Multisine is the best one.

The following is the summary of popular process excitation methods for the purpose of process control and process (black-box) modeling. Random muti-step sequences (RMS) and P control with a setpoint change method among them can be used to perturb nonlinear process. Binary signals are only for linear processes because it cannot perturb the input nonlinearity.

1. Step signal (Step)

It is one of the most popular methods in industry.

Advantages: Simplicity; preferred in industry

Disadvantages: a long excitation (perturbation) time up to steady-state; small amount of high frequency information; only for linear process modeling; open-loop excitation (sensitive to disturbances)

2. Random binary sequences (RBS)

Advantages: uncorrelated sequences, resulting in well-posed estimation and more accurate estimation

Disadvantages: a long excitation (perturbation) time (equivalently, a large number of data) for a complete uncorrelation; only for linear process modeling; open-loop excitation (sensitive to disturbances)

3. Pseudo-random binary sequences (PRBS)

Advantages: uncorrelated sequences, resulting in well-posed estimation and more accurate estimation; almost uncorrelation even under a small number of data

Disadvantages: only for linear process modeling; open-loop excitation (sensitive to disturbances)

4. Random muti-step sequences (RMS)

Advantages: uncorrelated sequences, resulting in well-posed estimation and more accurate estimation; applicable to linear/nonlinear process modeling

Disadvantages: a long excitation (perturbation) time (equivalently, a large number of data) for a complete uncorrelation; open-loop activation (sensitive to disturbances)

5. Relay feedback signal (Relay)

It had been initially developed for the PID autotuning. Now, various types have been developed.

Advantages: Short excitation (perturbation); termination condition is clear; activating high frequency information; closed-loop excitation (insensitive to disturbances); several non-parametric estimation methods are applicable.

Disadvantages: implementation is somewhat complicated; usually only for linear process modeling

6. P controller with a setpoint change

Advantages: activating operating frequency information; closed-loop excitation (insensitive to disturbances); applicable to linear/nonlinear process modeling

Disadvantages: controller gains should be set properly.

Professors Sung's reply is very complete. Let me just remark the following which is sometimes forgotten. In linear system excitation the key concept is: span the required frequency range while keeping amplitudes as low as can be reliably measured". In the case of nonlinear system excitation, the amplitudes typically must span a much wider operating range, in order to excite amplitude-related nonlinearities i.e. saturation. As for the frequency content, while it is still important, it is not so important as for the linear case for one simple reason: nonlinear systems transfer spectral power among different frequencies. For instance, it is possible to get a very good model for a chaotic system excited by a pure sine (one frequency)!

I suggest reading:

Experimental design and identifiability for non-linear systems, 

DOI:10.1080/00207728708963958

I. J. LEONTARITIS & S. A. BILLINGS

pages 189-202

International Journal of Systems Science

Volume 18, Issue 1, 1987

There are a few remedies to deal with multicollinearity. Disturbance is sometimes helpful while dealing with multicollinearity. Also helpful may be keeping the number of degrees of freedom minimum.

The recursive least squares algorithm (RLS) is the recursive application of the well-known least squares (LS) regression algorithm, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. The method allows for the dynamical application of LS to time series acquired in real-time. As with LS, there may be several correlation equations with the corresponding set of dependent (observed) variables. For the recursive least squares algorithm with forgetting factor (RLS-FF), acquired data is weighted according to its age, with increased weight given to the most recent data.

Years ago, while investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS-FF algorithm to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, hence giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The power dissipated by agitation was accessed by a torque meter (pilot plant). The proposed (adaptive) control algorithm compared favourably with PID. Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):

Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...