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The balanced bridge feedback (BBF) technique developed in communication engineering is applied to the multiloop pointing control problem. Using colocated sensors, BBF decouples the motor loop from the mechanical plant and increases the feedback bandwidth in the motor and plant loops.
Several important aspects of the Regulator with a Prescribed Degree of Stability (RPDS) methodology and its applications are considered. The solution of the time varying RPDS problem as well as the characterization of RPDS closed loop eigenstructure properties are obtained. Based on the asymptotic behavior of RPDS root loci, a one step algorithm for designing Regulators with Prescribed Damping Ratio (RPDR) is developed. The robustness properties of RPDS are characterized in terms of the properties of the return difference and the inverse return difference matrices for the RPDS state feedback loop. This class of regulators is found to possess excellent multiloop margins with respect to stability and degree of stability properties. The ability of RPDS design to tolerate changing operating conditions and unmodelled dynamics are illustrated with a multiterminal dc/ac power system example. The output feedback realization of RPDS requires the use of Linear Quadratic Gaussian (LQG) methodology.
Singular value analysis can give conservative stability margin results. Applying structure to the uncertainty can reduce this conservatism. This paper presents flight-determined stability margins for the X-29A lateral-directional, multiloop control system. These margins are compared with the predicted unscaled singular values and scaled structured singular values. The algorithm was further evaluated with flight data by changing the roll-rate-to-aileron command-feedback gain by +/- 20 percent. Minimum eigenvalues of the return difference matrix which bound the singular values are also presented. Extracting multiloop singular values from flight data and analyzing the feedback gain variations validates this technique as a measure of robustness. This analysis can be used for near-real-time flight monitoring and safety testing.
Singular value analysis can give conservative stability margin results. Applying structure to the uncertainty can reduce this conservatism. This paper presents flight-determined stability margins for the X-29A lateral-directional, multiloop control system. These margins are compared with the predicted unscaled singular values and scaled structured singular values. The algorithm was further evaluated with flight data by changing the roll-rate-to-aileron-command-feedback gain by +/- 20 percent. Also presented are the minimum eigenvalues of the return difference matrix which bound the singular values. Extracting multiloop singular values from flight data and analyzing the feedback gain variations validates this technique as a measure of robustness. This analysis can be used for near-real-time flight monitoring and safety testing.
A single-engine, propeller-driven, general-aviation model was incorporated into the nonlinear simulation and into the linear analysis of root loci and frequency response. Full-scale wind tunnel data provided its aerodynamic model, and the thrust model included the airspeed dependent effects of power and propeller efficiency. Also, the parameters of the Jet Transport model were changed to correspond more closely to the Boeing 727. In order to study their effects on steady-state repsonse to vertical wind inputs, altitude and total specific energy (air-relative and inertial) feedback capabilities were added to the nonlinear and linear models. Multiloop system design goals were defined. Attempts were made to develop controllers which achieved these goals.
This report presents the development and application of a sensitivity analysis technique for multiloop flight control systems. This analysis yields very useful information on the sensitivity of the relative-stability criteria of the control system, with variations or uncertainties in the system and controller elements. The sensitivity analysis technique developed is based on the computation of the singular values and singular-value gradients of a feedback-control system. The method is applicable to single-input/single-output as well as multiloop continuous-control systems. Application to sampled-data systems is also explored. The sensitivity analysis technique was applied to a continuous yaw/roll damper stability augmentation system of a typical business jet, and the results show that the analysis is very useful in determining the system elements which have the largest effect on the relative stability of the closed-loop system. As a secondary product of the research reported here, the relative stability criteria based on the concept of singular values were explored.
Closed-loop stability is investigated for multivariable linear time-invariant systems controlled by optimal full state feedback linear quadratic (LQ) regulators, with nonlinear gains present in the feedback channels. Estimates are obtained for the region of attraction when the nonlinearities escape the (0.5, infinity) sector in regions away from the origin and for the region of ultimate boundedness when the nonlinearities escape the sector near the origin. The expressions for these regions also provide methods for selecting the performance function parameters in order to obtain LQ designs with better tolerance for nonlinearities. The analytical results are illustrated by applying them to the problem of controlling the rigid-body pitch angle and elastic motion of a large, flexible space antenna.
A multivariable control design method based on constrained parameter optimization was applied to the design of a multiloop aircraft flight control system. Specifically, the design method is applied to the following: (1) direct synthesis of a multivariable 'inner-loop' feedback control system based on total energy control principles; (2) synthesis of speed/altitude-hold designs as 'outer-loop' feedback/feedforward control systems around the above inner loop; and (3) direct synthesis of a combined 'inner-loop' and 'outer-loop' multivariable control system. The design procedure offers a direct and structured approach for the determination of a set of controller gains that meet design specifications in closed-loop stability, command tracking performance, disturbance rejection, and limits on control activities. The presented approach may be applied to a broader class of multiloop flight control systems. Direct tradeoffs between many real design goals are rendered systematic by this method following careful problem formulation of the design objectives and constraints. Performance characteristics of the optimization design were improved over the current autopilot design on the B737-100 Transport Research Vehicle (TSRV) at the landing approach and cruise flight conditions; particularly in the areas of closed-loop damping, command responses, and control activity in the presence of turbulence.
Measurements of driver describing functions in steering control tasks have been made using a driving simulator. The task was to regulate against a random crosswind gust input on a straight roadway, in order to stay in the center of the lane. Although driving is a multiloop task in general, the forcing function and situation were configured so that an inner-loop visual cue feedback of heading angle of heading rate would dominate, and the driver's response was interpreted to be primarily single-loop. The driver describing functions were measured using an STI describing function analyzer. Three replications for each subject showed good repeatability within a subject. There were some intersubject differences as expected, but the crossover frequencies, effective time delays, and stability margins were generally consistent with the prior data and models for similar manual control tasks. The results further confirm the feasibility of measuring human operator response properties in nominal control tasks with full (real-world) visual field displays.
Stability margin for multiloop flight control systems has become a critical issue, especially in highly maneuverable aircraft designs where there are inherent strong cross-couplings between the various feedback control loops. To cope with this issue, we have developed computer algorithms based on non-differentiable optimization theory. These algorithms have been developed for computing the Multivariable Stability Margin (MSM). The MSM of a dynamical system is the size of the smallest structured perturbation in component dynamics that will destabilize the system. These algorithms have been coded and appear to be reliable. As illustrated by examples, they provide the basis for evaluating the robustness and performance of flight control systems.
Distributed RC active two-port network and voltage amplifier provides advantage over lumped elements in that second-order bandpass function is obtained with single distributed passive element. Incorporating positive and negative feedback loops provides improvement in Q, sensitivity, and gain-Q sensitivity product compared to single-loop networks.
A hybrid state-space controller is developed for suboptimal digital control of multirate multiloop multivariable continuous-time systems. First, an LQR is designed for a continuous-time subsystem which has a large bandwidth and is connnected in the inner loop of the overall system. The designed LQR would optimally place the eigenvalues of a closed-loop subsystem in the common region of an open sector bounded by sector angles + or - pi/2k for k = 2 or 3 from the negative real axis and the left-hand side of a vertical line on the negative real axis in the s-plane. Then, the developed continuous-time state-feedback gain is converted into an equivalent fast-rate discrete-time state-feedback gain via a digital redesign technique (Tsai et al. 1989, Shieh et al. 1990) reviewed here. A real state reconstructor is redeveloped utilizing the fast-rate input-output data of the system of interest. The design procedure of multiloop multivariable systems using multirate samplers is shown, and a terminal homing missile system example is used to demonstrate the effectiveness of the proposed method.
A proposed multiloop power supply would generate a potential as high as 1.25 kV with rise and fall times <100 s. This power supply would, moreover, be programmable to generate output potentials from 20 to 1,250 V and would be capable of supplying a current of at least 300 A at 1,250 V. This power supply is intended to be a means of electronic shuttering of a microchannel plate that would be used to intensify the output of a charge-coupled-device imager to obtain exposure times as short as 1 ms. The basic design of this power supply could also be adapted to other applications in which high voltages and high slew rates are needed. At the time of reporting the information for this article, there was no commercially available power supply capable of satisfying the stated combination of voltage, rise-time, and fall-time requirements. The power supply would include a preregulator that would be used to program a voltage 1/30 of the desired output voltage. By means of a circuit that would include a pulse-width modulator (PWM), two voltage doublers, and a transformer having two primary and two secondary windings, the preregulator output voltage would be amplified by a factor of 30. A resistor would limit the current by controlling a drive voltage applied to field-effect transistors (FETs) during turn-on of the PWM. Two feedback loops would be used to regulate the high output voltage. A pulse transformer would be used to turn on four FETs to short-circuit output capacitors when the outputs of the PWM were disabled. Application of a 0-to-5-V square to a PWM shut-down pin would cause a 20-to-1,250-V square wave to appear at the output.