Study of a Simulation Tool To Determine Achievable Control Dynamics and Control Power Requirements With Perfect Tracking

This paper contains a study of two methods for use in a generic nonlinear simulation tool that could be used to determine achievable control dynamics and control power requirements while performing perfect tracking maneuvers over the entire flight envelope. The two methods are NDI (nonlinear dynamic inversion) and the SOFFT (Stochastic Optimal Feedforward and Feedback Technology) feedforward control structure. Equivalent discrete and continuous SOFFT feedforward controllers have been developed. These equivalent forms clearly show that the closed-loop plant model loop is a plant inversion and is the same as the NDl formulation. The main difference is that the NDl formulation has a closed-loop controller structure whereas SOFFT uses an open-loop command model. Continuous, discrete, and hybrid controller structures have been developed and integrated into the formulation. Linear simulation results show that seven different configurations all give essentially the same response, with the NDI hybrid being slightly different. The SOFFT controller gave better tracking performance compared to the NDI controller when a nonlinear saturation element was added. Future plans include evaluation using a nonlinear simulation. Introduction There is a need within the aerospace community for a generic nonlinear piloted simulation tool that can be used to determine achievable control dynamics and control power requirements while it is performing perfect tracking maneuvers over the entire flight envelope. For this application the control law needs to be simple, and ideally it should be applicable to any aircraft without the need for adjustments. In addition, control law robustness should never be an issue. A simulation tool such as this would potentially have many applications within the control and general aerospace communities. One application of this tool would allow a quick and easy comparison of various aerodynamic databases, while performing the same maneuvers. These databases could range from crude to high fidelity and could be used at various stages of development. This capability might be particularly important during evaluation of some of the novel control effector concepts presently being explored (ref. 1). A designer could adjust various parameters and evaluate force and moment capability relative to the entire aircraft database, and it could be done at various stages of development. A second application could be the adjustment of flying qualities with pilot ratings while performing a variety of expected worst-case maneuvers. This application could help determine achievable dynamics and give the control designer guidelines for the best performance possible. Having this information, the designer could be more efficient while trying to improve performance. Another example is the development of guidelines for reconfigurable control systems to accommodate failures. Control allocation configurations could also be evaluated since the control law is capable of perfect tracking, and the designer would not have to be concerned about the effect of control law deficiencies on the evaluation. A control allocation configuration must be selected a priori. For a given flying qualities model, various control allocation configurations can be compared, or vice-versa, for a given control allocation, various flying qualities models can be evaluated. With a selected flying qualities model and a control allocation configuration, other variables such as stick shaping, deadband width, and stick gains could be evaluated. It is likely that the large aerospace companies have a variety of tools available to accomplish the above objectives, although they may not have this specific tool. Thtrre is a need for smaller companies and government research organizations to have tools with the above capabilities to improve research efficiency. A tool with the capability described was developed (ref. 2) by the Defence Research Agency (DRA) in the United Kingdom as part of a NASA/DRA Cooperative Aeronautical Research Program. The DRA called this exact nonlinear dynamic inversion (NDI) since the methodology is based upon dynamic inversion that was developed for flight control law design (ref. 3). The DRA application was to use the NDI as an analysis tool during simulation and extract moments and appropriate coefficients from the simulation. The ability to extract the appropriate terms from the simulation allows the control approach to be exact; therefore, control law robustness is not an issue. The approach was successfully demonstrated on the HARV (High-Alpha Research Vehicle) (ref. 4) in the NASA Langley Differential Maneuvering Simulator. One deficiency with the reference 2 approach is that the incorporation of flying qualities was not developed. The control law only consisted of firstorder responses, whereas military specifications (ref. 5) require higher-order responses. To offset this deficiency, the SOFVF (Stochastic Optimal Feedforward and Feedback Technology) (refs. 6 and 7) methodology was investigated for applicability. SOFFF was developed for flight control application, and the feedforward structure allows precise tracking with the ability to incorporate any desired flying qualities into a command model which is imbedded within the feedforward controller. The approach was developed for a discrete controller by using linear models. Therefore, a disadvantage is that linear derivatives must be calculated in real time and then transformed to discrete form. The advantage over reference 2 is that higher order models can be used for exact tracking. This paper contains a study of the two approaches for use in the development of a real-time piloted simulation tool which can be used to determine achievable control dynamics and control power requirements. The first section contains a review of the DRA approach to NDI. A review of the SOFFT approach is discussed in the second section and includes equations for both discrete and continuous controllers. Implementing SOFFT into a form similar to NDI shows that SOFFI" also includes a plant inversion. The third section contains an analysis of the closed-loop plant model that illustrates the transfer function characteristics for both the continuous and discrete models. The fourth section shows an approach for incorporating flying qualities into the closed-loop NDI structure for both continuous formulations and discrete formulations. Hybrid formulation,, are then developed for both NDI and SOFFT. In the final section, simulation results illustrate that the methods give the same performance for purely linear plant models with all-continuous or all-discret_" control systems. The hybrid SOFFT controller gave essentially the same results while the hybrid NDI controller had a slight error in the pitch rate response. In addition, the SOFFT structure gives better performance when a nonlinearity such as actuator saturation is included. Symbols A system matrix for continuous systems filter pole for plant inversion structure, rad/sec aq Av, Act, Aq, AO Bz Bv, B a, Bq C