstractThis paper proposes a linear recursive Bayesian filter for minimum variance unbiased joint input and state estimation of structural systems. Unlike the augmented Kalman filter (AKF), the proposed filter falls within the category of Bayesian filters in which unknown inputs are estimated without attributing any fictitious input model or statistics. Also, in contrast with the existing algorithms in the latter category, such as the Gillijns and De Moor Filters (GDFs), the developed filter applies to systems with and without direct feedthrough, in particular, systems with a rank‐deficient feedforward matrix. Because of the latter features, the filter is referred to as universal filter (UF) for convenience. The numerical examples show that the UF performs better than the AKF. Due to its structure, the UF does not require the tuning of the hyperparameters for inputs, and therefore the problematic instability of the AKF is not encountered in the case of a large modeling error variance of the input. For systems with direct feedthrough, the error and covariance propagation terms differ due to the distinct state space. Consequently, the UF can enhance estimations due to the well‐conditionedness of the relevant inversion problem. Moreover, the UF can deal with systems with rank‐deficient feedforward matrix where these systems are not covered by GDFs.

Low power control for magnetically suspended control moment gyro based on current adaptive adjustment‐gimbal angular velocity feedforward method

Magnetically suspended control moment gyro (MSCMG) outputs gyro moment by changing the direction of the rotor angular momentum to adjust the spacecraft attitude. In the process of outputting moment, due to the moving-gimbal effect, the power consumption of magnetic bearing occupies a large proportion in MSCMG. The existing low power control methods have problems that adjustment time is long and the effect of reducing energy consumption depends on the model accuracy. To solve these problems, the method of current adaptive adjustment-gimbal angular velocity feedforward (CAA-GAVF) is proposed. The CAA-GAVF method controls rotor deflect actively so that the permanent magnet can generate moment to offset the coupling moment of moving-gimbal effect, thus reducing the power consumption of control current. In CAA-GAVF, the deflection angle of rotor is quickly adjusted by the feedforward of gimbal angular velocity. The current integral value is used to adjust the feedforward matrix adaptively and precisely. The experimental results show that the power consumption of CAA-GAVF method is reduced to 43.3% of the traditional control method.

Gimbal Angular Velocity Feedforward Method for Magnetically Suspended Control Moment Gyro with Hybrid Magnetic Bearing#

Control moment gyro(CMG) has the advantages of high precision and large output moment. It is the key actuator of agile spacecraft attitude control system. Magnetically suspended CMG(MSCMG) supports high-speed rotor through magnetic bearing, which has the advantages of no friction, no wear, high precision and long life. Hybrid magnetic bearing(HMB) generates bias magnetic field by replacing bias current with permanent magnet, which greatly reduces the power consumption. However, when MSCMG output moment, moving-gimbal effect makes the control current of HMB increase sharply, which result in the rapid increase of power consumption. To solve this problem, gimbal angular velocity feedforward(GAVF) method is proposed in this paper. Firstly, the model of HMB-rotor system containing moving-gimbal effect is established. Secondly, GAVF method is introduced to make the rotor deflect by designing a feedforward matrix with gimbal angular velocity and stiffness of HMB which is determined with rotor deflection angle and rotation speed. Thus, the gyroscopic moment is mainly offset by the bias magnetic field of HMB. Finally, an adaptive compensation method based on GAVF is proposed to maintain the system performance under parameter perturbation. By the above, the power consumption of control current during moment output process is reduced. Simulation and experiment results show the effectiveness of the proposed method.

Static output feedback passivation revisited and global asymptotic stabilizing properties of a controller

SummaryThe class of systems that can be globally asymptotically stabilized by the well‐known control law , is extended, in respect to literature. This control law is suitable for application to systems of unknown structure, and it is shown that it is more advantageous than the linear control law. The stability proof is based on solutions of a newly introduced problem, which is a specialization of the passivation by static output feedback control of a system with nonzero feedforward matrix. Necessary and sufficient conditions for existence of a solution of the problem are given, which include the minimum phase property of the given system. It is explained why the new concept cannot be applied to nonminimum phase systems. It is proved that a class of nonminimum phase systems can be stabilized by the same control law, where is a matrix function, rather than a constant matrix. Illustrative example are given.

Efficient vibro-acoustic identification of boundary conditions by low-rank parametric model order reduction

Abstract A novel method is presented that detects the proper boundary conditions of a test setup in a short time period by combing numerical models with experimental data. This allows for detection and localization of possible anomalies in the assumed boundary conditions of the system. The method works by combining a low-rank parametric model order reduction technique with a model updating strategy, where the boundary conditions of a numerical finite element model are updated by using frequency response function data. This combination makes it possible to update a large amount of parameters, because the assumed low-rank nature of the changes enables the use of non-parametric model order reduction techniques for the calculation of the reduced basis. This is possible, because the system can be rewritten in such a way that the parameter dependencies only show up in the feed-forward matrix of the system, thus no a priori sampling of the parameter space is required. Thus, the resulting model can identify a large amount of parameters, including the identification of local changes in the boundary conditions. The method is validated with a test-setup in which an aluminum plate is attached to an acoustic cavity and the boundary conditions are varied gradually, by removing the bolts that are clamping the plate. By applying the proposed model updating scheme to the rotational stiffness along the edge in combination with an additional damping term, it is shown that the proposed method can detect which bolts are removed and also leads to a good match in the frequency response functions. Moreover, it is shown that these results are achieved in only a few minutes, in contrast to the same procedure with full order models.

Control of Rotor's Vernier-Gimballing for a Magnetically Suspended Flywheel

For a magnetically suspended flywheel (MSFW) with two degree of freedom radial magnetic bearings (2-DOF RMBs), both the Vernier-gimballing control method and the Vernier-gimballing characteristics are researched to make the spinning rotor tilt around the radial axes by a pair of 2-DOF RMBs to generate a large torque. The process of Vernier-gimballing is analyzed and the model of rotor's Vernier-gimballing is established based on the presented 2-DOF RMBs, and the gyroscopic coupling is pointed out originally as the main problem in rotor's Vernier-gimballing control. To solve this problem, the reasons of Vernier-gimballing control precision's degradation are researched and the compensation torques generated by a novel feedforward matrix (FFM) are presented considering the negative displacement–force stiffness of 2-DOF RMB. Simulations and series of experiments done on an MSFW with 50 N · m · s angular momentum indicated that this presented control method with an FFM and compensation of negative displacement–force stiffness can effectively improve the precision of rotor's Vernier-gimballing control.

Direct yaw moment control for distributed drive electric vehicle handling performance improvement

For a distributed drive electric vehicle (DDEV) driven by four in-wheel motors, advanced vehicle dynamic control methods can be realized easily because motors can be controlled independently, quickly and precisely. And direct yaw-moment control (DYC) has been widely studied and applied to vehicle stability control. Good vehicle handling performance: quick yaw rate transient response, small overshoot, high steady yaw rate gain, etc, is required by drivers under normal conditions, which is less concerned, however. Based on the hierarchical control methodology, a novel control system using direct yaw moment control for improving handling performance of a distributed drive electric vehicle especially under normal driving conditions has been proposed. The upper-loop control system consists of two parts: a state feedback controller, which aims to realize the ideal transient response of yaw rate, with a vehicle sideslip angle observer; and a steering wheel angle feedforward controller designed to achieve a desired yaw rate steady gain. Under the restriction of the effect of poles and zeros in the closed-loop transfer function on the system response and the capacity of in-wheel motors, the integrated time and absolute error (ITAE) function is utilized as the cost function in the optimal control to calculate the ideal eigen frequency and damper coefficient of the system and obtain optimal feedback matrix and feedforward matrix. Simulations and experiments with a DDEV under multiple maneuvers are carried out and show the effectiveness of the proposed method: yaw rate rising time is reduced, steady yaw rate gain is increased, vehicle steering characteristic is close to neutral steer and drivers burdens are also reduced. The control system improves vehicle handling performance under normal conditions in both transient and steady response. State feedback control instead of model following control is introduced in the control system so that the sense of control intervention to drivers is relieved.

A Unified Approach to Reduced-Redundancy Transceivers: Superfast Linear and Block-Iterative Generalized Decision Feedback Equalizers

This paper shows, under general input data models, how block memoryless equalizers should be formulated considering reduced-redundancy transmissions for superfast detection. We propose linear and DFE-based, both multicarrier (MC) and single-carrier-frequency-domain (SC-FD) transceivers, along with efficient methods for the equalizer calculation, in a unified manner. We argue that, under a one-tap block decision feedback, transmitted redundancy can be reduced below the minimum <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\lceil(L-1)/2\rceil$</tex></formula> samples allowed in the linear case, where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$L$</tex></formula> is the channel length, even down to zero-redundancy, with improved BER performance. This is quantified in light of the optimal reconstruction delay set for a minimum-norm zero-forcing feedforward matrix in terms of the channel zeros location. The proposed MC and SC-FD block DFEs do not cancel inter-block-interference (IBI) via zeros-jamming; Instead, it removes IBI completely, in part by decision-feedback, and in part by zero-padding, which allows for much lower redundancy transmissions. The remaining ISI is further eliminated through a one-step block-iterative-generalized-DFE (BI-GDFE) obtained in the minimum-mean-square-error (MMSE) sense. Unlike computationally demanding block DFEs that eliminate ISI via successive cancelation, the proposed DFE schemes are as efficient as a superfast block-linear equalizer, requiring at most 3 receive branches to realize the order- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M$</tex></formula> feedforward matrices in <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">${\cal O}(M \log M)$</tex></formula> operations.

On the Study of a Novel Decision Feedback Equalizer with Block Delay Detection for Joint Transceiver Optimization

This paper presents a novel decision feedback equalizer (DFE) with block delay detection for the joint transceiver design that uses channel state information (CSI). The block delay detection in the proposed DFE offers a degree of freedom for optimizing the precoder of the transmitter, provided the transmission power is constrained. In the proposed DFE, the feedforward matrix is devised to enable a block-based equalizer that can be cooperated with an intrablock decision feedback equalizer for suppressing the intersymbol interference (ISI) for the transmitted block with a certain block delay. In this design, the interblock interference (IBI) for the delay block is eliminated in advance by applying the recently developed oblique projection framework to the implementation of the feedforward matrix. With knowledge of full CSI, the block delay and the associated block-based precoder are jointly designed such that the average bit-error-rate (BER) is minimized, subject to the transmission power constraint. Separate algorithms are derived for directly determining the BER-minimized block delays for intrablock minimum mean-squared error (MMSE) and zero-forcing (ZF) equalization criteria. Theoretical derivations indicate that the proposed MMSE design simultaneously maximize the Gaussian mutual information of a transceiver, even under the cases of existing IBI. Simulation results validate the proposed DFE for devising an optimum transceiver with CSI, and show the superior BER performance of the optimized transceiver using proposed DFE. Relying on analytic results and simulation cases also builds a sub-optimum MMSE design of the proposed DFE using the BER-minimized block delay for ZF criterion, which exhibits almost identical BER performance as the proposed MMSE design in most of the signal-to-noise ratio (SNR) range.

A fast algorithm with convergence for generalized predictive function control of Hnon chaotic system

A kind of fast generalized predictive function control algorithm with convergence of tracking for Hnon chaotic system is proposed. First, based on the existing generalized predictive function control algorithm, the matrix inversion computation in the control law is avoided because special basis functions are selected according to the motion characteristics of chaotic system and the change trend of practical control input. Then, by introducing the determinate feedforward gain matrix into performance index function, it is convergent that the output of Hnon chaotic system follows reference signal. The simulated results show the effectiveness of this algorithm.

Optimal Linear Non-Regenerative Multi-Hop MIMO Relays with MMSE-DFE Receiver at the Destination

In this paper, we study multi-hop non-regenerative multiple-input multiple-output (MIMO) relay communications with any number of hops. We design the optimal source precoding matrix and the optimal relay amplifying matrices for such relay network where a nonlinear minimal mean-squared error (MMSE)-decision feedback equalizer (DFE) is used at the destination node. We first derive the structure of the optimal source and relay matrices. Then based on the link between most commonly used MIMO system design objectives and the diagonal elements of the MSE matrix, we classify the objective functions into two categories: Schur-convex and Schur-concave composite objective functions. We show that when the composite objective function is Schur-convex, the MMSE-DFE receiver together with the optimal source and relay matrices enable an arbitrary number of source symbols to be transmitted at one time, and yield a significantly improved BER performance compared with non-regenerative MIMO relay systems using linear receivers at the destination. We also show that for Schur-concave composite objective functions, the optimal source and relay matrices, and the optimal feed-forward matrix at the destination node jointly diagonalize the multi-hop MIMO relay channel, and thus in such case, the nonlinear MMSE-DFE receiver is essentially equivalent to a linear MMSE receiver.

Linear output feedback compensation of rank-one systems

A new method is presented for arbitrarily assigning the closed-loop poles of a linear multi-input/multi-output system using linear output feedback. The method employs a new notion of rank-one system representations and involves the use of state transformation matrices which preserve such representations while reducing the degree of the feedforward matrix.

Performance enhancement of limited-bandwidth active automotive suspensions by road preview

A refined approach for the implementation of preview control in discrete time based on methods from earlier work is given. This allows the use of multiple preview inputs and reduces the system order of a discrete-time preview system significantly with respect to former methods, while describing the dynamic system in an exact form and yielding an equivalent control law. This method is applied to a limited-bandwidth quarter-car system, which incorporates an actuator in series with a passive spring, the combination being in parallel with a passive damper. Control design is carried out using discrete-time linear quadratic regulator (LQR) theory with tyre deflection, suspension working space, vertical body acceleration and control demand. How the optimal preview control law works in a physical sense is worked out regarding the feedforward gain matrix. It is shown that, as a part of the optimal control strategy, the preview controller "concentrates" in some sense on what it can do best for any amount of preview time. The conclusions from that are backed up considering performance indices and their components for variation of preview time, actuator bandwidth and the constraints in the cost function. Emphasis is put on the investigation of how the actuator bandwidth influences the performance capabilities of the system. General relationships between cast reduction, cost-component reduction, preview time and system bandwidth are exposed. By increasing preview time, the cost function can be reduced until it reaches a saturation value, which depends on the actuator bandwidth chosen. Increasing the actuator bandwidth beyond a certain value has only a small influence on the preview time needed for the diminishing returns to set in. Improving the road holding requires fast actuators, but comparatively short preview distances. Ride comfort can be influenced by a rather slow controller, but requires a long preview time.

An optimal proportional-plus-integral/tracking control law for aircraft applications

An optimal proportional-plus-integral/tracking control law is formulated. The control law has a command augmentation system configuration suitable for implementation on a digital computer on-board an aircraft. The proposed configuration offers the flexibility for choosing a feedforward matrix incorporating a set of additional control elements and for shaping the transient response without affecting the steady-state tracking property. Assuming the system is open-loop stable, then in the presence of a "jam" the disengaged system will maintain the steady-state tracking property which is desirable for aircraft continuing their mission.

Generalization of decoupling control

This correspondence develops sufficient conditions for decoupling of an r -input m -output multivariable control system via control law with a rectangular feedforward matrix. A synthesis example of the decoupling control system is given and studied.

Stability of a discrete closed-loop system which includes a Kalman filter†

This paper describes a method of determining the stability at the sampling instants, of a discrete closed-loop system which includes a Kalman filter. This is done by determining the z-plane poles of a special augmented transition matrix. While this result stems from stochastic optimal control work, the method applies to any, not just optimal, values of the feedback matrix, M, and filter feedforward matrix K. It is still applicable when the filter model and the plant are dissimilar in coefficient values and order.