Comparison of Mixed H 2 H∞ with Regional Pole Placement Control and H 2 Optimal Control for the Design of Steam Condenser

This paper investigates the comparison between mixed H 2 /H∞ with regional pole placement control and H 2 optimal control for the design of steam condenser. The comparison have been made for a step change in the steam condenser pressure set point for a step change of 10 & 23 seconds using MATLAB/Simulink environment for the steam condenser with mixed H 2 /H∞ with regional pole placement controller, steam condenser with H 2 optimal controller and steam condenser without controller. The steam condenser with mixed H 2 /H∞ with regional pole placement controller presented excellent and superior dynamic performance in response to the two step changes and an improvement in settling time. The overall simulation results demonstrated that the steam condenser with mixed H 2 /H∞ with regional pole placement controller can be an efficient alternative to the steam condenser with H 2 optimal controller for the steam condenser

Theoretical constraints in the design of multivariable control systems

The research being performed under NASA Grant NAG1-1361 involves a more clear understanding and definition of the constraints involved in the pole-zero placement or assignment process for multiple input, multiple output systems. Complete state feedback to more than a single controller under conditions of complete controllability and observability is redundant if pole placement alone is the design objective. The additional feedback gains, above and beyond those required for pole placement can be used for eignevalue assignment or zero placement of individual closed loop transfer functions. Because both poles and zeros of individual closed loop transfer functions strongly affect the dynamic response to a pilot command input, the pole-zero placement problem is important. When fewer controllers than degrees of freedom of motion are available, complete design freedom is not possible, the transmission zeros constrain the regions of possible pole-zero placement. The effect of transmission zero constraints on the design possibilities, selection of transmission zeros and the avoidance of producing non-minimum phase transfer functions is the subject of the research being performed under this grant

Coupled Riccati equations for complex plane constraint

A new Linear Quadratic Gaussian design method is presented which provides prescribed imaginary axis pole placement for optimal control and estimation systems. This procedure contributes another degree of design freedom to flexible spacecraft control. Current design methods which interject modal damping into the system tend to have little affect on modal frequencies, i.e., they predictably shift open plant poles horizontally in the complex plane to form the closed loop controller or estimator pole constellation, but make little provision for vertical (imaginary axis) pole shifts. Imaginary axis shifts which reduce the closed loop model frequencies (the bandwidths) are desirable since they reduce the sensitivity of the system to noise disturbances. The new method drives the closed loop modal frequencies to predictable (specified) levels, frequencies as low as zero rad/sec (real axis pole placement) can be achieved. The design procedure works through rotational and translational destabilizations of the plant, and a coupling of two independently solved algebraic Riccati equations through a structured state weighting matrix. Two new concepts, gain transference and Q equivalency, are introduced and their use shown

Pole Assignment With Improved Control Performance by Means of Periodic Feedback

This technical note is concerned with the pole placement of continuous-time linear time-invariant (LTI) systems by means of LQ suboptimal periodic feedback. It is well-known that there exist infinitely many generalized sampled-data hold functions (GSHF) for any controllable LTI system to place the modes of its discrete-time equivalent model at prescribed locations. Among all such GSHFs, this technical note aims to find the one which also minimizes a given LQ performance index. To this end, the GSHF being sought is written as the sum of a particular GSHF and a homogeneous one. The particular GSHF can be readily obtained using the conventional pole-placement techniques. The homogeneous GSHF, on the other hand, is expressed as a linear combination of a finite number of functions such as polynomials, sinusoidals, etc. The problem of finding the optimal coefficients of this linear combination is then formulated as a linear matrix inequality (LMI) optimization. The procedure is illustrated by a numerical example

Predictive pole-placement control with linear models

The predictive pole-placement control method introduced in this paper embeds the classical pole-placement state feedback design into a quadratic optimisation-based model-predictive formulation. This provides an alternative to model-predictive controllers which are based on linear–quadratic control. The theoretical properties of the controller in a linear continuous-time setting are presented and a number of illustrative examples are given. These results provide the foundation for novel linear and nonlinear constrained predictive control methods based on continuous-time models

Optimized estimator for real-time dynamic displacement measurement using accelerometers

This paper presents a method for optimizing the performance of a real-time, long term, and accurate accelerometer based displacement measurement technique, with no physical reference point. The technique was applied in a system for measuring machine frame displacement. The optimizer has three objectives with the aim to minimize phase delay, gain error and sensor noise. A multi-objective genetic algorithm was used to find Pareto optimal estimator parameters. The estimator is a combination of a high pass filter and a double integrator. In order to reduce the gain and phase errors two approaches have been used: zero placement and pole-zero placement. These approaches were analysed based on noise measurement at 0g-motion and compared. Only the pole-zero placement approach met the requirements for phase delay, gain error, and sensor noise. Two validation experiments were carried out with a Pareto optimal estimator. First, long term measurements at 0g-motion with the experimental setup were carried out, which showed displacement error of 27.6 ± 2.3 nm. Second, comparisons between the estimated and laser interferometer displacement measurements of the vibrating frame were conducted. The results showed a discrepancy lower than 2 dB at the required bandwidth

On Pole Placement and Invariant Subspaces

The classical eigenvalue assignment problem is revisited in this note. We derive an analytic expression for pole placement which represents a slight generalization of the celebrated Bass-Gura and Ackermann formulae, and also is closely related to the modal procedure of Simon and Mitter.Comment: Presented at ICAT201

Novel fuzzy logic controllers with self-tuning capability

Two controllers which extend the PD+I fuzzy logic controller to deal with the plant having time varying nonlinear dynamics are proposed. The adaptation ability of the first self tuning PD+I fuzzy logic controller (STPD+I_31) is achieved by adjusting the output scaling factor automatically thereby contributing to significant improvement in performance. Second controller (STPD+I_9) is the simplified version of STPD+I_31 which is designed under the imposed constraint that allows only minimum number of rules in the rule bases. The proposed controllers are compared with two classical nonlinear controllers: the pole placement self tuning PID controller and sliding mode controller. All the controllers are applied to the two-links revolute robot for the tracking control. The tracking performance of STPD+I_31 and STPD+I_9 are much better than the pole placement self tuning PID controller during high speed motions while the performance are comparable at low and medium speed. In addition, STPD+I_31 and STPD+I_9 outperform sliding mode controller using same method of comparison study

Intermittent predictive control of an inverted pendulum

Intermittent predictive pole-placement control is successfully applied to the constrained-state control of a prestabilised experimental inverted pendulum